%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "3.172", %%% date = "20 March 2026", %%% time = "14:56:37 MDT", %%% filename = "toms.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "34836 67404 331544 3220383", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; mathematical software; TOMS; %%% Transactions on Mathematical Software", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a BibTeX bibliography for ACM %%% Transactions on Mathematical Software (TOMS) %%% (CODEN ACMSCU, ISSN 0098-3500 (print), %%% 1557-7295 (electronic)), completely covering %%% all issues from March 1975 -- date. All %%% papers, including editorials, policy %%% statements, remarks, and corrigenda are %%% included. %%% %%% The ACM maintains World Wide Web pages with %%% journal tables of contents for 1985--date at %%% %%% http://dl.acm.org/pub.cfm?id=J782 %%% http://toms.acm.org/ %%% http://www.acm.org/dl/toc.html %%% http://www.acm.org/toms/ %%% http://www.acm.org/pubs/contents/journals/toms/ %%% %%% Source code for all ACM Algorithms from 1960 %%% to date is available at %%% %%% http://www.acm.org/calgo/contents/ %%% %%% That data has been automatically converted to %%% BibTeX form, corrected for spelling and page %%% number errors, and merged into this file. %%% %%% At version 3.172, the COMPLETE year coverage %%% looks like this: %%% %%% 1960 ( 1) 1983 ( 43) 2006 ( 34) %%% 1961 ( 1) 1984 ( 46) 2007 ( 28) %%% 1962 ( 1) 1985 ( 40) 2008 ( 23) %%% 1963 ( 2) 1986 ( 34) 2009 ( 51) %%% 1964 ( 2) 1987 ( 29) 2010 ( 37) %%% 1965 ( 1) 1988 ( 40) 2011 ( 25) %%% 1966 ( 1) 1989 ( 32) 2012 ( 21) %%% 1967 ( 1) 1990 ( 34) 2013 ( 31) %%% 1968 ( 1) 1991 ( 41) 2014 ( 29) %%% 1969 ( 2) 1992 ( 36) 2015 ( 25) %%% 1970 ( 2) 1993 ( 37) 2016 ( 54) %%% 1971 ( 1) 1994 ( 38) 2017 ( 44) %%% 1972 ( 4) 1995 ( 31) 2018 ( 25) %%% 1973 ( 3) 1996 ( 33) 2019 ( 45) %%% 1974 ( 7) 1997 ( 31) 2020 ( 38) %%% 1975 ( 38) 1998 ( 31) 2021 ( 40) %%% 1976 ( 49) 1999 ( 28) 2022 ( 48) %%% 1977 ( 46) 2000 ( 33) 2023 ( 40) %%% 1978 ( 43) 2001 ( 21) 2024 ( 29) %%% 1979 ( 54) 2002 ( 24) 2025 ( 30) %%% 1980 ( 57) 2003 ( 26) 2026 ( 4) %%% 1981 ( 47) 2004 ( 28) %%% 1982 ( 34) 2005 ( 30) %%% %%% Article: 1862 %%% InProceedings: 1 %%% Misc: 1 %%% TechReport: 1 %%% %%% Total entries: 1865 %%% %%% Abstracts, Keywords, Categories and Subject %%% Descriptors are available for some issues. %%% Eventually, this coverage should be %%% extended to the entire collection, in the %%% interests of enhancing search capabilities. %%% %%% This bibliography includes ACM Algorithms %%% 493 -- 735 (or the latest), including %%% Algorithm 568, published in ACM %%% Transactions on Programming Languages and %%% Systems (TOPLAS). For ACM Algorithms 1 -- %%% 492, see the companion bibliographies, %%% cacm1960.bib and cacm1970.bib. %%% %%% All published Remarks and Corrigenda are %%% cross-referenced in both directions, so %%% that citing a paper will automatically %%% generate citations for those Remarks and %%% Corrigenda. There is one important paper, %%% on multiple-precision integer division, %%% included from the journal Software --- %%% Practice and Experience because it is %%% cross-referenced to a TOMS paper. %%% %%% Algorithms published in Communications of %%% the ACM, prior to the founding of TOMS in %%% 1975, are also included in this %%% bibliography, if a TOMS paper contains %%% Remarks or Corrigenda for them. %%% %%% Source code for ACM Algorithms from 380 %%% onwards, with some omissions, is available %%% via netlib, and via anonymous ftp to %%% %%% ftp://netlib.bell-labs.com/netlib/toms %%% %%% ACM also markets a CD-ROM containing %%% algorithms 495 (March 1975) through 798 %%% (December 1999): the ``CALGO Special Edition %%% CD'', organized as a Web site (see entry %%% ACM:2002:CSE at the end of this file). %%% %%% The initial draft of entries for 1981 -- 1990 %%% was extracted from the ACM Computing Archive %%% CD ROM for the 1980s, with manual corrections %%% and additions from bibliographies in the TeX %%% User Group collection, the author's personal %%% bibliography files, Aake Bjoerck's %%% %%% ftp://math.liu.se/pub/references/habook.bib %%% %%% G. W. Stewart's %%% %%% ftp://thales.cs.umd.edu/pub/references/ref.bib %%% %%% John R. Rice and Richard J. Hanson's %%% Algorithm 620 (available as a BibTeX file via %%% netlib, with additions up to Algorithm 678), %%% and the very large Karlsruhe computer science %%% bibliography collection at %%% %%% ftp://ftp.ira.uka.de/pub/bibliography/ %%% %%% to which many people of have contributed. %%% %%% Math Review MRclass and MRnumber values for %%% 341 entries were supplied from a search of %%% the American Mathematical Society's %%% MathSciNet database for version 2.26 %%% [06-Dec-1996]. That search also turned up %%% a few small errors in author names and %%% title words; they have been corrected to %%% match the original journal articles. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% Numerous heuristic checks on the validity %%% of the TOMS bibliography files have also %%% been made using software developed by the %%% author for maintenance of the TeX Users %%% Group and BibNet bibliography collections. %%% %%% Every entry from March 1975 -- June 1994 %%% has been compared directly with the article %%% cover pages in the original journal issues %%% to ensure correctness. Several errors were %%% uncovered this way in earlier sources of %%% BibTeX entries and citation data. %%% %%% Considerable effort has been expended to %%% ensure accuracy of this bibliography, %%% because it is expected to be widely used %%% and distributed. Capitalization of %%% original titles, and use of initials or %%% full names in author lists, should match %%% the journal exactly, with two exceptions. %%% (1) Algorithms have been sometimes entitled %%% ``ALGORITHM xyz...'', and sometimes %%% ``Algorithm xyz...''. The latter usage has %%% been adhered to throughout. (2) Remarks %%% and Corrigenda in the journal occasionally %%% fail to cite the full title of the original %%% paper; that has been rectified in the %%% interests of clarity and consistency. %%% %%% ACM copyrights explicitly permit abstracting %%% with credit, so article abstracts, keywords, %%% and subject classifications have been %%% included in this bibliography wherever %%% available. Article reviews have been %%% omitted, until their copyright status has %%% been clarified. %%% %%% bibsource keys in the bibliography entries %%% below indicate the entry originally came %%% from the computer science bibliography %%% archive, even though it has likely since %%% been corrected and updated. %%% %%% URL keys in the bibliography point to %%% World Wide Web locations of additional %%% information about the entry. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed by the %%% author for the BibNet Project. %%% %%% In this bibliography, entries are sorted %%% by journal, and then by publication order, %%% with the help of ``bibsort -byvolume''. The %%% bibsort utility is available from %%% %%% ftp://ftp.math.utah.edu/pub/bibsort %%% %%% The author will be grateful for reports of %%% errors of any kind in this bibliography. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility." %%% } %%% ==================================================================== @Preamble{"\input bibnames.sty" # "\hyphenation{Cher-kas-sky Cue-vas Ka-chit-vich-yan-u-kul Rich-ard Za-bo-row-ski}" # "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" # "\ifx \undefined \circled \def \circled #1{(#1)} \fi" # "\ifx \undefined \k \let \k = \c \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" # "\ifx \undefined \ocirc \def \ocirc #1{{\accent'27#1}} \fi" # "\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi" # "\ifx \undefined \reg \def \reg {\circled{R}} \fi" # "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} @String{ack-kr = "Karin Remington, Celera Genomics 45 West Gude Drive Rockville, Maryland 20850 Tel: +1 240 453-3038 FAX: +1 240 453-4375 e-mail: \path|remingka@celera.com|"} @String{ack-nj = "Norbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: \path=norbert@iit.com="} @String{ack-rfb = "Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: \path=boisvert@cam.nist.gov="} %%% ==================================================================== %%% Journal abbreviations: @String{j-CACM = "Communications of the ACM"} @String{j-COMP-J = "The Computer Journal"} @String{j-COMP-STAT = "Computational Statistics"} @String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"} @String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"} @String{j-SPE = "Soft{\-}ware\emdash Prac{\-}tice and Experience"} @String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and Simulation"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} @String{j-TOPLAS = "ACM Transactions on Programming Languages and Systems"} %%% ==================================================================== %%% Publishers and their addresses: @String{pub-IEEE = "IEEE Computer Society Press"} @String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} %%% ==================================================================== %%% Bibliography entries from Communications of the ACM. @Article{Ellenberger:1960:NSP, author = "K. W. Ellenberger", title = "{ACM Algorithm 30}: Numerical Solution of the Polynomial Equation", journal = j-CACM, volume = "3", number = "12", pages = "643--643", month = dec, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Feb 07 16:37:16 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Novotny:1985:RNS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Herndon:1961:SNF, author = "J. R. Herndon", title = "{ACM Algorithm 49}: Spherical {Neumann} Function", journal = j-CACM, volume = "4", number = "4", pages = "179--179", month = apr, year = "1961", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Coleman:1978:RSN}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Merner:1962:CEI, author = "J. N. Merner", title = "{ACM Algorithm 149}: Complete Elliptic Integral", journal = j-CACM, volume = "5", number = "12", pages = "605--605", month = dec, year = "1962", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Skovgaard:1978:RCE}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ludwig:1963:IBR, author = "O. G. Ludwig", title = "{ACM Algorithm 179}: Incomplete Beta Ratio", journal = j-CACM, volume = "6", number = "6", pages = "314--314", month = jun, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Pike:1976:RIB}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kase:1963:TOP, author = "R. H. Kase", title = "{ACM Algorithm 219}: Topological Ordering for {Pert} Networks", journal = j-CACM, volume = "6", number = "12", pages = "738--739", month = dec, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Tenney:1977:RTO}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1964:AAB, author = "W. Gautschi", title = "{ACM Algorithm 236}: {Bessel} Functions of the First Kind [{S17}]", journal = j-CACM, volume = "7", number = "8", pages = "479--480", month = aug, year = "1964", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/355586.355587", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Skovgaard:1975:RBF}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "$J_n(x)$; Bessel functions of the first kind; special functions", } @Article{Boothroyd:1964:G, author = "J. Boothroyd", title = "{ACM Algorithm 246}: {Graycode}", journal = j-CACM, volume = "7", number = "12", pages = "701--701", month = dec, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Sep 10 09:12:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Misra:1975:RG,Er:1985:RG}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1965:LFA, author = "W. Gautschi", title = "{ACM Algorithm 259}: {Legendre} Functions for Arguments Larger than One", journal = j-CACM, volume = "8", number = "8", pages = "488--492", month = aug, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Jansen:1977:RLF}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fletcher:1966:ITB, author = "W. Fletcher", title = "{ACM Algorithm 284}: Interchange of Two Blocks of Data", journal = j-CACM, volume = "9", number = "5", pages = "326--326", month = may, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Ito:1976:RIT}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hill:1967:CSI, author = "I. D. Hill and M. C. Pike", title = "{ACM Algorithm 299}: Chi-Squared Integral", journal = j-CACM, volume = "10", number = "4", pages = "243--244", month = apr, year = "1967", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{elLozy:1976:RAC,Hill:1985:RCS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bell:1968:NRD, author = "J. R. Bell", title = "{ACM Algorithm 334}: Normal Random Deviates", journal = j-CACM, volume = "11", number = "7", pages = "498--498", month = jul, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Tracht:1982:RNR}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morris:1969:TP, author = "J. Morris", title = "{ACM Algorithm 346}: ${F}$-Test Probabilities", journal = j-CACM, volume = "12", number = "3", pages = "184--185", month = mar, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Cormack:1988:RTP}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{TadeudeMedeiros:1969:APF, author = "A. {Tadeu de Medeiros} and G. Schwachheim", title = "{Algorithm 349}: Polygamma functions with arbitrary precision", journal = j-CACM, volume = "12", number = "4", pages = "213--214", month = apr, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Jun 16 10:30:24 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See certification \cite{Lewis:1975:CPF}.", acknowledgement = ack-nhfb, classcodes = "C7300 (Natural sciences computing)", corpsource = "Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", keywords = "mathematics; subroutines", } @Article{Hill:1970:SD, author = "G. W. Hill", title = "{ACM Algorithm 395}: {Student}'s $t$-Distribution", journal = j-CACM, volume = "13", number = "10", pages = "617--619", month = oct, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hill:1970:SQ, author = "G. W. Hill", title = "{ACM Algorithm 396}: {Student}'s $t$-Quantiles", journal = j-CACM, volume = "13", number = "10", pages = "619--620", month = oct, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Apr 29 15:20:10 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remarks \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McNamee:1971:SMP, author = "J. M. McNamee", title = "{ACM Algorithm 408}: a Sparse Matrix Package ({Part I})", journal = j-CACM, volume = "14", number = "4", pages = "265--273", month = apr, year = "1971", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Sipala:1977:RSM,Gustavson:1978:RSM,Harms:1980:RSM}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gentleman:1972:CCQ, author = "W. M. Gentleman", title = "{ACM Algorithm 424}: {Clenshaw--Curtis} Quadrature", journal = j-CACM, volume = "15", number = "5", pages = "353--355", month = may, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Geddes:1979:RCC}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Akima:1972:ISC, author = "H. Akima", title = "{ACM Algorithm 433}: Interpolation and Smooth Curve Fitting Based on Local Procedures", journal = j-CACM, volume = "15", number = "10", pages = "914--918", month = oct, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Anderson:1976:RIS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{March:1972:EPT, author = "D. L. March", title = "{ACM Algorithm 434}: Exact Probabilities for ${R\times{C}}$ Contingency Tables", journal = j-CACM, volume = "15", number = "11", pages = "991--992", month = nov, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Sep 09 14:13:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Boulton:1976:REP}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fullerton:1972:MIG, author = "W. Fullerton", title = "{ACM Algorithm 435}: Modified Incomplete Gamma Function", journal = j-CACM, volume = "15", number = "11", pages = "993--995", month = nov, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Schoene:1978:RMI}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{MacHura:1973:RFM, author = "M. MacHura and A. Mulawa", title = "{ACM Algorithm 450}: {Rosenbrock} Function Minimization", journal = j-CACM, volume = "16", number = "8", pages = "482--483", month = aug, year = "1973", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Davies:1976:RRF}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brenner:1973:MTP, author = "N. Brenner", title = "{ACM Algorithm 467}: Matrix Transposition in Place", journal = j-CACM, volume = "16", number = "11", pages = "692--694", month = nov, year = "1973", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Leathers:1979:RAS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Akima:1974:BIS, author = "H. Akima", title = "{ACM Algorithm 474}: Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures", journal = j-CACM, volume = "17", number = "1", pages = "26--31", month = jan, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Anderson:1979:RBI}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Loeser:1974:SPT, author = "R. Loeser", title = "Some Performance Tests of `Quicksort' and Descendants", journal = j-CACM, volume = "17", number = "3", pages = "143--152", month = mar, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Apr 29 15:23:43 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Mackay:1977:RPT}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wright:1974:VSP, author = "T. Wright", title = "{ACM Algorithm 475}: Visible Surface Plotting Program", journal = j-CACM, volume = "17", number = "3", pages = "152--155", month = mar, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Duta:1976:RVS,vanSwieten:1979:RAV}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Page:1974:MST, author = "R. L. Page", title = "{ACM Algorithm 479}: a Minimal Spanning Tree Clustering Method", journal = j-CACM, volume = "17", number = "6", pages = "321--323", month = jun, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{White:1976:RMS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Watkins:1974:MTD, author = "S. L. Watkins", title = "{ACM Algorithm 483}: Masked Three-Dimensional Plot Program with Rotations", journal = j-CACM, volume = "17", number = "9", pages = "520--523", month = sep, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Feinstein:1975:RMT}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Veillon:1974:NIL, author = "F. Veillon", title = "{ACM Algorithm 486}: Numerical Inversion of {Laplace} Transform", journal = j-CACM, volume = "17", number = "10", pages = "587--589", month = oct, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Koppelaar:1976:RNI,Veillon:1977:RNI}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pomeranz:1974:ECD, author = "J. Pomeranz", title = "{ACM Algorithm 487}: Exact Cumulative Distribution of the {Kolmogorov--Smirnov} Statistic for Small Samples", journal = j-CACM, volume = "17", number = "12", pages = "703--704", month = dec, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Pomeranz:1976:REC}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Floyd:1975:ASF, author = "R. W. Floyd and R. L. Rivest", title = "{ACM Algorithm 489}: The Algorithm {SELECT} --- for Finding the $i{\rm th}$ Smallest of $n$ Elements", journal = j-CACM, volume = "18", number = "3", pages = "173--173", month = mar, year = "1975", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Wed Dec 04 12:25:43 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Brown:1976:RAS}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ginsberg:1975:DFR, author = "E. S. Ginsberg and D. Zaborowski", title = "{ACM Algorithm 490}: The Dilogarithm Function of a Real Argument", journal = j-CACM, volume = "18", number = "4", pages = "200--202", month = apr, year = "1975", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Morris:1976:RDF}.", fjournal = "Communications of the ACM", journal-URL = "https://dl.acm.org/loi/toms", } %%% ==================================================================== %%% Bibliography entries from IEEE Transactions on Computers @Article{Kramer:1998:PWC, author = "W. Kr{\"a}mer", title = "A priori worst case error bounds for floating-point computations", journal = j-IEEE-TRANS-COMPUT, volume = "47", number = "7", pages = "750--756", month = jul, year = "1998", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/12.709374", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 6 09:35:55 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Tang:1992:TDI}.", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374", abstract = "A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $exp(x) - 1$ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach", acknowledgement = ack-nhfb, author-dates = "1952--2014 (WK)", fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } %%% ==================================================================== %%% Bibliography entries from Software---Practice and Experience @Article{BrinchHansen:1994:MLD, author = "Per {Brinch Hansen}", title = "Multiple-length Division Revisited: a Tour of the Minefield", journal = j-SPE, volume = "24", number = "6", pages = "579--601", month = jun, year = "1994", CODEN = "SPEXBL", ISSN = "0038-0644 (print), 1097-024X (electronic)", ISSN-L = "0038-0644", bibdate = "Thu Apr 29 15:16:58 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "This paper derives an algorithm for division of long integers, and implements it as a literate program, although without identifier cross-references. See also related work \cite{Regener:1984:MID} on division.", acknowledgement = ack-nhfb, fjournal = "Soft{\-}ware\emdash Prac{\-}tice and Experience", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X", } %%% ==================================================================== %%% Bibliography entries from ACM Transactions on Mathematical Software. @Article{Rice:1975:PS, author = "John R. Rice", title = "Purpose and Scope", journal = j-TOMS, volume = "1", number = "1", pages = "1--3", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355627", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anonymous:1975:ADS, author = "{Anonymous}", title = "Algorithms Distribution Service", journal = j-TOMS, volume = "1", number = "1", pages = "4--4", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355628", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355626.355628; http://www.acm.org/pubs/citations/journals/toms/1975-1-1/p4-no_author/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fosdick:1975:AP, author = "Lloyd D. Fosdick", title = "Algorithms Policy", journal = j-TOMS, volume = "1", number = "1", pages = "5--6", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355629", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anonymous:1975:PMS, author = "{Anonymous}", title = "Papers from {Mathematical Software II}", journal = j-TOMS, volume = "1", number = "1", pages = "7--12", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355630", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355626.355630; http://www.acm.org/pubs/citations/journals/toms/1975-1-1/p7-no_author/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cody:1975:FPS, author = "W. J. Cody", title = "The {FUNPACK} Package of Special Function Subroutines", journal = j-TOMS, volume = "1", number = "1", pages = "13--25", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355631", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jenkins:1975:PTP, author = "M. A. Jenkins and J. F. Traub", title = "Principles for Testing Polynomial Zerofinding Programs", journal = j-TOMS, volume = "1", number = "1", pages = "26--34", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355632", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10 (65H05)", MRnumber = "53 #2009", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "James Howland", } @Article{Parlett:1975:ICC, author = "B. N. Parlett and Y. Wang", title = "The Influence of the Compiler on the Cost of Mathematical Software\emdash in Particular on the Cost of Triangular Factorization", journal = j-TOMS, volume = "1", number = "1", pages = "35--46", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355633", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:35:13 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cs; lud; nla; software", } @Article{Glover:1975:RWA, author = "Fred Glover and Darwin Klingman", title = "Real World Applications of Network Related Problems and Breakthroughs in Solving Them Efficiently", journal = j-TOMS, volume = "1", number = "1", pages = "47--55", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355634", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ng:1975:CCM, author = "Edward W. Ng", title = "A Comparison of Computational Methods and Algorithms for the Complex Gamma Function", journal = j-TOMS, volume = "1", number = "1", pages = "56--70", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355635", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "52 #2148", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "R. H. Bartels", } @Article{Byrne:1975:PNS, author = "G. D. Byrne and A. C. Hindmarsh", title = "A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations", journal = j-TOMS, volume = "1", number = "1", pages = "71--96", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355636", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L99 (68A10)", MRnumber = "51 #14600", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Sean McKee", } @Article{Powell:1975:VUM, author = "M. J. D. Powell", title = "A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives", journal = j-TOMS, volume = "1", number = "2", pages = "97--107", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355638", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "(Reviewer: R. P. Brent (CR {17} \#29471)) 65K05", MRnumber = "53 #14908", bibdate = "Sat Dec 20 10:45:23 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Miller:1975:SRA, author = "Webb Miller", title = "Software for Roundoff Analysis", journal = j-TOMS, volume = "1", number = "2", pages = "108--128", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355639", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05", MRnumber = "53 #9622", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "James H. Wilkinson", } @Article{Malcolm:1975:LVG, author = "Michael A. Malcolm and R. Bruce Simpson", title = "Local Versus Global Strategies for Adaptive Quadrature", journal = j-TOMS, volume = "1", number = "2", pages = "129--146", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355640", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "51 #7248", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Thomas A. Atchison", } @Article{Stoutemyer:1975:AOU, author = "David R. Stoutemyer", title = "Analytical Optimization Using Computer Algebraic Manipulation", journal = j-TOMS, volume = "1", number = "2", pages = "147--164", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355641", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C99", MRnumber = "58 #4363", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Barinka:1975:SEC, author = "Lawrence L. Barinka", title = "Some Experience with Constructing, Testing, and Certifying a Standard Mathematical Subroutine Library", journal = j-TOMS, volume = "1", number = "2", pages = "165--177", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355642", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jenkins:1975:AZR, author = "M. A. Jenkins", title = "{Algorithm 493}: Zeros of a Real Polynomial [{C2}]", journal = j-TOMS, volume = "1", number = "2", pages = "178--189", month = jun, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355637.355643", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:27:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1975:SPP, author = "John R. Rice", title = "Software Package Policy", journal = j-TOMS, volume = "1", number = "3", pages = "193--195", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355645", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bailey:1975:UAM, author = "Carl B. Bailey and Rondall E. Jones", title = "Usage and Argument Monitoring of Mathematical Library Routines", journal = j-TOMS, volume = "1", number = "3", pages = "196--209", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355646", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{George:1975:ARR, author = "James E. George", title = "Algorithms to Reveal the Representation of Characters, Integers, and Floating-Point Numbers", journal = j-TOMS, volume = "1", number = "3", pages = "210--216", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355647", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aird:1975:CAU, author = "T. J. Aird and Robert E. Lynch", title = "Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems", journal = j-TOMS, volume = "1", number = "3", pages = "217--231", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355648", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F35", MRnumber = "52 #2176", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Ian Gladwell", } @Article{Sincovec:1975:SNP, author = "Richard F. Sincovec and Niel K. Madsen", title = "Software for Nonlinear Partial Differential Equations", journal = j-TOMS, volume = "1", number = "3", pages = "232--260", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355649", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sincovec:1975:APS, author = "Richard F. Sincovec and Niel K. Madsen", title = "{Algorithm 494}: {PDEONE}, Solutions of Systems of Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "1", number = "3", pages = "261--263", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355650", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 18:06:09 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Barrodale:1975:ASO, author = "I. Barrodale and C. Phillips", title = "{Algorithm 495}: Solution of an Overdetermined System of Linear Equations in the {Chebychev} Norm [{F4}]", journal = j-TOMS, volume = "1", number = "3", pages = "264--270", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355651", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 16:10:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Chebyshev approximation; nla", } @Article{Kaufman:1975:ALA, author = "Linda Kaufman", title = "{Algorithm 496}: The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]", journal = j-TOMS, volume = "1", number = "3", pages = "271--281", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355652", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:21:30 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Kaufman:1976:RLA}.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Skovgaard:1975:RBF, author = "Ove Skovgaard", title = "Remark on ``{Algorithm 236}: {Bessel} Functions of the First Kind [{S17}]''", journal = j-TOMS, volume = "1", number = "3", pages = "282--284", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355653", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:11 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Gautschi:1964:AAB}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Feinstein:1975:RMT, author = "Robert Feinstein", title = "Remark on ``{Algorithm 483}: Masked Three-Dimensional Plot Program with Rotations [{J6}]''", journal = j-TOMS, volume = "1", number = "3", pages = "285--285", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.355654", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:09 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Watkins:1974:MTD}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Misra:1975:RG, author = "Jayadev Misra", title = "Remark on ``{Algorithm 246}: {Graycode} [{Z}]''", journal = j-TOMS, volume = "1", number = "3", pages = "285--285", month = sep, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355644.356449", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 20:42:41 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Boothroyd:1964:G,Er:1985:RG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Stone:1975:PTE, author = "Harold S. Stone", title = "Parallel Tridiagonal Equation Solvers", journal = j-TOMS, volume = "1", number = "4", pages = "289--307", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355657", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10 (68A20)", MRnumber = "52 #9676", bibdate = "Fri Aug 26 23:35:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nla; prll; tridiagonal matrix", reviewer = "V. A. Valkovskii", } @Article{Lambiotte:1975:STL, author = "Jules J. {Lambiotte, Jr.} and Robert G. Voigt", title = "The Solution of Tridiagonal Linear Systems on the {CDC STAR 100} Computer", journal = j-TOMS, volume = "1", number = "4", pages = "308--329", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355658", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10 (68A20)", MRnumber = "52 #9677", bibdate = "Sat Aug 27 00:20:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "linear system; nla; tridiagonal matrix; vect", reviewer = "V. A. Valkovskii", } @Article{Bus:1975:TEA, author = "J. C. P. Bus and T. J. Dekker", title = "Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function", journal = j-TOMS, volume = "1", number = "4", pages = "330--345", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355659", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05", MRnumber = "52 #7112", bibdate = "Fri Aug 26 23:12:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nlop", reviewer = "Ian Gladwell", } @Article{Norman:1975:CFP, author = "A. C. Norman", title = "Computing with Formal Power Series", journal = j-TOMS, volume = "1", number = "4", pages = "346--356", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355660", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:22:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Neves:1975:AIF, author = "Kenneth W. Neves", title = "Automatic Integration of Functional Differential Equations: An Approach", journal = j-TOMS, volume = "1", number = "4", pages = "357--368", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355661", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Q05", MRnumber = "52 #7171", bibdate = "Sat Aug 27 00:22:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. C. Rheinboldt", } @Article{Neves:1975:AAI, author = "Kenneth W. Neves", title = "{Algorithm 497}: Automatic Integration of Functional Differential Equations [{D2}]", journal = j-TOMS, volume = "1", number = "4", pages = "369--371", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355662", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:24:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Prince:1975:AAF, author = "P. J. Prince", title = "{Algorithm 498}: {Airy} Functions Using {Chebyshev} Series Approximations", journal = j-TOMS, volume = "1", number = "4", pages = "372--379", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355663", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:24:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Razaz:1981:RAF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lewis:1975:CPF, author = "John Gregg Lewis", title = "Certification of ``{Algorithm 349}: Polygamma Functions with Arbitrary Precision''", journal = j-TOMS, volume = "1", number = "4", pages = "380--381", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355664", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:10:19 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{TadeudeMedeiros:1969:APF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bromage:1975:CVS, author = "Gordon E. Bromage", title = "Certification of ``{Algorithm 475}: Visible Surface Plotting Program [{J6}]''", journal = j-TOMS, volume = "1", number = "4", pages = "381--382", month = dec, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355656.355665", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:22:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1976:PAA, author = "John R. Rice", title = "Parallel Algorithms for Adaptive Quadrature. {III}. Program Correctness", journal = j-TOMS, volume = "2", number = "1", pages = "1--30", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355667", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (68A10)", MRnumber = "54 #9058c", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Frederick N. Fritsch", } @Article{Griss:1976:ASS, author = "Martin L. Griss", title = "The Algebraic Solution of Sparse Linear Systems via Minor Expansion", journal = j-TOMS, volume = "2", number = "1", pages = "31--49", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355668", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "54 #4073", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Charles R. Johnson", } @Article{Duris:1976:GCP, author = "Charles S. Duris", title = "Generating and Compounding Product-Type {Newton-Coates} Quadrature Formulas", journal = j-TOMS, volume = "2", number = "1", pages = "50--58", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355669", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "53 #1919", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Thomas A. Atchison", } @Article{Bays:1976:IPR, author = "Carter Bays and S. D. Durham", title = "Improving a Poor Random Number Generator", journal = j-TOMS, volume = "2", number = "1", pages = "59--64", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355670", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lyness:1976:CNA, author = "J. N. Lyness and J. J. Kaganove", title = "Comments on the Nature of Automatic Quadrature Routines", journal = j-TOMS, volume = "2", number = "1", pages = "65--81", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355671", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "53 #1921", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Henning Esser", } @Article{Kinsner:1976:AES, author = "W. Kinsner and E. Della Torre", title = "{Algorithm 499}: An Efficient Scanning Technique [{Z}]", journal = j-TOMS, volume = "2", number = "1", pages = "82--86", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355672", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:35:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shanno:1976:AMU, author = "D. F. Shanno and K. H. Phua", title = "{Algorithm 500}: Minimization of Unconstrained Multivariate Functions [{E4}]", journal = j-TOMS, volume = "2", number = "1", pages = "87--94", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355673", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:25:28 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remarks \cite{Dunham:1977:RMU,Shanno:1980:RMU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Simpson:1976:AFT, author = "Joseph C. Simpson", title = "{Algorithm 501}: {Fortran} Translation of {Algorithm 409}, Discrete {Chebychev} Curve Fit [{E2}]", journal = j-TOMS, volume = "2", number = "1", pages = "95--97", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355674", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 23:07:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Futrell:1978:RTA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kubicek:1976:ADS, author = "Milan Kub{\'\i}{\v{c}}ek", title = "{Algorithm 502}: Dependence of Solution of Nonlinear Systems on a Parameter [{C5}]", journal = j-TOMS, volume = "2", number = "1", pages = "98--107", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355675", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 18:03:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355666.355675; http://www.acm.org/pubs/citations/journals/toms/1976-2-1/p98-kubiviek/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boulton:1976:REP, author = "D. M. Boulton", title = "Remark on ``{Algorithm 434}: Exact Probabilities for ${R}\times{C}$ Contingency Tables [{G2}]''", journal = j-TOMS, volume = "2", number = "1", pages = "108--108", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355676", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{March:1972:EPT}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duta:1976:RVS, author = "Lucian D. Duta", title = "Remark on ``{Algorithm 475}: Visible Surface Plotting Program [{J6}]''", journal = j-TOMS, volume = "2", number = "1", pages = "109--110", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355677", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Wright:1974:VSP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{White:1976:RMS, author = "G. M. White and S. Goudreau and J. L. Legros", title = "Remark on ``{Algorithm 479}: a Minimal Spanning Tree Clustering Method [{Z}]''", journal = j-TOMS, volume = "2", number = "1", pages = "110--111", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355678", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Page:1974:MST}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pomeranz:1976:REC, author = "J. Pomeranz", title = "Remark on ``{Algorithm 487}: Exact Cumulative Distribution of the {Kolmogorov--Smirnov} Statistic for Small Samples [{S14}]''", journal = j-TOMS, volume = "2", number = "1", pages = "111--111", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355679", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Pomeranz:1974:ECD}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morris:1976:RDF, author = "Robert Morris", title = "Remark on ``{Algorithm 490}: The Dilogarithm Function of a Real Argument [{S22}]''", journal = j-TOMS, volume = "2", number = "1", pages = "112--112", month = mar, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355666.355680", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ginsberg:1975:DFR}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1976:TPS, author = "John R. Rice", title = "{TOMS} Policy Statement: The Rights of Program Authors in the Evaluation of Programs", journal = j-TOMS, volume = "2", number = "2", pages = "113--114", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355682", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ford:1976:DSN, author = "B. Ford and D. K. Sayers", title = "Developing a Single Numerical Algorithms Library for Different Machine Ranges", journal = j-TOMS, volume = "2", number = "2", pages = "115--131", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355683", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Paul:1976:SEF, author = "George Paul and M. Wayne Wilson", title = "Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?", journal = j-TOMS, volume = "2", number = "2", pages = "132--142", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355684", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The question whether elementary mathematical function library routines should be incorporated into a computer system as part of the machine instruction set is discussed. The prime issues affecting such a decision are accuracy, substitution, and user expectations, Support of the COMPLEX arithmetic data type is also a complicating factor. These issues are discussed and conclusions are drawn.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "computer instruction sets; elementary mathematical functions; hardware function evaluation; mathematical function libraries; programming languages", } @Article{Janko:1976:LIS, author = "Wolfgang Janko", title = "A List Insertion Sort for Keys With Arbitrary Key Distribution", journal = j-TOMS, volume = "2", number = "2", pages = "143--153", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355685", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Atkinson:1976:APL, author = "Kendall Atkinson", title = "An Automatic Program for Linear {Fredholm} Integral Equations of the Second Kind", journal = j-TOMS, volume = "2", number = "2", pages = "154--171", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355686", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R05", MRnumber = "54 #6528", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Christopher T. H. Baker", } @Article{Shampine:1976:GEE, author = "L. F. Shampine and H. A. Watts", title = "Global Error Estimates for Ordinary Differential Equations", journal = j-TOMS, volume = "2", number = "2", pages = "172--186", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355687", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "54 #1621", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "J. Hurt", } @Article{Ericksen:1976:ICP, author = "J. H. Ericksen and R. Wilhelmson", title = "Implementation of a Convective Problem Requiring Auxiliary Storage", journal = j-TOMS, volume = "2", number = "2", pages = "187--195", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355688", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 10:18:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Atkinson:1976:AAP, author = "Kendall Atkinson", title = "{Algorithm 503}: An Automatic Program for {Fredholm} Integral Equations of the Second Kind [{D5}]", journal = j-TOMS, volume = "2", number = "2", pages = "196--199", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355689", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:51:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1976:AGG, author = "L. F. Shampine and H. A. Watts", title = "{Algorithm 504}: {GERK}: Global Error Estimation For Ordinary Differential Equations [{D}]", journal = j-TOMS, volume = "2", number = "2", pages = "200--203", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355690", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:52:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Janko:1976:ALI, author = "Wolfgang Janko", title = "{Algorithm 505}: a List Insertion Sort for Keys with Arbitrary Key Distribution [{S20}]", journal = j-TOMS, volume = "2", number = "2", pages = "204--206", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355691", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:52:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pike:1976:RIB, author = "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten", title = "Remark on ``{Algorithm 179}: Incomplete Beta Ratio [{S14}]''", journal = j-TOMS, volume = "2", number = "2", pages = "207--208", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355692", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ludwig:1963:IBR}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anderson:1976:RIS, author = "Michael R. Anderson", title = "Remark on ``{Algorithm 433}: Interpolation and Smooth Curve Fitting Based on Local Procedures [{E2}]''", journal = j-TOMS, volume = "2", number = "2", pages = "208--208", month = jun, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355681.355693", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1972:ISC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wyatt:1976:PEP, author = "W. T. {Wyatt, Jr.} and D. W. Lozier and D. J. Orser", title = "A Portable Extended Precision Arithmetic Package and Library With {Fortran} Precompiler", journal = j-TOMS, volume = "2", number = "3", pages = "209--231", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355695", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355694.355695; http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gentleman:1976:AAC, author = "W. M. Gentleman and S. C. Johnson", title = "Analysis of Algorithms, a Case Study: Determinants of Matrices with Polynomial Entries", journal = j-TOMS, volume = "2", number = "3", pages = "232--241", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355696", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F30", MRnumber = "54 #1575", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "K. Moszynski", } @Article{Barwell:1976:CAS, author = "Victor Barwell and Alan George", title = "A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations", journal = j-TOMS, volume = "2", number = "3", pages = "242--251", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355697", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "54 #6472", bibdate = "Fri Aug 26 23:35:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "indefinite system; linear system; nla; symmetric matrix", reviewer = "F. Szidarovszky", } @Article{Bartels:1976:HIU, author = "Richard Bartels and Alec Steingart", title = "{Hermite} Interpolation Using a Triangular Polynomial Basis", journal = j-TOMS, volume = "2", number = "3", pages = "252--256", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355698", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15 (65D20)", MRnumber = "55 #4602", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Hwa-Shan Ho", } @Article{Hall:1976:NSS, author = "C. A. Hall and R. W. Luczak and A. G. Serdy", title = "Numerical Solution of Steady State Heat Flow Problems Over Curved Domains", journal = j-TOMS, volume = "2", number = "3", pages = "257--274", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355699", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N10", MRnumber = "54 #4135", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Stephen Hilbert", } @Article{Stewart:1976:AHE, author = "G. W. Stewart", title = "{Algorithm 506}: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]", journal = j-TOMS, volume = "2", number = "3", pages = "275--280", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355700", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 18:03:53 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Flamm:1982:RHE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "eig; Hessenberg matrix; nla; QR algorithm; software", } @Article{Herriot:1976:APQ, author = "John G. Herriot and Christian H. Reinsch", title = "{Algorithm 507}: Procedures for Quintic Natural Spline Interpolation [{E1}]", journal = j-TOMS, volume = "2", number = "3", pages = "281--289", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355701", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:01:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hanson:1982:RPQ}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Loeser:1976:SAQ, author = "Rudolf Loeser", title = "Survey on Algorithms 347, 426, and Quicksort", journal = j-TOMS, volume = "2", number = "3", pages = "290--299", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355702", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davies:1976:RRF, author = "Alan M. Davies", title = "Remark on ``{Algorithm 450}: {Rosenbrock} Function Minimization [{E4}]''", journal = j-TOMS, volume = "2", number = "3", pages = "300--301", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355703", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:28 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{MacHura:1973:RFM}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brown:1976:RAS, author = "Theodore Brown", title = "Remark on ``{Algorithm 489}: The Algorithm {SELECT}\emdash for Finding the $i$th Smallest of $n$ Elements [{M1}]''", journal = j-TOMS, volume = "2", number = "3", pages = "301--304", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355704", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:31 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Floyd:1975:ASF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pavlidis:1976:UAP, author = "Theodosios Pavlidis", title = "The Use of Algorithms of Piecewise Approximations for Picture Processing Applications", journal = j-TOMS, volume = "2", number = "4", pages = "305--321", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355706", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gibbs:1976:CSB, author = "Norman E. Gibbs and William G. {Poole Jr.} and Paul K. Stockmeyer", title = "A Comparison of Several Bandwidth and Profile Reduction Algorithms", journal = j-TOMS, volume = "2", number = "4", pages = "322--330", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355707", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:07:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "band matrix; band reduction; nla; profile reduction; sparse", } @Article{Mahendrarajah:1976:CTA, author = "A. Mahendrarajah and F. Fiala", title = "A Comparison of Three Algorithms for Linear Zero-One Programs", journal = j-TOMS, volume = "2", number = "4", pages = "331--334", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355708", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:08:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weinberger:1976:FPA, author = "P. J. Weinberger and L. P. Rothschild", title = "Factoring Polynomials Over Algebraic Number Fields", journal = j-TOMS, volume = "2", number = "4", pages = "335--350", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355709", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "12A20 (12-04)", MRnumber = "56 #8521", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "I. Gerst", } @Article{Pinkert:1976:EMF, author = "James R. Pinkert", title = "An Exact Method for Finding the Roots of a Complex Polynomial", journal = j-TOMS, volume = "2", number = "4", pages = "351--363", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355710", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "12-04 (12D10 30A08 65H05)", MRnumber = "56 #299", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "E. Frank", } @Article{Rubin:1976:PI, author = "Frank Rubin", title = "Partition of Integers", journal = j-TOMS, volume = "2", number = "4", pages = "364--374", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355711", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10 (05A17 10A45)", MRnumber = "57 #4605", bibdate = "Sat Aug 27 00:30:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "S. Zaks", } @Article{Crane:1976:AMB, author = "H. L. {Crane Jr.} and Norman E. Gibbs and William G. {Poole Jr.} and Paul K. Stockmeyer", title = "{Algorithm 508}: Matrix Bandwidth and Profile Reduction [{F1}]", journal = j-TOMS, volume = "2", number = "4", pages = "375--377", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355712", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:11:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Lewis:1982:RMB}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gibbs:1976:AHP, author = "Norman E. Gibbs", title = "{Algorithm 509}: a Hybrid Profile Reduction Algorithm [{F1}]", journal = j-TOMS, volume = "2", number = "4", pages = "378--387", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355713", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:11:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Lewis:1982:RMB}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wilson:1976:APL, author = "D. G. Wilson", title = "{Algorithm 510}: Piecewise Linear Approximation to Tabulated Data [{E2}]", journal = j-TOMS, volume = "2", number = "4", pages = "388--391", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355714", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 01:12:13 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ito:1976:RIT, author = "M. R. Ito", title = "Remark on ``{Algorithm 284}: Interchange of Two Blocks of Data [{K2}]''", journal = j-TOMS, volume = "2", number = "4", pages = "392--393", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355715", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Fletcher:1966:ITB}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{elLozy:1976:RAC, author = "Mohamed {el Lozy}", title = "Remark on ``{Algorithm 299}: Chi-Squared Integral [{S15}]''", journal = j-TOMS, volume = "2", number = "4", pages = "393--395", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355716", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:04:46 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hill:1967:CSI,Hill:1985:RCS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Koppelaar:1976:RNI, author = "Henk Koppelaar and Peter Molenaar", title = "Remark on ``{Algorithm 486}: Numerical Inversion of {Laplace} Transform [{D5}]''", journal = j-TOMS, volume = "2", number = "4", pages = "395--396", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355717", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:27:20 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kaufman:1976:RLA, author = "Linda Kaufman", title = "Remark on ``{Algorithm 496}: The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "2", number = "4", pages = "396--396", month = dec, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355705.355718", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Kaufman:1975:ALA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McClellan:1977:ESL, author = "Michael T. McClellan", title = "The Exact Solution of Linear Equations with Rational Function Coefficients", journal = j-TOMS, volume = "3", number = "1", pages = "1--25", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355720", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A15", MRnumber = "55 #11696", bibdate = "Sat Aug 27 22:12:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Jo Ann Howell", } @Article{Stoutemyer:1977:AEA, author = "David R. Stoutemyer", title = "Automatic Error Analysis Using Computer Algebraic Manipulation", journal = j-TOMS, volume = "3", number = "1", pages = "26--43", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355721", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05", MRnumber = "55 #13765", bibdate = "Fri Sep 02 22:30:11 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper shows how the inherent error and the fixed-point or floating-point roundoff of chopoff error of an expression can be determined automatically using a computer algebra language such as {REDUCE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "R. P. Brent", } @Article{Shampine:1977:SND, author = "L. F. Shampine", title = "Stiff and Nonstiff Differential Equation Solvers, {II}: Detecting Stiffness with {Runge--Kutta} Methods", journal = j-TOMS, volume = "3", number = "1", pages = "44--53", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355722", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "56 #4175", bibdate = "Sat Aug 27 22:12:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. H. Enright", } @Article{Tran-Thong:1977:FPF, author = "Tr{\^a}\`n-Th{\^o}\'ng and Bede Liu", title = "Floating Point Fast {Fourier} Transform Computation Using Double Precision Floating Point Accumulators", journal = j-TOMS, volume = "3", number = "1", pages = "54--59", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355723", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65T05", MRnumber = "55 #11658", bibdate = "Sat Aug 27 22:12:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Most commonly available fast Fourier transform (FFT) subroutines use single precision chopping arithmetic, and the resulting normalized roundoff error, in computing an $N$-point transform with $N = \prod_{i = 1}^M a_i$ is $O(M^2)$. This paper proposes a modification of these subroutines for use on computers with a hardwired double precision arithmetic unit. The resulting normalized roundoff error is $O(M)$ and is independent of the $a_i$. The modification leads to a negligible increase in storage. For most computers, the increase in the execution time is small. For certain computers, such as IBM System/360 models 91 and 195, the modification can result in a decrease in the execution time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "computer arithmetic; double-length summation; fast Fourier transform; roundoff error", } @Article{Gonzalez:1977:EAK, author = "Teofilo Gonzalez and Sartaj Sahni and W. R. Franta", title = "An Efficient Algorithm for the {Kolmogorov--Smirnov} and {Lilliefors} Tests", journal = j-TOMS, volume = "3", number = "1", pages = "60--64", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355724", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C99", MRnumber = "55 #11561", bibdate = "Sat Aug 27 22:12:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Hannah Chen", } @Article{Kaufman:1977:STQ, author = "Linda Kaufman", title = "Some Thoughts on the {QZ} Algorithm for Solving the Generalized Eigenvalue Problem", journal = j-TOMS, volume = "3", number = "1", pages = "65--75", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355725", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15", MRnumber = "55 #6814", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "gieg; nla; QZ algorithm", reviewer = "W. Niethammer", } @Article{Amos:1977:CSI, author = "D. E. Amos and S. L. Daniel and M. K. Weston", title = "{CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$}", journal = j-TOMS, volume = "3", number = "1", pages = "76--92", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355726", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "55 #6781", bibdate = "Tue Sep 06 19:20:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Sven-{\AA}ke Gustafson", } @Article{Amos:1977:ACS, author = "D. E. Amos and S. L. Daniel and M. K. Weston", title = "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x \ge 0, \nu \ge 0$} [{S18}]", journal = j-TOMS, volume = "3", number = "1", pages = "93--95", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355727", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:14:12 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See erratum \cite{Amos:1978:ECS}.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Benson:1977:ANA, author = "A. Benson and D. J. Evans", title = "{Algorithm 512}: a Normalized Algorithm for Solution of the Positive Definite Symmetric Quindiagonal Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "3", number = "1", pages = "96--103", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355728", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:22:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cate:1977:AAS, author = "Esko G. Cate and David W. Twigg", title = "{Algorithm 513}: Analysis of In-Situ Transposition [{F1}]", journal = j-TOMS, volume = "3", number = "1", pages = "104--110", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355729", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10", MRnumber = "55 #13866", bibdate = "Thu Apr 29 15:17:56 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Leathers:1979:RAS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Ralph A. Willoughby", } @Article{Veillon:1977:RNI, author = "Fran{\c{c}}oise Veillon", title = "Remark on ``{Algorithm 486}: Numerical Inversion of {Laplace} Transform''", journal = j-TOMS, volume = "3", number = "1", pages = "111--111", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355730", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:43 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dunham:1977:RMU, author = "Charles Dunham", title = "Remark on ``{Algorithm 500}: Minimization of Unconstrained Multivariate Functions [{E4}]''", journal = j-TOMS, volume = "3", number = "1", pages = "112--112", month = mar, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355719.355731", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:27:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Shanno:1976:AMU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aird:1977:PMS, author = "Thomas J. Aird", title = "Portability of Mathematical Software Coded in {Fortran}", journal = j-TOMS, volume = "3", number = "2", pages = "113--127", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355733", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Stoutemyer:1977:ASI, author = "David R. Stoutemyer", title = "Analytically Solving Integral Equations by Using Computer Algebra", journal = j-TOMS, volume = "3", number = "2", pages = "128--146", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355734", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R05", MRnumber = "56 #4205", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Sean McKee", } @Article{McClellan:1977:CAE, author = "Michael T. McClellan", title = "A Comparison of Algorithms for the Exact Solution of Linear Equations", journal = j-TOMS, volume = "3", number = "2", pages = "147--158", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355735", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "55 #13753", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "H. R. Schwarz", } @Article{Farden:1977:SSS, author = "David C. Farden", title = "The Solution of a Special Set of {Hermitian} {Toeplitz} Linear Equations", journal = j-TOMS, volume = "3", number = "2", pages = "159--163", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355736", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ichida:1977:CFO, author = "Kozo Ichida and Takeshi Kiyono and Fujiichi Yoshimoto", title = "Curve Fitting by a One-Pass Method With a Piecewise Cubic Polynomial", journal = j-TOMS, volume = "3", number = "2", pages = "164--174", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355737", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ellis:1977:ANM, author = "T. M. R. Ellis and D. H. McLain", title = "{Algorithm 514}: a New Method of Cubic Curve Fitting Using Local Data [{E2}]", journal = j-TOMS, volume = "3", number = "2", pages = "175--179", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355738", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Buckles:1977:AGV, author = "B. P. Buckles and M. Lybanon", title = "{Algorithm 515}: Generation of a Vector from the Lexicographical Index [{G6}]", journal = j-TOMS, volume = "3", number = "2", pages = "180--182", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355739", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McKean:1977:AAO, author = "J. W. McKean and T. A. {Ryan, Jr.}", title = "{Algorithm 516}: An Algorithm for Obtaining Confidence Intervals and Point Estimates Based on Ranks in the Two Sample Location Problem [{G1}]", journal = j-TOMS, volume = "3", number = "2", pages = "183--185", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355740", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chan:1977:APC, author = "S. P. Chan and R. Feldman and B. N. Parlett", title = "{Algorithm 517}: a Program for Computing the Condition Numbers of Matrix Eigenvalues Without Computing Eigenvectors [{F2}]", journal = j-TOMS, volume = "3", number = "2", pages = "186--203", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355741", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:34:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "condition estimation; eig; nla; nonsymmetric matrix; pert; software", } @Article{Mackay:1977:RPT, author = "M. Mackay and J. E. Radue", title = "Remark on ``{Some} Performance Tests of `{Quicksort}' and Descendants''", journal = j-TOMS, volume = "3", number = "2", pages = "204--204", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355742", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:07:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Loeser:1974:SPT}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jansen:1977:RLF, author = "J. K. M. Jansen", title = "Remark on ``{Algorithm 259}: {Legendre} Functions for Arguments Larger than One''", journal = j-TOMS, volume = "3", number = "2", pages = "204--205", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.356467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:59:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Gautschi:1965:LFA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Friedman:1977:AFB, author = "Jerome H. Friedman and Jon Louis Bentley and Raphael Ari Finkel", title = "An Algorithm for Finding Best Matches in Logarithmic Expected Time", journal = j-TOMS, volume = "3", number = "3", pages = "209--226", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355745", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:53:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355744.355745; http://www.acm.org/pubs/citations/journals/toms/1977-3-3/p209-bentley/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ito:1977:MRP, author = "Tetsuro Ito and Makoto Kizawa", title = "The Matrix Rearrangement Procedure for Graph-Theoretical Algorithms and Its Application to the Generation of Fundamental Cycles", journal = j-TOMS, volume = "3", number = "3", pages = "227--231", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355746", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cody:1977:CRF, author = "W. J. Cody and Rose M. Motley and L. Wayne Fullerton", title = "The Computation of Real Fractional Order {Bessel} Functions of the Second Kind", journal = j-TOMS, volume = "3", number = "3", pages = "232--239", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355747", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1977:ERI, author = "Walter Gautschi", title = "Evaluation of Repeated Integrals of the Coerror Function", journal = j-TOMS, volume = "3", number = "3", pages = "240--252", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355748", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Walker:1977:EMG, author = "Alastair J. Walker", title = "An Efficient Method for Generating Discrete Random Variables with General Distributions", journal = j-TOMS, volume = "3", number = "3", pages = "253--256", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355749", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kinderman:1977:CGR, author = "A. J. Kinderman and J. F. Monahan", title = "Computer Generation of Random Variables Using the Ratio of Uniform Deviates", journal = j-TOMS, volume = "3", number = "3", pages = "257--260", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355750", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:58:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7496", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Cohen:1977:SSF, author = "Jacques Cohen and Joel Katcoff", title = "Symbolic Solution of Finite-Difference Equations", journal = j-TOMS, volume = "3", number = "3", pages = "261--271", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355751", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fateman:1977:ADC, author = "Richard J. Fateman", title = "An Algorithm for Deciding the Convergence of the Rational Iteration $x_{n+1} = f(x_n)$", journal = j-TOMS, volume = "3", number = "3", pages = "272--278", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355752", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hill:1977:AIB, author = "G. W. Hill", title = "{Algorithm 518}: Incomplete {Bessel} Function {$I_0$}. {The von Mises} Distribution [{S14}]", journal = j-TOMS, volume = "3", number = "3", pages = "279--284", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355753", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 24 15:46:06 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kallman:1977:ATA, author = "Ralph Kallman", title = "{Algorithm 519}: Three Algorithms for Computing {Kolmogorov--Smirnov} Probabilities with Arbitrary Boundaries and a Certification of {Algorithm 487} [{S14}]", journal = j-TOMS, volume = "3", number = "3", pages = "285--294", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355754", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:01:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weglarz:1977:AAR, author = "Jan Weglarz and Jacek Blazewicz and Wojciech Cellary and Roman Slowinski", title = "{Algorithm 520}: An Automatic Revised Simplex Method for Constrained Resource Network Scheduling [{H}]", journal = j-TOMS, volume = "3", number = "3", pages = "295--300", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355755", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1977:ARI, author = "Walter Gautschi", title = "{Algorithm 521}: Repeated Integrals of the Coerror Function [{S15}]", journal = j-TOMS, volume = "3", number = "3", pages = "301--302", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355756", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:03:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sipala:1977:RSM, author = "Paolo Sipala", title = "Remark on ``{Algorithm 408}: a Sparse Matrix Package ({Part I}) [{F4}]''", journal = j-TOMS, volume = "3", number = "3", pages = "303--303", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.355757", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{McNamee:1971:SMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tenney:1977:RTO, author = "Dennis Tenney", title = "Remark on ``{Algorithm 219}: Topological Ordering for {PERT} Networks''", journal = j-TOMS, volume = "3", number = "3", pages = "303--303", month = sep, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355744.356472", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Kase:1963:TOP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hillstrom:1977:STA, author = "Kenneth E. Hillstrom", title = "A Simulation Test Approach to the Evaluation of Nonlinear Optimization Algorithms", journal = j-TOMS, volume = "3", number = "4", pages = "305--315", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355760", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:06:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Powell:1977:PQA, author = "M. J. D. Powell and M. A. Sabin", title = "Piecewise Quadratic Approximations on Triangles", journal = j-TOMS, volume = "3", number = "4", pages = "316--325", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355761", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15", MRnumber = "58 #3319", bibdate = "Sat Aug 27 23:07:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Skeel:1977:BLM, author = "Robert D. Skeel and Antony K. Kong", title = "Blended Linear Multistep Methods", journal = j-TOMS, volume = "3", number = "4", pages = "326--345", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355762", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "57 #1904", bibdate = "Fri Sep 30 01:01:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "R. Leonard Brown", } @Article{Payne:1977:NRN, author = "W. H. Payne", title = "Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm", journal = j-TOMS, volume = "3", number = "4", pages = "346--358", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355763", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10", MRnumber = "57 #1827", bibdate = "Sat Aug 27 23:09:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7752", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", language = "English", location = "SEL: Wi", references = "0", reviewer = "Artenio De Matteis", revision = "16/01/94", } @Article{Boyce:1977:IPF, author = "William M. Boyce", title = "An Improved Program for the Full {Steiner} Tree Problem", journal = j-TOMS, volume = "3", number = "4", pages = "359--385", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355764", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90B10 (05C30)", MRnumber = "57 #11690", bibdate = "Sat Aug 27 23:07:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Fan R. K. Chung", } @Article{Cabay:1977:CTE, author = "S. Cabay and T. P. L. Lam", title = "Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations", journal = j-TOMS, volume = "3", number = "4", pages = "386--397", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355765", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "57 #7962a", bibdate = "Fri Sep 30 01:01:45 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. Borsch-Supan", } @Article{Eddy:1977:NCH, author = "William F. Eddy", title = "A New Convex Hull Algorithm for Planar Sets", journal = j-TOMS, volume = "3", number = "4", pages = "398--403", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355766", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:07:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cabay:1977:AEC, author = "S. Cabay and T. P. L. Lam", title = "{Algorithm 522}: {ESOLVE}, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "3", number = "4", pages = "404--410", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355767", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "57 #7962b", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. Borsch-Supan", } @Article{Eddy:1977:ACN, author = "W. F. Eddy", title = "{Algorithm 523}: {CONVEX}, a New Convex Hull Algorithm for Planar Sets [{Z}]", journal = j-TOMS, volume = "3", number = "4", pages = "411--412", month = dec, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355759.355768", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dinkel:1978:SAP, author = "John J. Dinkel and Gary A. Kochenberger and S. N. Wong", title = "Sensitivity Analysis Procedures for Geometric Programs: Computational Aspects", journal = j-TOMS, volume = "4", number = "1", pages = "1--14", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355770", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355769.355770; http://www.acm.org/pubs/citations/journals/toms/1978-4-1/p1-wong/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Blue:1978:PFP, author = "James L. Blue", title = "A Portable {Fortran} Program to Find the {Euclidean} Norm of a Vector", journal = j-TOMS, volume = "4", number = "1", pages = "15--23", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355771", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68A10", MRnumber = "57 \#18205", bibdate = "Sat Aug 27 23:14:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS; floating-point arithmetic; floating-point overflow; floating-point underflow; nla; norm; software", reviewer = "A. D. Booth", } @Article{Ivie:1978:SMP, author = "John Ivie", title = "Some {MACSYMA} Programs for Solving Recurrence Relations", journal = j-TOMS, volume = "4", number = "1", pages = "24--33", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:42:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Celis:1984:RCE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lasdon:1978:DTG, author = "L. S. Lasdon and A. D. Waren and A. Jain and M. Ratner", title = "Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming", journal = j-TOMS, volume = "4", number = "1", pages = "34--50", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355773", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tsao:1978:MNI, author = "Nai-Kuan Tsao and Rose Marie Prior", title = "On Multipoint Numerical Interpolation", journal = j-TOMS, volume = "4", number = "1", pages = "51--56", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brent:1978:FMP, author = "Richard P. Brent", title = "A {Fortran} Multiple-Precision Arithmetic Package", journal = j-TOMS, volume = "4", number = "1", pages = "57--70", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355775", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brent:1978:AMF, author = "Richard P. Brent", title = "{Algorithm 524}: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]", journal = j-TOMS, volume = "4", number = "1", pages = "71--81", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355776", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:35:50 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Brent:1979:RMF,Brent:1980:AIB,Smith:1998:AMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1978:AAA, author = "John R. Rice", title = "{Algorithm 525}: {ADAPT}, Adaptive Smooth Curve Fitting [{E2}]", journal = j-TOMS, volume = "4", number = "1", pages = "82--94", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355777", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Futrell:1978:RTA, author = "R. Futrell", title = "Remark on ``{Fortran} Translation of {Algorithm 409}: Discrete {Chebychev} Curve Fit [{E2}]''", journal = j-TOMS, volume = "4", number = "1", pages = "95--95", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.355778", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 23:07:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Simpson:1976:AFT}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Skovgaard:1978:RCE, author = "Ove Skovgaard", title = "Remark on ``{Algorithm 149}: Complete Elliptic Integral [{S21}]''", journal = j-TOMS, volume = "4", number = "1", pages = "95--95", month = mar, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355769.356473", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Merner:1962:CEI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1978:AP, author = "Fred T. Krogh", title = "Algorithms Policy", journal = j-TOMS, volume = "4", number = "2", pages = "97--99", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355781", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:23:41 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ford:1978:PET, author = "Brian Ford", title = "Parametrization of the Environment for Transportable Numerical Software", journal = j-TOMS, volume = "4", number = "2", pages = "100--103", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355782", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fox:1978:PMS, author = "P. A. Fox and A. D. Hall and N. L. Schryer", title = "The {PORT} Mathematical Subroutine Library", journal = j-TOMS, volume = "4", number = "2", pages = "104--126", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355783", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", abstract = "The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed. Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of predefined machine constants. The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "dynamic storage allocation; error handling; libraries; numerical analysis; portability", } @Article{Enright:1978:IEM, author = "W. H. Enright", title = "Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations", journal = j-TOMS, volume = "4", number = "2", pages = "127--136", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355784", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L10", MRnumber = "58 #3483", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Henning Esser", } @Article{Duff:1978:ITA, author = "I. S. Duff and J. K. Reid", title = "An Implementation of {Tarjan}'s Algorithm for the Block Triangularization of a Matrix", journal = j-TOMS, volume = "4", number = "2", pages = "137--147", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355785", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 19:40:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "graph; sparse", } @Article{Akima:1978:MBI, author = "Hiroshi Akima", title = "A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points", journal = j-TOMS, volume = "4", number = "2", pages = "148--159", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355786", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Akima:1978:ABI, author = "Hiroshi Akima", title = "{Algorithm 526}: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]", journal = j-TOMS, volume = "4", number = "2", pages = "160--164", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355787", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 20:54:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Akima:1979:RBI,Preusser:1985:RBI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bank:1978:AFI, author = "Randolph E. Bank", title = "{Algorithm 527}: {A Fortran} Implementation of the Generalized Marching Algorithm [{D3}]", journal = j-TOMS, volume = "4", number = "2", pages = "165--176", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355788", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:30:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fox:1978:AFP, author = "P. A. Fox and A. D. Hall and N. L. Schryer", title = "{Algorithm 528}: Framework for a Portable Library [{Z}]", journal = j-TOMS, volume = "4", number = "2", pages = "177--188", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355789", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:30:46 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", note = "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", annote = "The three program packages presented here provide a framework for a portable FORTRAN subroutine library. They were developed for the BELL Laboratories library PORT(1). The packages are: machine-dependent constants, automatic error handling, and dynamic storage allocation using a stack.", country = "USA", date = "19/03/80", descriptors = "Reliability; program construction; mathematical method; FORTRAN; portability; error handling; memory management; library", enum = "988", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", language = "English", location = "RWTH-AC-DFV: TELL", references = "1", revision = "20/03/92", } @Article{Duff:1978:APB, author = "I. S. Duff and J. K. Reid", title = "{Algorithm 529}: Permutations To Block Triangular Form [{F1}]", journal = j-TOMS, volume = "4", number = "2", pages = "189--192", month = jun, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355780.355790", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:31:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bailey:1978:ASS, author = "P. B. Bailey and M. K. Gordon and L. F. Shampine", title = "Automatic Solution of the {Sturm--Liouville} Problem", journal = j-TOMS, volume = "4", number = "3", pages = "193--208", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355792", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L15", MRnumber = "80a:65181", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355791.355792; http://www.acm.org/pubs/citations/journals/toms/1978-4-3/p193-gordon/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Polak:1978:TPP, author = "S. J. Polak and J. Schrooten and C. Barneveld Binkhuysen", title = "{TEDDY2}, a Program Package for Parabolic Composite Region Problems", journal = j-TOMS, volume = "4", number = "3", pages = "209--227", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355793", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04", MRnumber = "80a:65009", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Larson:1978:ECE, author = "John Larson and Ahmed Sameh", title = "Efficient Calculation of the Effects of Roundoff Errors", journal = j-TOMS, volume = "4", number = "3", pages = "228--236", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355794", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05", MRnumber = "80a:65092a", bibdate = "Thu Apr 29 15:22:59 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See errata \cite{Larson:1979:ECE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "na; rounding error", } @Article{Brown:1978:SPA, author = "W. S. Brown", title = "The Subresultant {PRS} Algorithm", journal = j-TOMS, volume = "4", number = "3", pages = "237--249", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355795", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "12-04 (68C20)", MRnumber = "82g:12001", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gustavson:1978:TFA, author = "Fred G. Gustavson", title = "Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition", journal = j-TOMS, volume = "4", number = "3", pages = "250--269", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355796", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F30 (65-04)", MRnumber = "80a:65086", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chen:1978:PPB, author = "S. C. Chen and D. J. Kuck and A. H. Sameh", title = "Practical Parallel Band Triangular Systems Solvers", journal = j-TOMS, volume = "4", number = "3", pages = "270--277", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355797", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "80a:65065", bibdate = "Fri Aug 26 23:35:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "linear system; nla; prll; tridiagonal matrix", } @Article{Ward:1978:ECS, author = "R. C. Ward and L. J. Gray", title = "Eigensystem Computation for Skew-Symmetric and a Class of Symmetric Matrices", journal = j-TOMS, volume = "4", number = "3", pages = "278--285", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355798", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15", MRnumber = "80a:65082", bibdate = "Sat Aug 27 23:37:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "eig; nla; skew-symmetric matrix; symmetric matrix", } @Article{Ward:1978:AAC, author = "R. C. Ward and L. J. Gray", title = "{Algorithm 530}: An Algorithm for Computing the Eigensystem of Skew-Symmetric Matrices and a Class of Symmetric Matrices [{F2}]", journal = j-TOMS, volume = "4", number = "3", pages = "286--289", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355799", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:37:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Snyder:1978:ACP, author = "William V. Snyder", title = "{Algorithm 531}: Contour Plotting [{J6}]", journal = j-TOMS, volume = "4", number = "3", pages = "290--294", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355800", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:38:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Coleman:1978:RSN, author = "John P. Coleman", title = "Remark on ``{Algorithm 49}: Spherical {Neumann} Function''", journal = j-TOMS, volume = "4", number = "3", pages = "295--295", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355801", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Herndon:1961:SNF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gustavson:1978:RSM, author = "Fred G. Gustavson", title = "Remark on ``{Algorithm 408}: a Sparse Matrix Package ({Part I}) [{F4}]''", journal = j-TOMS, volume = "4", number = "3", pages = "295--295", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.356474", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{McNamee:1971:SMP}.", URL = "http://doi.acm.org/10.1145/355791.356474; http://www.acm.org/pubs/citations/journals/toms/1978-4-3/p295-mcnamee/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Schoene:1978:RMI, author = "Andrew Y. Schoene", title = "Remark on ``{Algorithm 435}: Modified Incomplete Gamma Function [{S14}]''", journal = j-TOMS, volume = "4", number = "3", pages = "296--304", month = sep, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355791.355803", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Fullerton:1972:MIG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Baker:1978:SAC, author = "Christopher T. H. Baker and Malcolm S. Keech", title = "Stability Analysis of Certain {Runge--Kutta} Procedures for {Volterra} Integral Equations", journal = j-TOMS, volume = "4", number = "4", pages = "305--315", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356476", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R20", MRnumber = "80a:65264", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fairweather:1978:IRQ, author = "Graeme Fairweather", title = "An Investigation of {Romberg} Quadrature", journal = j-TOMS, volume = "4", number = "4", pages = "316--322", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356477", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1978:SPA, author = "Lawrence F. Shampine", title = "Stability Properties of {Adams} Codes", journal = j-TOMS, volume = "4", number = "4", pages = "323--329", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356478", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "80c:65157", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sherman:1978:ASG, author = "Andrew H. Sherman", title = "Algorithms for Sparse {Gaussian} Elimination with Partial Pivoting", journal = j-TOMS, volume = "4", number = "4", pages = "330--338", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356494", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tendler:1978:SSI, author = "Joel M. Tendler and Theodore A. Bickart and Zdenek Picel", title = "A Stiffly Stable Integration Process Using Cyclic Composite Methods", journal = j-TOMS, volume = "4", number = "4", pages = "339--368", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356495", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Miller:1978:SRA, author = "Webb Miller and David Spooner", title = "Software for Roundoff Analysis. {II}", journal = j-TOMS, volume = "4", number = "4", pages = "369--387", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356496", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05 (65F99)", MRnumber = "81i:65035", bibdate = "Sat Aug 27 23:48:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cs; rounding error; software", } @Article{Miller:1978:ASR, author = "Webb Miller and David Spooner", title = "{Algorithm 532}: Software for Roundoff Analysis [{Z}]", journal = j-TOMS, volume = "4", number = "4", pages = "388--390", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356497", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:48:45 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sherman:1978:ANF, author = "Andrew H. Sherman", title = "{Algorithm 533}: {NSPIV}, {A Fortran} Subroutine for Sparse {Gaussian} Elimination with Partial Pivoting [{F4}]", journal = j-TOMS, volume = "4", number = "4", pages = "391--398", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356498", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:49:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tendler:1978:ASS, author = "Joel M. Tendler and Theodore A. Bickart and Zdenek Picel", title = "{Algorithm 534}: {STINT}: {STiff} (differential equations) {INTegrator} [{D2}]", journal = j-TOMS, volume = "4", number = "4", pages = "399--403", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356499", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:50:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Garbow:1978:AQA, author = "Burton S. Garbow", title = "{Algorithm 535}: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]", journal = j-TOMS, volume = "4", number = "4", pages = "404--410", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356500", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:40:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Garbow:1982:RQA,Garbow:1984:RQA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amos:1978:ECS, author = "Donald E. Amos", title = "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$} [{S18}]''", journal = j-TOMS, volume = "4", number = "4", pages = "411--411", month = dec, year = "1978", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356502.356501", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Amos:1977:ACS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zave:1979:DAP, author = "Pamela Zave and Werner C. Rheinboldt", title = "Design of an Adaptive, Parallel Finite-Element System", journal = j-TOMS, volume = "5", number = "1", pages = "1--17", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355816", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N30 (65-04)", MRnumber = "80c:65213", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:1979:SDF, author = "I. S. Duff and J. K. Reid", title = "Some Design Features of a Sparse Matrix Code", journal = j-TOMS, volume = "5", number = "1", pages = "18--35", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355817", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Proskurowski:1979:NSH, author = "Wlodzimierz Proskurowski", title = "Numerical Solution of {Helmholtz}'s Equation by Implicit Capacitance Matrix Methods", journal = j-TOMS, volume = "5", number = "1", pages = "36--49", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355818", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N20", MRnumber = "80b:65129", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "John Crank", } @Article{Yohe:1979:SIA, author = "J. M. Yohe", title = "Software for Interval Arithmetic: a Reasonably Portable Package", journal = j-TOMS, volume = "5", number = "1", pages = "50--63", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355819", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:55:38 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "interval arithmetic; na; software", } @Article{More:1979:NSN, author = "Jorge J. Mor{\'e} and Michel Y. Cosnard", title = "Numerical Solution of Nonlinear Equations", journal = j-TOMS, volume = "5", number = "1", pages = "64--85", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355820", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05", MRnumber = "80c:65110", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kahaner:1979:EAD, author = "David K. Kahaner and Mark B. Wells", title = "An Experimental Algorithm for ${N}$-Dimensional Adaptive Quadrature", journal = j-TOMS, volume = "5", number = "1", pages = "86--96", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355821", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:41:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Knoble:1979:EOW, author = "H. D. Knoble and C. {Forney, Jr.} and F. S. Bader", title = "An Efficient One-Way Enciphering Algorithm", journal = j-TOMS, volume = "5", number = "1", pages = "97--107", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355822", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Knoble:1979:AEO, author = "H. D. Knoble", title = "{Algorithm 536}: An Efficient One-Way Enciphering Algorithm [{Z}]", journal = j-TOMS, volume = "5", number = "1", pages = "108--111", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355823", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:58:53 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Leeb:1979:ACV, author = "Walter R. Leeb", title = "{Algorithm 537}: Characteristic Values of {Mathieu}'s Differential Equation", journal = j-TOMS, volume = "5", number = "1", pages = "112--117", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355824", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Nikolai:1979:AEE, author = "Paul J. Nikolai", title = "{Algorithm 538}: Eigenvectors and Eigenvalues of Real Generalized Symmetric Matrices by Simultaneous Iteration [{F2}]", journal = j-TOMS, volume = "5", number = "1", pages = "118--125", month = mar, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355815.355825", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1979:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "5", number = "2", pages = "129--131", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355827", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:01:38 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Schrage:1979:MPF, author = "Linus Schrage", title = "A More Portable {Fortran} Random Number Generator", journal = j-TOMS, volume = "5", number = "2", pages = "132--138", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355828", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{George:1979:DUI, author = "Alan George and Joseph W. H. Liu", title = "The Design of a User Interface for a Sparse Matrix Package", journal = j-TOMS, volume = "5", number = "2", pages = "139--162", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355829", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Payne:1979:CG, author = "W. H. Payne and F. M. Ives", title = "Combination Generators", journal = j-TOMS, volume = "5", number = "2", pages = "163--172", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355830", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{deBoor:1979:ECM, author = "Carl {de Boor}", title = "Efficient Computer Manipulation of Tensor Products", journal = j-TOMS, volume = "5", number = "2", pages = "173--182", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355831", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04", MRnumber = "80d:65006a", bibdate = "Thu Apr 29 15:18:18 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrigenda \cite{deBoor:1979:CCM}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cleary:1979:AAF, author = "John Gerald Cleary", title = "Analysis of an Algorithm for Finding Nearest Neighbors in {Euclidean} Space", journal = j-TOMS, volume = "5", number = "2", pages = "183--192", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355832", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68H05 (68G10)", MRnumber = "80e:68236", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Crowder:1979:RCE, author = "Harlan Crowder and Ron S. Dembo and John M. Mulvey", title = "On Reporting Computational Experiments with Mathematical Software", journal = j-TOMS, volume = "5", number = "2", pages = "193--203", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355833", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Crary:1979:VPN, author = "Fred D. Crary", title = "A Versatile Precompiler for Nonstandard Arithmetics", journal = j-TOMS, volume = "5", number = "2", pages = "204--217", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355834", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Geddes:1979:SCP, author = "K. O. Geddes", title = "Symbolic Computation of {Pad{\'e}} Approximants", journal = j-TOMS, volume = "5", number = "2", pages = "218--233", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355835", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F99 68C20)", MRnumber = "80c:65005", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bogen:1979:ASI, author = "Richard A. Bogen", title = "Addendum to ``{Analytically} Solving Integral Equations by Using Computer Algebra''", journal = j-TOMS, volume = "5", number = "2", pages = "234--237", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355836", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R20", MRnumber = "80k:65102", bibdate = "Sat Nov 19 13:07:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{elLozy:1979:RAS, author = "Mohamed {el Lozy}", title = "Remark on ``{Algorithm 395}: {Student}'s $t$-Distribution'' and Remark on ``{Algorithm 396}: {Student}'s Quantiles [{S14}]''", journal = j-TOMS, volume = "5", number = "2", pages = "238--239", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355837", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:05:53 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hill:1970:SD,Hill:1970:SQ,Hill:1981:RSD,Hill:1985:RCS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Geddes:1979:RCC, author = "K. O. Geddes", title = "Remark on ``{Algorithm 424}: {Clenshaw--Curtis} Quadrature [{O1}]''", journal = j-TOMS, volume = "5", number = "2", pages = "240--240", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355838", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Gentleman:1972:CCQ}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anderson:1979:RBI, author = "M. R. Anderson", title = "Remark on ``{Algorithm 474}: Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures''", journal = j-TOMS, volume = "5", number = "2", pages = "241--241", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355839", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1974:BIS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Akima:1979:RBI, author = "Hiroshi Akima", title = "Remark on ``{Algorithm} 526: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]''", journal = j-TOMS, volume = "5", number = "2", pages = "242--243", month = jun, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355826.355840", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1978:ABI,Preusser:1985:RBI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1979:SRR, author = "L. F. Shampine", title = "Storage Reduction for {Runge--Kutta} Codes", journal = j-TOMS, volume = "5", number = "3", pages = "245--250", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355842", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ehrlich:1979:SBE, author = "L. W. Ehrlich", title = "Solving the Biharmonic Equation on Irregular Regions", journal = j-TOMS, volume = "5", number = "3", pages = "251--258", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355843", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N20", MRnumber = "80e:65093", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gill:1979:DSF, author = "Philip E. Gill and Walter Murray and Susan M. Picken and Margaret H. Wright", title = "The Design and Structure of a {Fortran} Program Library for Optimization", journal = j-TOMS, volume = "5", number = "3", pages = "259--283", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355844", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{George:1979:IPN, author = "Alan George and Joseph W. H. Liu", title = "An Implementation of a Pseudoperipheral Node Finder", journal = j-TOMS, volume = "5", number = "3", pages = "284--295", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355845", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bennett:1979:SPE, author = "James Michael Bennett and Robert Neff Bryan", title = "A Single-Point Exchange Algorithm for Approximating Functions of Two Variables", journal = j-TOMS, volume = "5", number = "3", pages = "296--307", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355846", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15", MRnumber = "80e:65020", bibdate = "Sun Aug 28 00:06:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lawson:1979:BLA, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", title = "{Basic Linear Algebra Subprograms} for {Fortran} Usage", journal = j-TOMS, volume = "5", number = "3", pages = "308--323", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355847", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 19:42:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS; nla; software", } @Article{Lawson:1979:ABL, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", title = "{Algorithm 539}: {Basic Linear Algebra Subprograms} for {Fortran} Usage [{F1}]", journal = j-TOMS, volume = "5", number = "3", pages = "324--325", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355848", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:48:12 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA,Hanson:2004:AAV,Hanson:2018:RAM}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Madsen:1979:APG, author = "N. K. Madsen and R. F. Sincovec", title = "{Algorithm 540}: {PDECOL}, General Collocation Software for Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "3", pages = "326--351", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355849", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:21:53 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hopkins:1992:RPG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Swartztrauber:1979:AEF, author = "Paul N. Swartztrauber and Roland A. Sweet", title = "{Algorithm 541}: Efficient {Fortran} Subprograms for the Solution of Separable Elliptic Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "3", pages = "352--364", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355850", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 19:43:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/355841.355850; http://www.acm.org/pubs/citations/journals/toms/1979-5-3/p352-swartztrauber/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Steuerwalt:1979:CEF, author = "Michael Steuerwalt", title = "Certification of ``{Algorithm} 541: Efficient {Fortran} Subprograms for the Solution of Separable Elliptic Partial Differential Equations [{D3}]''", journal = j-TOMS, volume = "5", number = "3", pages = "365--371", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355851", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 24 09:58:08 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Larson:1979:ECE, author = "John Larson", title = "Errata: ``{Efficient} Calculation of the Effects of Roundoff Errors''", journal = j-TOMS, volume = "5", number = "3", pages = "372--372", month = sep, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355841.355852", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "372. 65G05", MRnumber = "80a:65092b", bibdate = "Sat Nov 19 13:07:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Larson:1978:ECE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gear:1979:EN, author = "C. W. Gear", title = "{Editor}'s Note", journal = j-TOMS, volume = "5", number = "4", pages = "373--373", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355854", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Enright:1979:APS, author = "W. H. Enright and M. S. Kamel", title = "Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure", journal = j-TOMS, volume = "5", number = "4", pages = "374--385", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355855", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gladwell:1979:IVR, author = "Ian Gladwell", title = "Initial Value Routines in the {NAG} Library", journal = j-TOMS, volume = "5", number = "4", pages = "386--400", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355856", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zlatev:1979:ASD, author = "Zahari Zlatev and Per Grove Thomsen", title = "Automatic Solution of Differential Equations Based on the User of Linear Multistep Methods", journal = j-TOMS, volume = "5", number = "4", pages = "401--414", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355857", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Stetter:1979:GEE, author = "Hans J. Stetter", title = "Global Error Estimation in {Adams PC}-Codes", journal = j-TOMS, volume = "5", number = "4", pages = "415--430", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355858", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Houstis:1979:HOF, author = "E. N. Houstis and T. S. Papatheodorou", title = "High-Order Fast Elliptic Equation Solvers", journal = j-TOMS, volume = "5", number = "4", pages = "431--441", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355859", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kaufman:1979:ADH, author = "L. Kaufman", title = "Application of Dense {Householder} Transformation to a Sparse Matrix", journal = j-TOMS, volume = "5", number = "4", pages = "442--450", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355860", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Householder transformation; nla; qrd; sparse", } @Article{Rayward-Smith:1979:CSN, author = "V. J. Rayward-Smith", title = "On Computing the {Smith} Normal Form of an Integer Matrix", journal = j-TOMS, volume = "5", number = "4", pages = "451--456", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355861", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wampler:1979:SWL, author = "Roy H. Wampler", title = "Solutions to Weighted Least Squares Problems by Modified {Gram--Schmidt} with Iterative Refinement", journal = j-TOMS, volume = "5", number = "4", pages = "457--465", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355862", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 19:44:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gram--Schmidt algorithm; iterative refinement; lsq; nla; qrd; weights", } @Article{Gautschi:1979:CPI, author = "Walter Gautschi", title = "A Computational Procedure for Incomplete Gamma Functions", journal = j-TOMS, volume = "5", number = "4", pages = "466--481", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355863", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1979:AIG, author = "W. Gautschi", title = "{Algorithm 542}: Incomplete Gamma Functions [{S14}]", journal = j-TOMS, volume = "5", number = "4", pages = "482--489", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355864", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:39:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Houstis:1979:AFF, author = "E. N. Houstis and T. S. Papatheodorou", title = "{Algorithm 543}: {FFT9}, Fast Solution of {Helmholtz}-Type Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "4", pages = "490--493", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355865", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:40:38 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wampler:1979:ALL, author = "Roy H. Wampler", title = "{Algorithm 544}: {L2A} and {L2B}, Weighted Least Squares Solutions by Modified {Gram--Schmidt} with Iterative Refinement [{F4}]", journal = j-TOMS, volume = "5", number = "4", pages = "494--499", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355866", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:04:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gram--Schmidt algorithm; iterative refinement; lsq; nla; qrd; weights", } @Article{Fraser:1979:AOM, author = "D. Fraser", title = "{Algorithm 545}: An Optimized Mass Storage {FFT} [{C6}]", journal = j-TOMS, volume = "5", number = "4", pages = "500--517", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355867", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Aug 28 00:41:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brent:1979:RMF, author = "R. P. Brent", title = "Remark on ``{Algorithm} 524: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]''", journal = j-TOMS, volume = "5", number = "4", pages = "518--519", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355868", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:35:42 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Brent:1978:AMF,Brent:1980:AIB,Smith:1998:AMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Leathers:1979:RAS, author = "Burton L. Leathers", title = "Remark on ``{Algorithm} 513: Analysis of In-Situ Transposition [{F1}]'' and Remark on ``{Algorithm} 467: Matrix Transposition in Place''", journal = j-TOMS, volume = "5", number = "4", pages = "520--520", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355869", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Cate:1977:AAS,Brenner:1973:MTP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{vanSwieten:1979:RAV, author = "A. C. M. {van Swieten} and J. Th. M. {de Hosson}", title = "Remark on ``{Algorithm} 475: Visible Surface Plotting Program''", journal = j-TOMS, volume = "5", number = "4", pages = "521--523", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355870", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Wright:1974:VSP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fox:1979:RFP, author = "Phyllis Fox", title = "Remark on ``{Algorithm} 528: Framework for a Portable Library [{Z}]''", journal = j-TOMS, volume = "5", number = "4", pages = "524--524", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355871", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:06 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", note = "See \cite{Fox:1978:AFP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{deBoor:1979:CCM, author = "Carl {de Boor}", title = "Corrigenda: ``{Efficient} Computer Manipulation of Tensor Products''", journal = j-TOMS, volume = "5", number = "4", pages = "525--525", month = dec, year = "1979", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355853.355872", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "525. 65-04", MRnumber = "80d:65006b", bibdate = "Sat Oct 24 15:50:17 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{deBoor:1979:ECM}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cheung:1980:CCE, author = "To-Yat Cheung", title = "Computational Comparison of Eight Methods for the Maximum Network Flow Problem", journal = j-TOMS, volume = "6", number = "1", pages = "1--16", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355874", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90B10 (68E10)", MRnumber = "80m:90046", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "breadth-first; computational comparison; depth-first; Dinic; Karzanov; Kinariwala-Rao; maximum network flow", } @Article{Ho:1980:CST, author = "James K. Ho and Etienne Loute", title = "A Comparative Study of Two Methods for Staircase Linear Problems", journal = j-TOMS, volume = "6", number = "1", pages = "17--30", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355875", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "comparison of algorithms; decomposition; factorization; large-scale systems; structured linear programs", } @Article{Michaels:1980:MPG, author = "William M. Michaels and Richard P. O'Neill", title = "A Mathematical Program Generator {MPGENR}", journal = j-TOMS, volume = "6", number = "1", pages = "31--44", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355876", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "large-scale optimization; linear and nonlinear programming; software verification; test problem generation", } @Article{Chung:1980:ACF, author = "Won L. Chung", title = "Automatic Curve Fittings Using an Adaptive Local Algorithm", journal = j-TOMS, volume = "6", number = "1", pages = "45--57", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355877", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:55:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "adaptive approximation; automatic curve fitting; data compression; interactive display; modeling and simulation systems; numerical stability; one-sided algorithm; piecewise cubic polynomials; {$L_2$} approximation with continuity constraints", } @Article{Clark:1980:REV, author = "Gordon M. Clark", title = "Recursive Estimation of the Variance of the Sample Average", journal = j-TOMS, volume = "6", number = "1", pages = "58--67", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355878", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68J05 (65C20)", MRnumber = "80m:68086", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "recursive calculation; sample autocovariances; simulation output analysis; variance estimation", } @Article{Power:1980:ISU, author = "Leigh R. Power", title = "Internal Sorting Using a Minimal Tree Merge Strategy", journal = j-TOMS, volume = "6", number = "1", pages = "68--79", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355879", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68E05", MRnumber = "80m:68056", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "internal sort; linked list; list processing; merge; minimal tree; natural merge sort; sort; straight merge sort", } @Article{deBoor:1980:SPS, author = "Carl {de Boor} and Richard Weiss", title = "{SOLVEBLOK}: a Package for Solving Almost Block Diagonal Linear Systems", journal = j-TOMS, volume = "6", number = "1", pages = "80--87", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355880", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 24 15:50:20 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "almost block diagonal systems; Gaussian elimination; ordinary differential equations; spline approximation", } @Article{deBoor:1980:AS, author = "Carl {de Boor} and Richard Weiss", title = "{Algorithm 546}: {SOLVEBLOK} [{F4}]", journal = j-TOMS, volume = "6", number = "1", pages = "88--91", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355881", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 24 15:50:24 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "almost block diagonal systems; Gaussian elimination; ordinary differential equations; spline approximation", } @Article{Duris:1980:AFR, author = "Charles S. Duris", title = "{Algorithm 547}: {FORTRAN} Routines for Discrete Cubic Spline Interpolation and Smoothing [{E1}], [{E3}]", journal = j-TOMS, volume = "6", number = "1", pages = "92--103", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355882", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:29:10 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrete cubic splines; discrete natural splines; discrete splines; interpolation; smoothing", } @Article{Carpaneto:1980:ASA, author = "Giorgio Carpaneto and Paolo Toth", title = "{Algorithm 548}: Solution of the Assignment Problem [{H}]", journal = j-TOMS, volume = "6", number = "1", pages = "104--111", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355883", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:29:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "assignment problem; Hungarian algorithm", } @Article{Eckhardt:1980:AWE, author = "Ulrich Eckhardt", title = "{Algorithm 549}: {Weierstrass}' Elliptic Functions [{S21}]", journal = j-TOMS, volume = "6", number = "1", pages = "112--120", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355884", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:31:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Weierstrass' elliptic functions", } @Article{Messner:1980:ASP, author = "A. M. Messner and G. Q. Taylor", title = "{Algorithm 550}: Solid Polyhedron Measure [{Z}]", journal = j-TOMS, volume = "6", number = "1", pages = "121--130", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355885", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 14:44:11 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "graphics; numerical integration; polyhedron", } @Article{Anonymous:1980:AAD, author = "{Anonymous}", title = "{ACM Algorithms Distribution Service} Expanded", journal = j-TOMS, volume = "6", number = "1", pages = "131--132", month = mar, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355873.355886", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chan:1980:NLS, author = "Tony F. Chan and William M. {Coughran, Jr.} and Eric H. Grosse and Michael T. Heath", title = "A Numerical Library and Its Support", journal = j-TOMS, volume = "6", number = "2", pages = "135--145", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355888", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "library management and organization; mathematical software; numerical analysis", } @Article{Brent:1980:AIB, author = "Richard P. Brent and Judith A. Hooper and J. Michael Yohe", title = "An {AUGMENT} Interface for {Brent}'s Multiple Precision Arithmetic Package", journal = j-TOMS, volume = "6", number = "2", pages = "146--149", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355889", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:35:33 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Brent:1978:AMF,Brent:1979:RMF,Smith:1998:AMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "arithmetic; AUGMENT interface; extended precision; floating point; multiple precision; portable software; precompiler interface; software package", } @Article{Kedem:1980:ADC, author = "Gershon Kedem", title = "Automatic Differentiation of Computer Programs", journal = j-TOMS, volume = "6", number = "2", pages = "150--165", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355890", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68C20 (68F25)", MRnumber = "81g:68058", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; factorable functions", } @Article{Rheinboldt:1980:DSA, author = "Werner C. Rheinboldt and Charles K. Mesztenyi", title = "On a Data Structure for Adaptive Finite Element Mesh Refinements", journal = j-TOMS, volume = "6", number = "2", pages = "166--187", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355891", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "access algorithms; finite elements; mesh refinements; tree structure", } @Article{Verwer:1980:ICS, author = "J. G. Verwer", title = "An Implementation of a Class of Stabilized Explicit Methods for the Time Integration of Parabolic Equations", journal = j-TOMS, volume = "6", number = "2", pages = "188--205", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355892", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "implementation of time integrators; numerical analysis; parabolic partial differential equations; semidiscretization", } @Article{Munksgaard:1980:SSS, author = "N. Munksgaard", title = "Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients", journal = j-TOMS, volume = "6", number = "2", pages = "206--219", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355893", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "conjugate gradients; fixed space factorization; linear equations; numerical drop tolerance modification; positive definite; preconditioning; sparse", } @Article{Abdelmalek:1980:SOS, author = "Nabih N. Abdelmalek", title = "{$L_1$} Solution of Overdetermined Systems of Linear Equations", journal = j-TOMS, volume = "6", number = "2", pages = "220--227", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355894", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrete linear {$L_1$} approximation; dual simplex algorithms; linear programming; overdetermined system of linear equations; triangular decomposition", } @Article{Abdelmalek:1980:AFS, author = "Nabih N. Abdelmalek", title = "{Algorithm 551}: {A FORTRAN} Subroutine for the {$L_1$} Solution of Overdetermined Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "6", number = "2", pages = "228--230", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355895", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:44:41 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrete linear {$L_1$} approximation; dual simplex algorithms; linear programming; overdetermined system of linear equations; triangular decomposition", } @Article{Barrodale:1980:ASC, author = "I. Barrodale and F. D. K. Roberts", title = "{Algorithm 552}: Solution of the Constrained $\ell_1$ Linear Approximation Problem [{F4}]", journal = j-TOMS, volume = "6", number = "2", pages = "231--235", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355896", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:46:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "constrained $\ell_1$ approximation; linear programming; simplex method", } @Article{Verwer:1980:AME, author = "J. G. Verwer", title = "{Algorithm 553}: {M3RK}, An Explicit Time Integrator for Semidiscrete Parabolic Equations [{D3}]", journal = j-TOMS, volume = "6", number = "2", pages = "236--239", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355897", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:49:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "explicit time integrator; parabolic partial differential equations; semidiscretization", } @Article{More:1980:ABF, author = "J. J. Mor{\'e} and M. Y. Cosnard", title = "{Algorithm 554}: {BRENTM}, {A Fortran} Subroutine for the Numerical Solution of Nonlinear Equations [{F5}]", journal = j-TOMS, volume = "6", number = "2", pages = "240--251", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355898", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:49:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Brent's method; nonlinear equations; numerical solution", } @Article{Watson:1980:ACY, author = "L. T. Watson and D. Fenner", title = "{Algorithm 555}: {Chow-Yorke} Algorithm for Fixed Points or Zeros of ${C}^2$ Maps [{C5}]", journal = j-TOMS, volume = "6", number = "2", pages = "252--259", month = jun, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355887.355899", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 10:17:11 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "continuation method; fixed point; fixed points of nonlinear systems; homotopy method; nonlinear systems; parameterized nonlinear system; zero; zero curve of a homotopy map; zeros of nonlinear systems", } @Article{Gear:1980:RKS, author = "C. W. Gear", title = "{Runge--Kutta} Starters for Multistep Methods", journal = j-TOMS, volume = "6", number = "3", pages = "263--279", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355901", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "81m:65119", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "integration; multistep; ordinary differential equations; Runge--Kutta", reviewer = "J. Sprekels", } @Article{Barton:1980:TSS, author = "David Barton", title = "On {Taylor} Series and Stiff Equations", journal = j-TOMS, volume = "6", number = "3", pages = "280--294", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355902", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "82e:65078", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "stiff ordinary differential equations; Taylor series", reviewer = "P. M. Dew", } @Article{Jackson:1980:AIV, author = "K. R. Jackson and R. Sacks-Davis", title = "An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff {ODE}s", journal = j-TOMS, volume = "6", number = "3", pages = "295--318", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355903", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "81m:65120", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "backward differential formulas; stiff ODEs; variable step-size methods", reviewer = "Hans J. Stetter", } @Article{Gupta:1980:NAO, author = "G. K. Gupta", title = "A Note About Overhead Costs in {ODE} Solvers", journal = j-TOMS, volume = "6", number = "3", pages = "319--326", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355904", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Adams methods; mathematical software; ordinary differential equations; Runge--Kutta methods; software evaluation", } @Article{Coleman:1980:SSI, author = "David Coleman and Paul Holland and Neil Kaden and Virginia Klema and Stephen C. Peters", title = "A System of Subroutines for Iteratively Reweighted Least Squares Computations", journal = j-TOMS, volume = "6", number = "3", pages = "327--336", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355905", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "curve fitting; data analysis; least squares; linear algebra; mathematical software; portability; robust estimation; weight functions", } @Article{George:1980:FIM, author = "Alan George and Joseph W. H. Liu", title = "A Fast Implementation of the Minimum Degree Algorithm Using Quotient Graphs", journal = j-TOMS, volume = "6", number = "3", pages = "337--358", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355906", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (68E10)", MRnumber = "82i:65022", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "graph algorithms; mathematical software; ordering algorithms; quotient graphs; sparse linear equations", reviewer = "Niels Munksgaard", } @Article{Bentley:1980:GSL, author = "Jon Louis Bentley and James B. Saxe", title = "Generating Sorted Lists of Random Numbers", journal = j-TOMS, volume = "6", number = "3", pages = "359--364", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355907", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10 (68-01)", MRnumber = "81k:65010", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "linear-time algorithm; probabilistic methods in algorithm design; random number generation; sorting", reviewer = "George Marsaglia", } @Article{Amos:1980:CEI, author = "Donald E. Amos", title = "Computation of Exponential Integrals", journal = j-TOMS, volume = "6", number = "3", pages = "365--377", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355908", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (68-04)", MRnumber = "82b:65011", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "exponential integral; Miller algorithm; recursion; Taylor series", reviewer = "M. M. Chawla", } @Article{Arthur:1980:PPA, author = "Jeffrey L. Arthur and A. Ravindran", title = "{PAGP}, a Partitioning Algorithm for (Linear) Goal Programming Problems", journal = j-TOMS, volume = "6", number = "3", pages = "378--386", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355909", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C05", MRnumber = "81i:90122", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "constraint partitioning; goal program; multiple objective optimization; simplex method", } @Article{Cheung:1980:MLP, author = "To-Yat Cheung", title = "Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach", journal = j-TOMS, volume = "6", number = "3", pages = "387--390", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355910", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "minimum cut; multifacility; optimal location; rectilinear distance", } @Article{Betts:1980:CAC, author = "J. T. Betts", title = "A Compact Algorithm for Computing the Stationary Point of a Quadratic Function Subject to Linear Constraints", journal = j-TOMS, volume = "6", number = "3", pages = "391--397", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355911", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C20 (65K05)", MRnumber = "81i:90162", bibdate = "Mon Aug 29 10:57:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "orthogonal decomposition; quadratic programming", } @Article{Kaagstrom:1980:ANC, author = "Bo K{\aa}gstr{\"o}m and Axel Ruhe", title = "An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix", journal = j-TOMS, volume = "6", number = "3", pages = "398--419", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355912", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15 (15A21)", MRnumber = "81m:65054", bibdate = "Fri Aug 26 23:38:10 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block diagonal form; canonical form; eig; eigenvalues; eigenvectors; Jordan form; Jordan normal form; nla; numerical multiple eigenvalues; principal vectors; software", reviewer = "Petr Liebl", } @Article{Amos:1980:AEI, author = "Donald E. Amos", title = "{Algorithm 556}: Exponential Integrals [{S13}]", journal = j-TOMS, volume = "6", number = "3", pages = "420--428", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355913", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:13:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark in \cite{Amos:1983:REI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "confluent hypergeometric functions; exponential integrals; Miller algorithm", } @Article{Arthur:1980:APP, author = "J. L. Arthur and A. Ravindran", title = "{Algorithm 557}: {PAGP}, a Partitioning Algorithm for (Linear) Goal Programming Problems [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "429--429", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355914", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:13:53 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "constraint partitioning; goal program; multiple objective optimization; simplex method", } @Article{Cheung:1980:APM, author = "To-Yat Cheung", title = "{Algorithm 558}: a Program for the Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "430--431", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355915", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:14:45 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "minimum cut; multifacility; optimal location; rectilinear distance", } @Article{Betts:1980:ASP, author = "J. T. Betts", title = "{Algorithm 559}: The Stationary Point of a Quadratic Function Subject to Linear Constraints [{E4}]", journal = j-TOMS, volume = "6", number = "3", pages = "432--436", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355916", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:15:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "orthogonal decomposition; quadratic programming", } @Article{Kaagstroem:1980:AJA, author = "Bo K{\aa{}}gstr{\"o}m and Axel Ruhe", title = "{Algorithm 560}: {JNF}, An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix [{F2}]", journal = j-TOMS, volume = "6", number = "3", pages = "437--443", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355917", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 15:16:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block diagonal form; canonical form; eig; eigenvalues; eigenvectors; Jordan form; Jordan normal form; nla; principal vectors; software", } @Article{Kahaner:1980:AFI, author = "D. K. Kahaner", title = "{Algorithm 561}: {FORTRAN} Implementation of Heap Programs for Efficient Table Maintenance [{Z}]", journal = j-TOMS, volume = "6", number = "3", pages = "444--449", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355918", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:17:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "heap; table maintenance", } @Article{Pape:1980:ASP, author = "U. Pape", title = "{Algorithm 562}: Shortest Path Lengths [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "450--455", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355919", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:17:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Pape:1983:RSP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "shortest path; shortest route problem", } @Article{Harms:1980:RSM, author = "U. Harms and H. Kollakowski and G. M{\"o}ller", title = "Remark on ``{Algorithm} 408: a Sparse Matrix Package (Part 1) [{F4}]''", journal = j-TOMS, volume = "6", number = "3", pages = "456--457", month = sep, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355900.355920", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{McNamee:1971:SMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Machura:1980:SSP, author = "Marek Machura and Roland A. Sweet", title = "A Survey of Software for Partial Differential Equations", journal = j-TOMS, volume = "6", number = "4", pages = "461--488", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355922", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65M99 (65-04 65N99)", MRnumber = "81k:65106", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "partial differential equations; software; survey", } @Article{Kurator:1980:PIS, author = "William G. Kurator and Richard P. O'Neill", title = "{PERUSE}: An Interactive System for Mathematical Programs", journal = j-TOMS, volume = "6", number = "4", pages = "489--509", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355923", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "interactive mathematical programming; model auditing; model debugging; model verification", } @Article{Brown:1980:EPB, author = "W. S. Brown and S. I. Feldman", title = "Environment Parameters and Basic Functions for Floating-Point Computation", journal = j-TOMS, volume = "6", number = "4", pages = "510--523", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355924", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "environment parameters; floating-point arithmetic; software portability", } @Article{Luk:1980:CSV, author = "Franklin T. Luk", title = "Computing the Singular-Value Decomposition on the {ILLIAC IV}", journal = j-TOMS, volume = "6", number = "4", pages = "524--539", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355925", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15", MRnumber = "81k:65044", bibdate = "Mon Aug 29 11:27:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Golub-Reinsch algorithm; Illiac; ILLIAC IV computer; Jacobi-like method; nla; parallel matrix computations; prll; singular-value decomposition; svd", } @Article{Sacks-Davis:1980:FLC, author = "R. Sacks-Davis", title = "Fixed Leading Coefficient Implementation of {SD}-Formulas for Stiff {ODE}s", journal = j-TOMS, volume = "6", number = "4", pages = "540--562", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355926", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "81k:65084", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ordinary differential equations; second-derivative method", } @Article{Bentley:1980:OET, author = "Jon Louis Bentley and Bruce W. Weide and Andrew C. Yao", title = "Optimal Expected-Time Algorithms for Closest Point Problems", journal = j-TOMS, volume = "6", number = "4", pages = "563--580", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355927", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68G10 (52-04 52A45 68E10 90C10)", MRnumber = "82g:68084", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "closest point problems; computational geometry; minimum spanning trees; nearest neighbor searching; optimal algorithms; probabilistic analysis of algorithms; Voronoi diagrams", reviewer = "Wolfgang Boehm", } @Article{Campbell:1980:TAM, author = "J. B. Campbell", title = "On {Temme}'s Algorithm for the Modified {Bessel} Function of the Third Kind", journal = j-TOMS, volume = "6", number = "4", pages = "581--586", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355928", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "82d:65019", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "mathematical software; Miller's algorithm; modified Bessel functions of the third kind", } @Article{Hoffman:1980:TPG, author = "K. L. Hoffman and D. R. Shier", title = "A Test Problem Generator for Discrete Linear {$L_1$} Approximation Problems", journal = j-TOMS, volume = "6", number = "4", pages = "587--593", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355929", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D99 (65K05)", MRnumber = "81m:65042", bibdate = "Mon Aug 29 11:23:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "least absolute deviation; problem generator; test data; {$L_1$} approximation", } @Article{Bartels:1980:LCD, author = "Richard H. Bartels and Andrew R. Conn", title = "Linearly Constrained Discrete $\ell_1$ Problems", journal = j-TOMS, volume = "6", number = "4", pages = "594--608", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355930", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C33 (65K05)", MRnumber = "82a:90165", bibdate = "Sat Aug 27 15:41:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "$\ell_1$ norm; data filling; discrete approximation; l1 approximation; linearly constrained approximation; nlop; software", } @Article{Bartels:1980:APL, author = "Richard H. Bartels and Andrew R. Conn", title = "{Algorithm 563}: a Program for Linearly Constrained Discrete $\ell_1$ Problems", journal = j-TOMS, volume = "6", number = "4", pages = "609--614", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355931", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:22:14 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Koenker:1996:RBC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrete $\ell_1$ approximation; l1 approximation; linear constraints; nlop; numerical analysis; overdetermined linear systems; software", } @Article{Hoffman:1980:ATP, author = "K. L. Hoffman and D. R. Shier", title = "{Algorithm 564}: a Test Problem Generator for Discrete Linear {$L_1$} Approximation Problems", journal = j-TOMS, volume = "6", number = "4", pages = "615--617", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355932", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "least absolute deviation; problem generator; test data; {$L_1$} approximation", } @Article{Shanno:1980:RMU, author = "D. F. Shanno and K. H. Phua", title = "Remark on ``{Algorithm} 500: Minimization of Unconstrained Multivariate Functions [{E4}]''", journal = j-TOMS, volume = "6", number = "4", pages = "618--622", month = dec, year = "1980", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355921.355933", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:07:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Shanno:1976:AMU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hiebert:1981:EMS, author = "K. L. Hiebert", title = "An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems", journal = j-TOMS, volume = "7", number = "1", pages = "1--16", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355935", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:46:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "augmented Gauss--Newton; Gauss--Newton; Levenberg--Marquardt; lsq; nllsq; nlop; nonlinear data fitting; nonlinear least squares; nonlinear regression; quasi-Newton; software evaluation", } @Article{More:1981:TUO, author = "Jorge J. Mor{\'e} and Burton S. Garbow and Kenneth E. Hillstrom", title = "Testing Unconstrained Optimization Software", journal = j-TOMS, volume = "7", number = "1", pages = "17--41", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355936", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C30", MRnumber = "83b:90144", bibdate = "Mon Aug 29 22:02:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nonlinear least squares; optimization software; performance testing; systems of nonlinear equations; unconstrained minimization", } @Article{Akl:1981:CCG, author = "Selim G. Akl", title = "A Comparison of Combination Generation Methods", journal = j-TOMS, volume = "7", number = "1", pages = "42--45", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355937", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:02:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithm; combinations", } @Article{Fritsch:1981:DIU, author = "F. N. Fritsch and D. K. Kahaner and J. N. Lyness", title = "Double Integration Using One-Dimensional Adaptive Quadrature Routines: a Software Interface Problem", journal = j-TOMS, volume = "7", number = "1", pages = "46--75", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355938", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "83c:65033a", bibdate = "Sat Nov 19 13:07:46 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Fritsch:1981:CIU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "adaptive integration; automatic quadrature routine; double integration; quadrature; software interface", } @Article{Friedman:1981:NPP, author = "Jerome H. Friedman and Margaret H. Wright", title = "A Nested Partitioning Procedure for Numerical Multiple Integration", journal = j-TOMS, volume = "7", number = "1", pages = "76--92", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355939", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "83d:65058", bibdate = "Mon Aug 29 22:02:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bounds-constrained optimization; numerical integration; quadrature; recursive partitioning", reviewer = "C. Dagnino", } @Article{Smith:1981:ERA, author = "J. M. Smith and F. W. J. Olver and D. W. Lozier", title = "Extended-Range Arithmetic and Normalized {Legendre} Polynomials", journal = j-TOMS, volume = "7", number = "1", pages = "93--105", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355940", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (65G05)", MRnumber = "83a:65017", bibdate = "Mon Aug 29 22:02:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow", } @Article{Melgaard:1981:GST, author = "David K. Melgaard and Richard F. Sincovec", title = "General Software for Two-Dimensional Nonlinear Partial Differential Equations", journal = j-TOMS, volume = "7", number = "1", pages = "106--125", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355941", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65M20", MRnumber = "83a:65082", bibdate = "Mon Aug 29 22:02:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "finite differences; method of lines; ordinary differential equations; partial differential equations", } @Article{Melgaard:1981:APS, author = "David K. Melgaard and Richard F. Sincovec", title = "{Algorithm 565}: {PDETWO}\slash {PSETM}\slash {GEARB}: Solution of Systems of Two-Dimensional Nonlinear Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "7", number = "1", pages = "126--135", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355942", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:16:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "finite differences; method of lines; ordinary differential equations; partial differential equations", } @Article{More:1981:AFS, author = "J. J. Mor{\'e} and B. S. Garbow and K. E. Hillstrom", title = "{Algorithm 566}: {FORTRAN} Subroutines for Testing Unconstrained Optimization Software [{C5} [{E4}]]", journal = j-TOMS, volume = "7", number = "1", pages = "136--140", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355943", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:13:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Averbukh:1994:RA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nonlinear least squares; optimization software; performance testing; systems of nonlinear equations; unconstrained minimization", } @Article{Lozier:1981:AER, author = "D. W. Lozier and J. M. Smith", title = "{Algorithm 567}: Extended-Range Arithmetic and Normalized {Legendre} Polynomials [{A1}], [{C1}]", journal = j-TOMS, volume = "7", number = "1", pages = "141--146", month = mar, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355934.355944", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow", } @Article{Golub:1981:BLM, author = "Gene H. Golub and Franklin T. Luk and Michael L. Overton", title = "A Block {L{\'a}nczos} Method for Computing the Singular Values of Corresponding Singular Vectors of a Matrix", journal = j-TOMS, volume = "7", number = "2", pages = "149--169", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355946", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65F15)", MRnumber = "84h:65045", bibdate = "Fri Sep 30 01:47:15 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block Lanczos method; Lanczos algorithm; large sparse matrix; nla; singular values; singular vectors; singular-value decomposition; svd; upper-triangular band matrix", } @Article{Wang:1981:PMT, author = "H. H. Wang", title = "A Parallel Method for Tridiagonal Equations", journal = j-TOMS, volume = "7", number = "2", pages = "170--183", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355947", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "83d:65092", bibdate = "Mon Aug 29 22:19:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cyclic reduction method; parallel computers; partition method; recursive doubling method; tridiagonal equations; vectors computers", } @Article{Stewart:1981:SIA, author = "William J. Stewart and Alan Jennings", title = "A Simultaneous Iteration Algorithm for Real Matrices", journal = j-TOMS, volume = "7", number = "2", pages = "184--198", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355948", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15", MRnumber = "83d:65118", bibdate = "Mon Aug 29 22:19:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "eigenvalues; eigenvectors; large sparse matrices; real unsymmetric matrices; simultaneous iteration", } @Article{Hill:1981:EIR, author = "Geoffrey W. Hill", title = "Evaluation and Inversion of the Ratios of Modified {Bessel} Functions, {$I_1(x)/I_0(x)$} and {$I_{1.5}(x)/I_{0.5}(x)$}", journal = j-TOMS, volume = "7", number = "2", pages = "199--208", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355949", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "83d:65046", bibdate = "Mon Aug 29 22:19:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "approximation; backward recursion; continued fractions; Fisher distribution; function inversion; modified Bessel function ratios; Newton--Raphson; von Mises distribution", } @Article{Ascher:1981:CSB, author = "U. Ascher and J. Christiansen and R. D. Russell", title = "Collocation Software for Boundary Value {ODE}'s", journal = j-TOMS, volume = "7", number = "2", pages = "209--222", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355950", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:48:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", annote = "collocation", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "B-spline; boundary-value problems; collocation; damped Newton's method; error estimates; general-purpose code; mesh selection; ordinary differential equations", } @Article{Ascher:1981:ACC, author = "U. Ascher and J. Christiansen and R. D. Russell", title = "{Algorithm 569}: {COLSYS}: Collocation Software for Boundary-Value {ODEs} [{D2}]", journal = j-TOMS, volume = "7", number = "2", pages = "223--229", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355951", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:26:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hake:1986:RCC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "B-spline; boundary-value problems; collocation; damped Newton's method; error estimates; general-purpose code; mesh selection; ordinary differential equations", } @Article{Stewart:1981:ALS, author = "William J. Stewart and Alan Jennings", title = "{Algorithm 570}: {LOPSI}: a Simultaneous Iteration Method for Real Matrices [{F2}]", journal = j-TOMS, volume = "7", number = "2", pages = "230--232", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355952", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:27:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "eigenvalues; eigenvectors; large sparse matrices; real unsymmetric matrices; simultaneous iteration", } @Article{Hill:1981:ASM, author = "Geoffrey W. Hill", title = "{Algorithm 571}: Statistics for von {Mises}' and {Fisher}'s Distributions of Directions: {$I_1(x)/I_0(x)$}, {$I_{1.5}(x)/I_{0.5}(x)$} and Their Inverses [{S14}]", journal = j-TOMS, volume = "7", number = "2", pages = "233--238", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355953", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:28:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "continued fraction; direction statistics; Fisher distribution; function inversion; modified Bessel function ratio; Newton--Raphson; von Mises distribution", } @Article{OLeary:1981:ASH, author = "Dianne P. O'Leary and Olof Widlund", title = "{Algorithm 572}: Solution of the {Helmholtz} Equation for the {Dirichlet} Problem on General Bounded Three-Dimensional Regions [{D3}]", journal = j-TOMS, volume = "7", number = "2", pages = "239--246", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355954", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:31:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "capacitance matrix; conjugate gradients; fast Poisson solvers; Helmholtz equation", } @Article{Hill:1981:RSD, author = "G. W. Hill", title = "Remark on ``{Algorithm} 395: {Student}'s $t$-Distribution''", journal = j-TOMS, volume = "7", number = "2", pages = "247--249", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355955", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hill:1970:SD,Hill:1970:SQ,elLozy:1979:RAS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hill:1981:RSQ, author = "G. W. Hill", title = "Remark on ``{Algorithm} 396: {Student}'s $t$-Quantiles''", journal = j-TOMS, volume = "7", number = "2", pages = "250--251", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355956", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hill:1970:SQ}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fritsch:1981:CIU, author = "F. N. Fritsch", title = "Corrigendum: ``{Double} Integration Using One-Dimensional Adaptive Quadrature Routines: a Software Interface Problem''", journal = j-TOMS, volume = "7", number = "2", pages = "252--252", month = jun, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355945.355957", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "252. 65D30", MRnumber = "83c:65033b", bibdate = "Mon Aug 29 22:19:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Fritsch:1981:DIU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ukkonen:1981:CER, author = "Esko Ukkonen", title = "On the Calculation of the Effects of Roundoff Errors", journal = j-TOMS, volume = "7", number = "3", pages = "259--271", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355959", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05", MRnumber = "82i:65030", bibdate = "Mon Aug 29 22:44:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic roundoff analysis; numerical linear algebra; numerical stability", } @Article{Linnainmaa:1981:SDP, author = "Seppo Linnainmaa", title = "Software for Doubled-Precision Floating-Point Computations", journal = j-TOMS, volume = "7", number = "3", pages = "272--283", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355960", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68B99 (65G99 68C05)", MRnumber = "82h:68041", bibdate = "Mon Aug 29 22:44:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accurate floating-point summation; exact multiplication; floating-point arithmetic; rounding errors; software portability", } @Article{Lii:1981:CBC, author = "K. S. Lii and K. N. Helland", title = "Cross-Bispectrum Computation and Variance Estimation", journal = j-TOMS, volume = "7", number = "3", pages = "284--294", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355961", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "62M15", MRnumber = "82m:62213", bibdate = "Mon Aug 29 22:44:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bispectra; time series analysis", } @Article{Dew:1981:SLR, author = "P. M. Dew and J. E. Walsh", title = "A Set of Library Routines for Solving Parabolic Equations in One Space Variable", journal = j-TOMS, volume = "7", number = "3", pages = "295--314", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355962", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 11:51:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", annote = "parabolic equations", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "method of lines; parabolic equations", } @Article{Duff:1981:AOM, author = "I. S. Duff", title = "On Algorithms for Obtaining a Maximum Transversal", journal = j-TOMS, volume = "7", number = "3", pages = "315--330", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355963", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:49:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block-triangular form; maximum assignment; maximum transversal; perm; sparse; sparse matrices; unsymmetric permutations", } @Article{McAllister:1981:ACS, author = "David F. McAllister and John A. Roulier", title = "An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline", journal = j-TOMS, volume = "7", number = "3", pages = "331--347", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355964", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D07", MRnumber = "82h:65009", bibdate = "Mon Aug 29 22:44:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernstein polynomial; convexity preserving; geometric design; monotonicity preserving; osculation; parametric curve; polynomial interpolation; shape preserving; spline", } @Article{Dennis:1981:ANL, author = "John E. {Dennis, Jr.} and David M. Gay and Roy E. Welsch", title = "An Adaptive Nonlinear Least-squares Algorithm", journal = j-TOMS, volume = "7", number = "3", pages = "348--368", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355965", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:10 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "lsq; nllsq; nlop; nonlinear least squares; nonlinear regression; quasi-Newton methods; secant methods; unconstrained optimization", } @Article{Dennis:1981:ANE, author = "John E. {Dennis, Jr.} and David M. Gay and Roy E. Welsch", title = "{Algorithm 573}: {NL2SOL}\emdash An Adaptive Nonlinear Least-Squares Algorithm [{E4}]", journal = j-TOMS, volume = "7", number = "3", pages = "369--383", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355966", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:52:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Gay:1983:RNE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "lsq; nllsq; nlop; nonlinear least squares; nonlinear regression; quasi-Newton methods; secant methods; software; unconstrained optimization", } @Article{McAllister:1981:ASP, author = "D. F. McAllister and J. A. Roulier", title = "{Algorithm 574}: Shape-Preserving Osculatory Quadratic Splines [{E1}, {E2}]", journal = j-TOMS, volume = "7", number = "3", pages = "384--386", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355967", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:55:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernstein polynomial; convexity preserving; monotonicity preserving; osculation; polynomial interpolation; shape preserving", } @Article{Duff:1981:APZ, author = "I. S. Duff", title = "{Algorithm 575}: Permutations for a Zero-Free Diagonal [{F1}]", journal = j-TOMS, volume = "7", number = "3", pages = "387--390", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355968", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:56:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block triangular form; maximum assignment; maximum transversal; sparse matrices; unsymmetric permutations", } @Article{Barrodale:1981:AFP, author = "I. Barrodale and G. F. Stuart", title = "{Algorithm 576}: {A FORTRAN} Program for Solving {${\bf Ax} = {\bf b}$} [{F4}]", journal = j-TOMS, volume = "7", number = "3", pages = "391--397", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355969", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:57:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gaussian elimination; linear equations; new pivoting strategy", } @Article{Carlson:1981:AAI, author = "B. C. Carlson and Elaine M. Notis", title = "{Algorithm 577}: Algorithms for Incomplete Elliptic Integrals [{S21}]", journal = j-TOMS, volume = "7", number = "3", pages = "398--403", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355970", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 22:58:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "$R$-functions; elliptic integrals; inverse circular functions; inverse hyperbolic functions; logarithms", } @Article{Razaz:1981:RAF, author = "M. Razaz and J. L. Schonfelder", title = "Remark on ``{Algorithm} 498: {Airy} Functions Using {Chebyshev} Series Approximations''", journal = j-TOMS, volume = "7", number = "3", pages = "404--405", month = sep, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355958.355971", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Prince:1975:AAF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1981:ETS, author = "Lawrence F. Shampine", title = "Evaluation of a Test Set for Stiff {ODE} Solvers", journal = j-TOMS, volume = "7", number = "4", pages = "409--420", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355973", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "83d:65215", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "stiff; test set; testing ODE codes", } @Article{Neves:1981:CIE, author = "Kenneth W. Neves", title = "Control of Interpolatory Error in Retarded Differential Equations", journal = j-TOMS, volume = "7", number = "4", pages = "421--444", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355974", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L99 (34K99)", MRnumber = "83d:65243", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic step-size reduction; delay differential equations; derivative jump discontinuities; local error control; Runge--Kutta methods", } @Article{Brown:1981:SRM, author = "W. S. Brown", title = "A Simple but Realistic Model of Floating-Point Computation", journal = j-TOMS, volume = "7", number = "4", pages = "445--480", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355975", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "computer arithmetic; environment parameters; error analysis; Euclidean norm; floating-point arithmetic; software portability", } @Article{Marsten:1981:DXL, author = "Roy E. Marsten", title = "The Design of the {XMP} Linear Programming Library", journal = j-TOMS, volume = "7", number = "4", pages = "481--497", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355976", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "linear programming; mathematical programming; optimization; software engineering; software libraries", } @Article{Pallottino:1981:EAD, author = "Stefano Pallottino and Tommaso Toffoli", title = "An Efficient Algorithm for Determining the Length of the Longest Dead Path in a ``{LIFO}'' Branch-and-Bound Exploration Schema", journal = j-TOMS, volume = "7", number = "4", pages = "498--504", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355977", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:08:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "branch-and-bound; length of longest dead path; LIFO tree search", } @Article{Duff:1981:MSU, author = "I. S. Duff", title = "{ME28}: a Sparse Unsymmetric Linear Equation Solver for Complex Equations", journal = j-TOMS, volume = "7", number = "4", pages = "505--511", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355978", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "complex sparse linear equations; drop tolerances; ME28; numerical software; real and complex arithmetic; sparse matrix", } @Article{Fornberg:1981:NDA, author = "Bengt Fornberg", title = "Numerical Differentiation of Analytic Functions", journal = j-TOMS, volume = "7", number = "4", pages = "512--526", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355979", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D25", MRnumber = "83d:65056", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "analytic functions; numerical differentiation; Taylor series coefficients", } @Article{DuCroz:1981:SLF, author = "J. J. {Du Croz} and S. M. Nugent and J. K. Reid and D. B. Taylor", title = "Solving Large Full Sets of Linear Equations in a Paged Virtual Store", journal = j-TOMS, volume = "7", number = "4", pages = "527--536", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355980", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gaussian elimination; paged virtual store", } @Article{DuCroz:1981:ASR, author = "J. J. {Du Croz} and S. M. Nugent and J. K. Reid and D. B. Taylor", title = "{Algorithm 578}: Solution of Real Linear Equations in a Paged Virtual Store [{F4}]", journal = j-TOMS, volume = "7", number = "4", pages = "537--541", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355981", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:12:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gaussian elimination; paged virtual store", } @Article{Fornberg:1981:ACC, author = "B. Fornberg", title = "{Algorithm 579}: {CPSC}: Complex Power Series Coefficients [{D4}]", journal = j-TOMS, volume = "7", number = "4", pages = "542--547", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355982", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:12:50 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "analytic functions; numerical differentiation; Taylor series coefficients", } @Article{Buckley:1981:AQS, author = "A. Buckley", title = "{Algorithm 580}: {QRUP}: a Set of {FORTRAN} Routines for Updating {QR} Factorizations [{F5}]", journal = j-TOMS, volume = "7", number = "4", pages = "548--549", month = dec, year = "1981", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355972.355983", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:13:39 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Buckley:1982:RQS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "matrix factorization; orthogonalization", } @Article{Krogh:1982:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "8", number = "1", pages = "1--4", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355985", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hiebert:1982:EMS, author = "K. L. Hiebert", title = "An Evaluation of Mathematical Software That Solves Systems of Nonlinear Equations", journal = j-TOMS, volume = "8", number = "1", pages = "5--20", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355986", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Brent's method; Brown's method; performance; quasi-Newton Powell's hybrid method", subject = "D.2.8 [Software Engineering]: Metrics\emdash performance measures; G.1.5 [Numerical Analysis]: Proofs of Nonlinear Equations\emdash systems of equations; G.4 [Mathematics of Computing]: Mathematical Software\emdash certification and testing", } @Article{Dunham:1982:CBC, author = "Charles B. Dunham", title = "Choice of Basis for {Chebyshev} Approximation", journal = j-TOMS, volume = "8", number = "1", pages = "21--25", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355987", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "41A50 (65D15)", MRnumber = "84i:41038", bibdate = "Mon Aug 29 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; condition numbers; design; Fraser--Hart--Remez algorithm; polynomials; rational functions", subject = "G.1.2 [Numerical Analysis]: Approximation\emdash Chebyshev approximation and theory", } @Article{Deo:1982:AGF, author = "Narsingh Deo and G. M. Prabhu and M. S. Krishnamoorthy", title = "Algorithms for Generating Fundamental Cycles in a Graph", journal = j-TOMS, volume = "8", number = "1", pages = "26--42", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355988", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68C05 (05C38 68E10)", MRnumber = "83h:68041", bibdate = "Mon Aug 29 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; fundamental-cycle set; NP-complete; spanning tree", reviewer = "Sukhamay Kundu", subject = "F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical algorithms and problems\emdash computations on discrete structures; G.2.2 [Discrete Mathematics]: Graph Theory", } @Article{Paige:1982:LAS, author = "Christopher C. Paige and Michael A. Saunders", title = "{LSQR}: An Algorithm for Sparse Linear Equations and Sparse Least Squares", journal = j-TOMS, volume = "8", number = "1", pages = "43--71", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355989", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F10 (65F20)", MRnumber = "83f:65048", bibdate = "Fri Aug 26 23:38:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; analysis of variance; conjugate gradients; Lanczos algorithm; lsq; nla", } @Article{Chan:1982:IAC, author = "Tony F. Chan", title = "An Improved Algorithm for Computing the Singular Value Decomposition", journal = j-TOMS, volume = "8", number = "1", pages = "72--83", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355990", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F30", MRnumber = "83f:65058", bibdate = "Mon Aug 29 23:23:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Householder transformation; nla; performance; singular values; software; svd", } @Article{Chan:1982:AIA, author = "Tony F. Chan", title = "{Algorithm 581}: An Improved Algorithm for Computing the Singular Value Decomposition [{F1}]", journal = j-TOMS, volume = "8", number = "1", pages = "84--88", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355991", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:11 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; nla; singular value decomposition; software; svd", } @Article{Tracht:1982:RNR, author = "Allen E. Tracht", title = "Remark on ``{Algorithm} 334: Normal Random Deviates''", journal = j-TOMS, volume = "8", number = "1", pages = "89--89", month = mar, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355984.355992", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Bell:1968:NRD}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1982:IRM, author = "L. F. Shampine", title = "Implementation of {Rosenbrock} Methods", journal = j-TOMS, volume = "8", number = "2", pages = "93--113", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355994", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "83f:65115", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; FORTRAN Codes; Rosenbrock Methods; theory", } @Article{Corliss:1982:SOD, author = "George Corliss and Y. F. Chang", title = "Solving Ordinary Differential Equations Using {Taylor} Series", journal = j-TOMS, volume = "8", number = "2", pages = "114--144", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355995", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "83g:65072", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; Taylor series method", reviewer = "L. F. Shampine", } @Article{Hoaglin:1982:EDA, author = "David C. Hoaglin and Virginia C. Klema and Stephen C. Peters", title = "Exploratory Data Analysis in a Study of the Performance of Nonlinear Optimization Routines", journal = j-TOMS, volume = "8", number = "2", pages = "145--162", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355996", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "experimentation; performance", } @Article{Ahrens:1982:CGP, author = "J. H. Ahrens and U. Dieter", title = "Computer Generation of {Poisson} Deviates from Modified Normal Distributions", journal = j-TOMS, volume = "8", number = "2", pages = "163--179", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355997", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10 (60-04 62E99)", MRnumber = "84c:65016", bibdate = "Mon Aug 29 23:31:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "6930", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "acceptance-rejection method; algorithms; Poisson distribution; theory", language = "English", location = "SEL: Wi", references = "0", reviewer = "James E. Gentle", revision = "16/01/94", } @Article{Lewis:1982:IGP, author = "John G. Lewis", title = "Implementation of the {Gibbs-Poole-Stockmeyer} and {Gibbs}-King Algorithms", journal = j-TOMS, volume = "8", number = "2", pages = "180--189", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355998", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; banded matrix; Gibbs-King algorithms; Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth; matrix profile; matrix wavefront", } @Article{Lewis:1982:AGP, author = "John G. Lewis", title = "{Algorithm 582}: The {Gibbs-Poole-Stockmeyer} and {Gibbs-King} Algorithms for Reordering Sparse Matrices", journal = j-TOMS, volume = "8", number = "2", pages = "190--194", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.355999", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:34:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; banded matrix; Gibbs-King algorithms; Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth; matrix profile; matrix wavefront", } @Article{Paige:1982:ALS, author = "Christopher C. Paige and Michael A. Saunders", title = "{Algorithm 583}: {LSQR}: Sparse Linear Equations and Least Squares Problems", journal = j-TOMS, volume = "8", number = "2", pages = "195--209", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.356000", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; analysis of variance; conjugate gradients; conjugate-gradient method; Lanczos algorithm; least squares; linear equations; lsq; nla; regression; software; sparse matrix", } @Article{Laurie:1982:ACA, author = "D. P. Laurie", title = "{Algorithm 584}: {CUBTRI}: Automatic Cubature over a Triangle", journal = j-TOMS, volume = "8", number = "2", pages = "210--218", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.356001", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:37:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hanson:1986:RCA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithm; quadrature rule; theory", } @Article{Flamm:1982:RHE, author = "David S. Flamm and Robert A. Walker", title = "Remark on ``{Algorithm} 506: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]''", journal = j-TOMS, volume = "8", number = "2", pages = "219--220", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.356002", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Stewart:1976:AHE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lewis:1982:RMB, author = "John G. Lewis", title = "Remark on ``{Algorithm}s 508 and 509: Matrix Bandwidth and Profile Reduction [{F1}] and a Hybrid Profile Reduction Algorithm [{F1}]''", journal = j-TOMS, volume = "8", number = "2", pages = "221--221", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.356003", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Crane:1976:AMB,Gibbs:1976:AHP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ellison:1982:UUI, author = "E. F. D. Ellison and Gautam Mitra", title = "{UIMP}: User Interface for Mathematical Programming", journal = j-TOMS, volume = "8", number = "3", pages = "229--255", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356005", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/356004.356005; http://www.acm.org/pubs/citations/journals/toms/1982-8-3/p229-mitra/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "matrix generator; report writer; solution analysis", } @Article{Schreiber:1982:NIS, author = "Robert Schreiber", title = "A New Implementation of Sparse {Gaussian} Elimination", journal = j-TOMS, volume = "8", number = "3", pages = "256--276", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356006", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05", MRnumber = "84d:65020", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; sparse matrix; sparse systems of linear equations; theory", } @Article{Sasaki:1982:EGE, author = "Tateaki Sasaki and Hirokazu Murao", title = "Efficient {Gaussian} Elimination Method for Symbolic Determinants and Linear Systems", journal = j-TOMS, volume = "8", number = "3", pages = "277--289", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356007", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F40 (68Q40)", MRnumber = "85b:65037", bibdate = "Mon Aug 29 23:27:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Cramer's method; expansion by minors; Gaussian elimination; symbolic determinant; symbolic linear systems", reviewer = "E. Bareiss", } @Article{Brezinski:1982:ASG, author = "C. Brezinski", title = "{Algorithm 585}: a Subroutine for the General Interpolation and Extrapolation Problems", journal = j-TOMS, volume = "8", number = "3", pages = "290--301", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356008", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:49:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; convergence acceleration; extrapolation; interpolation; least squares approximation; Neville--Aitken scheme", } @Article{Kincaid:1982:AIF, author = "David R. Kincaid and John R. Respess and David M. Young and Roger G. Grimes", title = "{Algorithm 586}: {ITPACK 2C}: {A FORTRAN} Package for Solving Large Sparse Linear Systems by Adaptive Accelerated Iterative Methods", journal = j-TOMS, volume = "8", number = "3", pages = "302--322", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356009", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:49:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; documentation; iterative methods; numerical software; sparse matrix", } @Article{Hanson:1982:ATA, author = "Richard J. Hanson and Karen H. Haskell", title = "{Algorithm 587}: Two Algorithms for the Linearly Constrained Least Squares Problem", journal = j-TOMS, volume = "8", number = "3", pages = "323--333", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356010", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 20:52:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Dadurkevicius:1989:RA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; covariance matrix; equality constraints; inconsistent constraints; inequality constraints; linear least squares solution", } @Article{Hanson:1982:RPQ, author = "R. J. Hanson", title = "Remark on ``{Algorithm} 507: Procedures for Quintic Natural Spline Interpolation [{E1}]''", journal = j-TOMS, volume = "8", number = "3", pages = "334--334", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356011", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Herriot:1976:APQ}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wolfe:1982:CCG, author = "Philip Wolfe", title = "Checking the Calculation of Gradients", journal = j-TOMS, volume = "8", number = "4", pages = "337--343", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356013", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:02:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nonlinearity; optimization", } @Article{Anderson:1982:FHT, author = "Walter L. Anderson", title = "Fast {Hankel} Transforms Using Related and Lagged Convolutions", journal = j-TOMS, volume = "8", number = "4", pages = "344--368", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356014", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:02:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bessel functions of the first kind; convolution integrals; Hankel transforms of integer order; linear digital filters", } @Article{Anderson:1982:AFH, author = "Walter L. Anderson", title = "{Algorithm 588}: Fast {Hankel} Transforms Using Related and Lagged Convolutions", journal = j-TOMS, volume = "8", number = "4", pages = "369--370", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356015", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:05:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bessel functions of the first kind; convolution integrals; Hankel transforms of integer order; linear digital filters", } @Article{Dongarra:1982:ASF, author = "Jack J. Dongarra", title = "{Algorithm 589}: {SICEDR}: {A FORTRAN} Subroutine for Improving the Accuracy of Computed Matrix Eigenvalues", journal = j-TOMS, volume = "8", number = "4", pages = "371--375", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356016", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:05:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; eigensystems improvement; iterative method; matrix eigensystems", } @Article{VanDooren:1982:ADE, author = "P. {Van Dooren}", title = "{Algorithm 590}: {DSUBSP} and {EXCHQZ}: {FORTRAN} Subroutines for Computing Deflating Subspaces with Specified Spectrum", journal = j-TOMS, volume = "8", number = "4", pages = "376--382", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356017", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:17:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Petkov:1984:RDE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithm; generalized eigenvalue; QZ algorithm", } @Article{Hemmerle:1982:ACM, author = "William J. Hemmerle", title = "{Algorithm 591}: a Comprehensive Matrix-Free Algorithm for Analysis of Variance", journal = j-TOMS, volume = "8", number = "4", pages = "383--401", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356018", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:08:00 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algebraic-model specification; algorithms; analysis of variance; balanced data operators; G-inverse solution; hypothesis testing; iterative improvement; linear models; missing cells; rank computations; storage-efficient algorithm; unbalanced data", } @Article{Garbow:1982:RQA, author = "B. S. Garbow", title = "Remark on ``{Algorithm} 535: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "8", number = "4", pages = "402--402", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356019", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Garbow:1978:AQA,Garbow:1984:RQA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dodson:1982:RBL, author = "David S. Dodson and Roger G. Grimes", title = "Remark on ``{Algorithm} 539: {Basic Linear Algebra Subprograms} for {Fortran} Usage [{F1}]''", journal = j-TOMS, volume = "8", number = "4", pages = "403--404", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356020", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:11:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Buckley:1982:RQS, author = "A. Buckley", title = "Remark on ``{Algorithm} 580: {QRUP}: a Set of {FORTRAN} Routines for Updating {QR} Factorizations [{F5}]''", journal = j-TOMS, volume = "8", number = "4", pages = "405--405", month = dec, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356012.356021", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Buckley:1981:AQS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morgan:1983:MCA, author = "Alexander P. Morgan", title = "A Method for Computing All Solutions to Systems of Polynomials Equations", journal = j-TOMS, volume = "9", number = "1", pages = "1--17", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356023", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "85f:65051", bibdate = "Sun Sep 04 19:32:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Eugene Allgower", } @Article{Greenberg:1983:FDA, author = "Harvey Greenberg", title = "A Functional Description of {ANALYZE}: a Computer-Assisted Analysis System for Linear Programming Models", journal = j-TOMS, volume = "9", number = "1", pages = "18--56", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356024", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:32:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Beck:1983:RGA, author = "P. Beck and L. Lasdon and M. Engquist", title = "A Reduced Gradient Algorithm for Nonlinear Network Problems", journal = j-TOMS, volume = "9", number = "1", pages = "57--70", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356025", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10", MRnumber = "84m:65077", bibdate = "Sun Sep 04 19:32:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Kailash C. Kapur", } @Article{Hanson:1983:CDE, author = "P. M. Hanson and W. H. Enright", title = "Controlling the defect in existing variable-order {Adams} codes for initial-value problems", journal = j-TOMS, volume = "9", number = "1", pages = "71--97", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356026", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65L07)", MRnumber = "85i:65086", bibdate = "Sat Aug 13 17:16:02 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability; theory", review = "ACM CR 40497", reviewer = "Syvert P. N{\o}rsett", subject = "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Error analysis \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems", } @Article{Gaffney:1983:AFS, author = "Patrick W. Gaffney", title = "{Algorithm 592}: {A FORTRAN} Subroutine for Computing the Optimal Estimate of {$f(x)$}", journal = j-TOMS, volume = "9", number = "1", pages = "98--116", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356027", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Proskurowski:1983:APH, author = "Wlodzimierz Proskurowski", title = "{Algorithm 593}: a Package for the {Helmholtz} Equation in Nonrectangular Planar Regions", journal = j-TOMS, volume = "9", number = "1", pages = "117--124", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356028", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Larson:1983:ASR, author = "John L. Larson and Mary E. Pasternak and John A. Wisniewski", title = "{Algorithm 594}: Software for Relative Error Analysis", journal = j-TOMS, volume = "9", number = "1", pages = "125--130", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356029", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Martello:1983:AEA, author = "Silvano Martello", title = "{Algorithm 595}: An Enumerative Algorithm for Finding {Hamiltonian} Circuits in a Directed Graph", journal = j-TOMS, volume = "9", number = "1", pages = "131--138", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356030", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gay:1983:RNE, author = "David M. Gay", title = "Remark on ``{Algorithm} 573: {NL2SOL}\emdash An Adaptive Nonlinear Least-Squares Algorithm''", journal = j-TOMS, volume = "9", number = "1", pages = "139--139", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356031", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:32:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Dennis:1981:ANE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "lsq; nllsq; nlop; software", } @Article{Dodson:1983:CRB, author = "David S. Dodson", title = "Corrigendum: Remark on ``{Algorithm} 539: {Basic Linear Algebra Subroutines} for {FORTRAN} Usage''", journal = j-TOMS, volume = "9", number = "1", pages = "140--140", month = mar, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356022.356032", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 21:11:39 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Hanson:1987:ATA,Louter-Nool:1988:ATA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fourer:1983:MLV, author = "Robert Fourer", title = "Modeling Languages Versus Matrix Generators for Linear Programming", journal = j-TOMS, volume = "9", number = "2", pages = "143--183", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357457", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Armstrong:1983:CSM, author = "R. D. Armstrong and D. S. Kung and P. Sinha and A. A. Zoltners", title = "A Computational Study of a Multiple-Choice Knapsack Algorithm", journal = j-TOMS, volume = "9", number = "2", pages = "184--198", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357458", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C10", MRnumber = "85a:90163", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cryer:1983:ESL, author = "C. W. Cryer", title = "The Efficient Solution of Linear Complementarity Problems for Tridiagonal {Minkowski} Matrices", journal = j-TOMS, volume = "9", number = "2", pages = "199--214", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357459", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C33 (65F10)", MRnumber = "84j:90088", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rheinboldt:1983:LPC, author = "Werner C. Rheinboldt and John V. Burkardt", title = "A Locally Parametrized Continuation Process", journal = j-TOMS, volume = "9", number = "2", pages = "215--235", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357460", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "85f:65052", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Dietrich Braess", } @Article{Rheinboldt:1983:APL, author = "Werner C. Rheinboldt and John V. Burkardt", title = "{Algorithm 596}: a Program for a Locally Parametrized Continuation Process", journal = j-TOMS, volume = "9", number = "2", pages = "236--241", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357461", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 12:18:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cody:1983:ASM, author = "W. J. Cody", title = "{Algorithm 597}: Sequence of Modified {Bessel} Functions of the First Kind", journal = j-TOMS, volume = "9", number = "2", pages = "242--245", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357462", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 6 22:16:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation G Mathematics of Computing, MISCELLANEOUS", } @Article{Davis:1983:AAC, author = "George J. Davis", title = "{Algorithm 598}: An Algorithm to Compute Solvents of the Matrix Equation {$AX^2 + BX + C = 0$}", journal = j-TOMS, volume = "9", number = "2", pages = "246--254", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357463", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ahrens:1983:ASG, author = "J. H. Ahrens and K. D. Kohrt and U. Dieter", title = "{Algorithm 599}: Sampling from {Gamma} and {Poisson} Distributions", journal = j-TOMS, volume = "9", number = "2", pages = "255--257", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357464", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 16:10:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "6932", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Herriot:1983:ATA, author = "John G. Herriot and Christian H. Reinsch", title = "{Algorithm 600}: Translation of {Algorithm} 507: {Procedures} for Quintic Natural Spline Interpolation", journal = j-TOMS, volume = "9", number = "2", pages = "258--259", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357465", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 5 23:07:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pape:1983:RSP, author = "U. Pape", title = "Remark on ``{Algorithm} 562: Shortest Path Lengths''", journal = j-TOMS, volume = "9", number = "2", pages = "260--260", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Pape:1980:ASP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1983:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "9", number = "2", pages = "261--264", month = jun, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/357456.357467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zave:1983:QEF, author = "Pamela Zave and George E. {Cole, Jr.}", title = "A Quantitative Evaluation of the Feasibility of, and Suitable Hardware Architectures for, an Adaptive, Parallel Finite-Element System", journal = j-TOMS, volume = "9", number = "3", pages = "271--292", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356045", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65W05 (65N30)", MRnumber = "86g:65244", bibdate = "Sun Sep 04 19:50:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Beny Neta", } @Article{Watkins:1983:NSS, author = "David S. Watkins and Ralph W. HansonSmith", title = "The Numerical Solution of Separably Stiff Systems by Precise Partitioning", journal = j-TOMS, volume = "9", number = "3", pages = "293--301", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356046", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "86g:65136", bibdate = "Sun Sep 04 19:51:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; measurement; performance", review = "ACM CR 8406-0468", subject = "G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations", } @Article{Duff:1983:MSI, author = "I. S. Duff and J. K. Reid", title = "The Multifrontal Solution of Indefinite Sparse Symmetric Linear Systems", journal = j-TOMS, volume = "9", number = "3", pages = "302--325", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356047", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65W05)", MRnumber = "86k:65030", bibdate = "Fri Aug 26 23:38:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "indefinite system; nla; sparse; symmetric matrix", reviewer = "Stephen W. Brady", } @Article{Tarjan:1983:SEI, author = "Robert E. Tarjan", title = "Space-Efficient Implementations of Graph Search Methods", journal = j-TOMS, volume = "9", number = "3", pages = "326--339", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356048", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68P10", MRnumber = "86m:68023", bibdate = "Sun Sep 04 19:50:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McNamee:1983:SMP, author = "J. M. McNamee", title = "A Sparse Matrix Package\emdash {Part II}: Special Cases", journal = j-TOMS, volume = "9", number = "3", pages = "340--343", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356049", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:50:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McNamee:1983:ASM, author = "J. M. McNamee", title = "{Algorithm 601}: a Sparse-Matrix Package\emdash {Part II}: Special Cases", journal = j-TOMS, volume = "9", number = "3", pages = "344--345", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356050", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fessler:1983:HAA, author = "Theodore Fessler and William F. Ford and David A. Smith", title = "{HURRY}: An Acceleration Algorithm for Scalar Sequences and Series", journal = j-TOMS, volume = "9", number = "3", pages = "346--354", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356051", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65B10", MRnumber = "791 970", bibdate = "Sun Sep 04 19:50:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fessler:1983:AHA, author = "Theodore Fessler and William F. Ford and David A. Smith", title = "{Algorithm 602}: {HURRY}: An Acceleration Algorithm for Scalar Sequences and Series", journal = j-TOMS, volume = "9", number = "3", pages = "355--357", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356052", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65B10", MRnumber = "791 971", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Diaz:1983:FPS, author = "J. C. D{\'i}az and G. Fairweather and P. Keast", title = "{FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination", journal = j-TOMS, volume = "9", number = "3", pages = "358--375", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356053", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "791 972", bibdate = "Sun Sep 04 19:50:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Diaz:1983:ACA, author = "J. C. D{\'i}az and G. Fairweather and P. Keast", title = "{Algorithm 603}: {COLROW} and {ARCECO}: {FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination", journal = j-TOMS, volume = "9", number = "3", pages = "376--380", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356054", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "791 973", bibdate = "Sun Sep 4 22:04:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Diaz:1988:RCA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sauer:1983:AFP, author = "Frederick W. Sauer", title = "{Algorithm 604}: a {FORTRAN} Program for the Calculation of an Extremal Polynomial", journal = j-TOMS, volume = "9", number = "3", pages = "381--383", month = sep, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356044.356055", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F10 65K10)", MRnumber = "86g:65007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hopkins:1983:APV, author = "T. R. Hopkins", title = "{Algorithm 605}: {PBASIC}: a Verifier Program for {American National Standard Minimal BASIC}", journal = j-TOMS, volume = "9", number = "4", pages = "391--394", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356057", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gaffney:1983:NIT, author = "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W. R. McKinney", title = "{NITPACK}: An Interactive Tree Package", journal = j-TOMS, volume = "9", number = "4", pages = "395--417", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356058", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 19:56:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gaffney:1983:ANI, author = "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W. R. McKinney", title = "{Algorithm 606}: {NITPACK}: An Interactive Tree Package", journal = j-TOMS, volume = "9", number = "4", pages = "418--426", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356059", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Snyder:1983:ATE, author = "W. V. Snyder and R. J. Hanson", title = "{Algorithm 607}: Text Exchange System: a Transportable System for Management and Exchange of Programs and other Text", journal = j-TOMS, volume = "9", number = "4", pages = "427--440", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356060", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Horn:1983:CLE, author = "B. K. P. Horn", title = "The Curve of Least Energy", journal = j-TOMS, volume = "9", number = "4", pages = "441--460", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356061", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D07 (65D10)", MRnumber = "87c:65009", bibdate = "Sun Sep 04 19:58:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "G. P. Bhattacharjee", } @Article{West:1983:AAS, author = "David H. West", title = "{Algorithm 608}: Approximate Solution of the Quadratic Assignment Problem", journal = j-TOMS, volume = "9", number = "4", pages = "461--466", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356062", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K05 (90C10)", MRnumber = "791 976", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amos:1983:UAE, author = "D. E. Amos", title = "Uniform Asymptotic Expansions for Exponential Integrals ${E}_n(x)$ and {Bickley} Functions $\hbox{Ki}_n(x)$", journal = j-TOMS, volume = "9", number = "4", pages = "467--479", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356063", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (33A70)", MRnumber = "87a:65043", bibdate = "Sun Sep 04 19:56:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Marietta J. Tretter", } @Article{Amos:1983:APFa, author = "D. E. Amos", title = "{Algorithm 609}: a Portable {FORTRAN} Subroutine for the {Bickley} Functions {$\hbox{Ki}_n(x)$}", journal = j-TOMS, volume = "9", number = "4", pages = "480--493", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356064", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (33A70 65-04)", MRnumber = "87a:65044", bibdate = "Sun Sep 4 20:00:39 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Marietta J. Tretter", } @Article{Amos:1983:APFb, author = "D. E. Amos", title = "{Algorithm 610}: a Portable {FORTRAN} Subroutine for Derivatives of the Psi Function", journal = j-TOMS, volume = "9", number = "4", pages = "494--502", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356065", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "791 979", bibdate = "Sun Sep 4 20:00:39 1994", bibsource = "ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", catcode = "G.1.0; G.1; G; D.3.2", CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.m Miscellaneous; D.3.2 Language Classifications; D.3.2 FORTRAN", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous; Mathematics of Computing, MISCELLANEOUS; Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN", fjournal = "ACM Transactions on Mathematical Software (TOMS)", genterm = "ALGORITHMS", guideno = "02212", journal-URL = "https://dl.acm.org/loi/toms", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.3 PROGRAMMING LANGUAGES", } @Article{Gay:1983:ASU, author = "David M. Gay", title = "{Algorithm 611}: Subroutines for Unconstrained Minimization Using a Model\slash Trust-Region Approach", journal = j-TOMS, volume = "9", number = "4", pages = "503--524", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356066", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (65-04 90C30)", MRnumber = "86f:65111", bibdate = "Fri Aug 26 23:38:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "lsq; nllsq; nlop", } @Article{Amos:1983:REI, author = "Donald E. Amos", title = "Remark on ``{Algorithm} 556: Exponential Integrals''", journal = j-TOMS, volume = "9", number = "4", pages = "525--525", month = dec, year = "1983", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356056.356067", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Amos:1980:AEI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{deDoncker:1984:AAI, author = "Elise {de Doncker} and Ian Robinson", title = "An Algorithm for Automatic Integration Over a Triangle Using Nonlinear Extrapolation", journal = j-TOMS, volume = "10", number = "1", pages = "1--16", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356069", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65V05)", MRnumber = "86e:65035a", bibdate = "Fri Mar 28 11:00:07 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{deDoncker:1984:ATI, author = "Elise {de Doncker} and Ian Robinson", title = "{Algorithm 612}: {TRIEX}: Integration Over a {TRIangle} Using Nonlinear {EXtrapolation}", journal = j-TOMS, volume = "10", number = "1", pages = "17--22", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356070", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65V05)", MRnumber = "86e:65035b", bibdate = "Sat Oct 24 15:51:01 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/356068.356070; http://www.acm.org/pubs/citations/journals/toms/1984-10-1/p17-doncker/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gear:1984:SOD, author = "C. W. Gear and O. {\O}sterby", title = "Solving Ordinary Differential Equations with Discontinuities", journal = j-TOMS, volume = "10", number = "1", pages = "23--44", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356071", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "86h:65097", bibdate = "Sun Sep 04 20:02:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. C. Rheinboldt", } @Article{Krogh:1984:ARI, author = "Fred T. Krogh and Kris Stewart", title = "Asymptotic ($h\rightarrow\infty$) Absolute Stability for {BDFs} Applied to Stiff Differential Equations", journal = j-TOMS, volume = "10", number = "1", pages = "45--57", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356072", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L20 (65-04)", MRnumber = "86j:65103", bibdate = "Sun Sep 04 20:02:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Gh. Adam", } @Article{Gaffney:1984:PES, author = "Patrick W. Gaffney", title = "A Performance Evaluation of Some {FORTRAN} Subroutines for the Solution of Stiff Oscillatory Ordinary Differential Equations", journal = j-TOMS, volume = "10", number = "1", pages = "58--72", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356073", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "86f:65117", bibdate = "Sun Sep 04 20:02:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kaufman:1984:BES, author = "Linda Kaufman", title = "Banded Eigenvalue Solvers on Vector Machines", journal = j-TOMS, volume = "10", number = "1", pages = "73--85", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356074", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65W05 (65F15)", MRnumber = "86f:65223", bibdate = "Fri Sep 30 01:11:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lenard:1984:RGT, author = "Melanie L. Lenard and Michael Minkoff", title = "Randomly Generated Test Problems for Positive Definite Quadratic Programming", journal = j-TOMS, volume = "10", number = "1", pages = "86--96", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356075", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (90C20)", MRnumber = "86e:65088", bibdate = "Sun Sep 04 20:02:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jones:1984:SRM, author = "Christopher B. Jones", title = "A Significance Rule for Multiple-Precision Arithmetic", journal = j-TOMS, volume = "10", number = "1", pages = "97--107", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356076", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05 (65G10)", MRnumber = "86e:65063", bibdate = "Sun Sep 04 20:02:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Multiple-precision arithmetic overcomes the round-off error incurred in conventional floating-point arithmetic, at the cost of increased processing overhead. Significance arithmetic takes into account the inexactness of the operands of a calculation, but can lead to loss of significant digits after a long series of operations. A new technique is described which alleviates the overhead of multiple-precision arithmetic by allowing nonsignificant digits to be discarded, while limiting the significance loss per operation to a controllable and acceptable rate. The technique is based on storing an inexact number interval, using a criterion of significance to determine the precision with which the limits of interval should be stored. A procedure referred to as a significance rule uses this criterion to remove some of the nonsignificant digits from the limits of an interval prior to storage. A certain number of nonsignificant digits are retained as guard digits. Calculations are performed using exact interval arithmetic and the significance-rule procedure is invoked after each operation to remove superfluous digits. Round-off in the procedure causes a slight increase in the interval width on each operation. This results in a cumulative loss of significance at a rate related to the number of guard digits.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Haymond:1984:AMS, author = "R. E. Haymond and J. P. Jarvis and D. R. Shier", title = "{Algorithm 613}: Minimum Spanning Tree for Moderate Integer Weights", journal = j-TOMS, volume = "10", number = "1", pages = "108--111", month = mar, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356068.356077", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shapiro:1984:IRG, author = "Henry D. Shapiro", title = "Increasing Robustness in Global Adaptive Quadrature Through Interval Selection Heuristics", journal = j-TOMS, volume = "10", number = "2", pages = "117--139", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.400", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D32 (65V05)", MRnumber = "87a:65053", bibdate = "Sun Sep 04 20:09:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sikorski:1984:OQS, author = "K. Sikorski and F. Stenger", title = "Optimal Quadratures in {$H_p$} Spaces", journal = j-TOMS, volume = "10", number = "2", pages = "140--151", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.448", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D32", MRnumber = "87a:65054a", bibdate = "Sun Sep 04 20:09:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "J. B. Butler, Jr.", } @Article{Sikorski:1984:AFS, author = "K. Sikorski and F. Stenger and J. Schwing", title = "{Algorithm 614}: {A FORTRAN} Subroutine for Numerical Integration in {$H_p$}", journal = j-TOMS, volume = "10", number = "2", pages = "152--160", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.449", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D32 (65-04)", MRnumber = "87a:65054b", bibdate = "Sun Sep 4 20:11:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "J. B. Butler, Jr.", } @Article{Rall:1984:DPS, author = "L. B. Rall", title = "Differentiation in {Pascal-SC}: Type {GRADIENT}", journal = j-TOMS, volume = "10", number = "2", pages = "161--184", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.418", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D25 (65-04 65H05)", MRnumber = "86j:65025", bibdate = "Sun Sep 04 20:09:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Stephen W. Brady", } @Article{Lawrie:1984:CCC, author = "D. H. Lawrie and A. H. Sameh", title = "The Computation and Communication Complexity of a Parallel Banded System Solver", journal = j-TOMS, volume = "10", number = "2", pages = "185--195", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.401", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65W05 (65F05 68Q25)", MRnumber = "86k:65138", bibdate = "Sat Nov 19 13:08:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Lawrie:1985:CCC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "D. Bini", } @Article{Reid:1984:SAB, author = "J. K. Reid and A. Jennings", title = "On Solving Almost Block Diagonal (Staircase) Linear Systems", journal = j-TOMS, volume = "10", number = "2", pages = "196--201", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.450", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65F50 65L10)", MRnumber = "86g:65063", bibdate = "Sun Sep 04 20:09:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Armstrong:1984:ABS, author = "R. D. Armstrong and P. O. Beck and M. T. Kung", title = "{Algorithm 615}: The Best Subset of Parameters in Least Absolute Value Regression", journal = j-TOMS, volume = "10", number = "2", pages = "202--206", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.319410", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D10 (65K05)", MRnumber = "791 987", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Petkov:1984:RDE, author = "P. {Hr.} Petkov and N. D. Christov and M. M. Konstantinov", title = "Remark on ``{Algorithm} 590: {DSUBSP} and {EXCHQZ}: {FORTRAN} Subroutines for Computing Deflating Subspaces with Specified Spectrum''", journal = j-TOMS, volume = "10", number = "2", pages = "207--207", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.319411", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 24 15:51:05 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{VanDooren:1982:ADE}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1984:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "10", number = "2", pages = "208--211", month = jun, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/399.319412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:09:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dongarra:1984:SMA, author = "Jack J. Dongarra and Stanley C. Eisenstat", title = "Squeezing the Most out of an Algorithm in {CRAY} {FORTRAN}", journal = j-TOMS, volume = "10", number = "3", pages = "219--230", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.319413", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F99", MRnumber = "791 988", bibdate = "Fri Aug 26 23:38:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cray; fortran; nla; vect", } @Article{Molchanov:1984:PCS, author = "I. N. Molchanov and V. S. Zubatenko and L. D. Nikolenko and M. F. Yakovlev", title = "A Program Complex for Solving Systems of Linear Algebraic Equations", journal = j-TOMS, volume = "10", number = "3", pages = "231--241", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1273", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65F10 65V05)", MRnumber = "86f:65061", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rivara:1984:DDS, author = "Mar{\'i}a-Cecilia Rivara", title = "Design and Data Structure of Fully Adaptive Multigrid, Finite-Element Software", journal = j-TOMS, volume = "10", number = "3", pages = "242--264", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1274", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N50 (65F50 65N30)", MRnumber = "86f:65207", bibdate = "Sat Aug 27 19:10:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Monahan:1984:AFC, author = "John F. Monahan", title = "{Algorithm 616}: Fast Computation of the {Hodges-Lehman} Location Estimator", journal = j-TOMS, volume = "10", number = "3", pages = "265--270", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.319414", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65U05 (62-04 62G05)", MRnumber = "791 991", bibdate = "Sun Sep 4 20:21:15 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "This paper reduces the previous complexity bound for the {Hodges-Lehman} location estimator from ${O}(n^2\log{n})$ to ${O}(n\log{n})$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kronmal:1984:ACA, author = "Richard A. Kronmal and Arthur V. {Peterson, Jr.}", title = "An Acceptance-Complement Analogue of the Mixture-plus-Acceptance-Rejection Method for Generating Random Variables", journal = j-TOMS, volume = "10", number = "3", pages = "271--281", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1272", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10 (65U05)", MRnumber = "86f:65027", bibdate = "Wed Aug 24 22:43:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7548", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Gill:1984:POP, author = "Philip E. Gill and Walter Murray and Michael A. Saunders and Margaret H. Wright", title = "Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints", journal = j-TOMS, volume = "10", number = "3", pages = "282--298", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1276", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (65F30 90C30)", MRnumber = "86h:65091", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aluffi-Pentini:1984:DEA, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "A Differential-Equations Algorithm for Nonlinear Equations", journal = j-TOMS, volume = "10", number = "3", pages = "299--316", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1631", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10 (65L05)", MRnumber = "87a:65085", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Hj. Wacker", } @Article{Aluffi-Pentini:1984:ADD, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "{Algorithm 617}: {DAFNE}: a Differential-Equations Algorithm for Nonlinear Equations", journal = j-TOMS, volume = "10", number = "3", pages = "317--324", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1632", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10 (65-04 65L05)", MRnumber = "87a:65086", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "Hj. Wacker", } @Article{Regener:1984:MID, author = "Eric Regener", title = "Multiprecision Integer Division Examples Using Arbitrary Radix", journal = j-TOMS, volume = "10", number = "3", pages = "325--328", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.2738", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65V05", MRnumber = "86g:65241", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{BrinchHansen:1994:MLD}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Coleman:1984:SES, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "Software for Estimating Sparse {Jacobian} Matrices", journal = j-TOMS, volume = "10", number = "3", pages = "329--345", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.1610", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65H10)", MRnumber = "86f:65086a", bibdate = "Mon Sep 05 09:48:14 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Coleman:1984:AFS, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "{Algorithm 618}: {Fortran} Subroutines for Estimating Sparse {Jacobian} Matrices", journal = j-TOMS, volume = "10", number = "3", pages = "346--347", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.319415", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65-04 65H10)", MRnumber = "86f:65086b", bibdate = "Sun Sep 04 20:28:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Piessens:1984:AAN, author = "Robert Piessens and Rudi Huysmans", title = "{Algorithm 619}: Automatic Numerical Inversion of the {Laplace} Transform [{D5}]", journal = j-TOMS, volume = "10", number = "3", pages = "348--353", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.319416", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R10", MRnumber = "791 999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Piessens:1984:RNI, author = "Robert Piessens", title = "Remark on ``{Algorithm} 486: Numerical Inversion of {Laplace} Transform''", journal = j-TOMS, volume = "10", number = "3", pages = "354--354", month = sep, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1271.319417", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:18:56 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Veillon:1977:RNI,Koppelaar:1976:RNI}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1984:ARK, author = "John R. Rice and Richard J. Hanson", title = "{Algorithm 620}: References and Keywords for {\em {Collected Algorithms} of the {ACM}}", journal = j-TOMS, volume = "10", number = "4", pages = "359--360", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356100", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:00:44 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hamilton:1985:RRK,Hopkins:1990:RRK}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Black:1984:NIS, author = "Cheryl M. Black and Robert P. Burton and Thomas H. Miller", title = "The Need for an Industry Standard of Accuracy for Elementary-Function Programs", journal = j-TOMS, volume = "10", number = "4", pages = "361--366", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356101", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "792 000", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Eiger:1984:BMS, author = "A. Eiger and K. Sikorski and F. Stenger", title = "A Bisection Method for Systems of Nonlinear Equations", journal = j-TOMS, volume = "10", number = "4", pages = "367--377", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.2705", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "86g:65102", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sommeijer:1984:ASL, author = "B. P. Sommeijer and P. J. {van der Houwen}", title = "{Algorithm 621}: Software with Low Storage Requirements for Two-Dimensional, Nonlinear, Parabolic Differential Equations", journal = j-TOMS, volume = "10", number = "4", pages = "378--396", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356103", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65M20", MRnumber = "792 002", bibdate = "Sat Oct 24 15:50:58 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bundy:1984:GIP, author = "Alan Bundy", title = "A Generalized Interval Package and Its Use for Semantic Checking", journal = j-TOMS, volume = "10", number = "4", pages = "397--409", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.2702", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G10", MRnumber = "86g:65088", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1984:ASM, author = "John R. Rice and Calvin Ribbens and William A. Ward", title = "{Algorithm 622}: a Simple Macroprocessor", journal = j-TOMS, volume = "10", number = "4", pages = "410--416", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356105", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:17:12 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Levin:1998:RAS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:1984:IDS, author = "Robert J. Renka", title = "Interpolation of Data on the Surface of a Sphere", journal = j-TOMS, volume = "10", number = "4", pages = "417--436", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.2703", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "86k:65013a", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8511-1051", reviewer = "G. P. Bhattacharjee", subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation", } @Article{Renka:1984:AIS, author = "Robert J. Renka", title = "{Algorithm 623}: Interpolation on the Surface of a Sphere", journal = j-TOMS, volume = "10", number = "4", pages = "437--439", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356107", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "86k:65013b", bibdate = "Fri Mar 28 11:02:10 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "G. P. Bhattacharjee", } @Article{Renka:1984:ATI, author = "Robert J. Renka", title = "{Algorithm 624}: Triangulation and Interpolation at Arbitrarily Distributed Points in the Plane", journal = j-TOMS, volume = "10", number = "4", pages = "440--442", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356108", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65V05)", MRnumber = "792 006", bibdate = "Fri Mar 28 11:02:31 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1984:NCG, author = "John R. Rice", title = "Numerical Computation with General Two-Dimensional Domains", journal = j-TOMS, volume = "10", number = "4", pages = "443--452", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356109", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N50", MRnumber = "792 007", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rice:1984:ATD, author = "John R. Rice", title = "{Algorithm 625}: a Two-Dimensional Domain Processor", journal = j-TOMS, volume = "10", number = "4", pages = "453--462", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356110", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N50", MRnumber = "792 008", bibdate = "Fri Mar 28 11:03:12 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Preusser:1984:CCS, author = "Albrecht Preusser", title = "Computing Contours by Successive Solution of Quintic Polynomial Equations", journal = j-TOMS, volume = "10", number = "4", pages = "463--472", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.2770", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05", MRnumber = "792 009", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Preusser:1984:ATE, author = "Albrecht Preusser", title = "{Algorithm 626}: {TRICP}\emdash a Contour Plot Program for Triangular Meshes", journal = j-TOMS, volume = "10", number = "4", pages = "473--475", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.2772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65N50)", MRnumber = "792 010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Garbow:1984:RQA, author = "B. S. Garbow", title = "Remark on ``{Algorithm} 535: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "10", number = "4", pages = "476--476", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356113", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Garbow:1978:AQA,Garbow:1982:RQA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Celis:1984:RCE, author = "Pedro Celis", title = "Remark: Corrections and Errors in {John Ivie}'s Some {MACSYMA} Programs for Solving Recurrence Relations", journal = j-TOMS, volume = "10", number = "4", pages = "477--478", month = dec, year = "1984", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2701.356114", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:32:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ivie:1978:SMP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tomlin:1985:IPS, author = "J. A. Tomlin and J. S. Welch", title = "Integration of a Primal Simplex Network Algorithm with a Large-Scale Mathematical Programming System", journal = j-TOMS, volume = "11", number = "1", pages = "1--11", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.3163", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K05 (90C05)", MRnumber = "86h:65087", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p1-tomlin/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Davidon:1985:ESD, author = "William C. Davidon and Jorge Nocedal", title = "Evaluation of Step Directions in Optimization Algorithms", journal = j-TOMS, volume = "11", number = "1", pages = "12--19", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.3164", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "86h:65089", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p12-davidon/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Cuyt:1985:CIM, author = "Annie A. M. Cuyt and L. B. Rall", title = "Computational Implementation of the Multivariate {Halley} Method for Solving Nonlinear Systems of Equations", journal = j-TOMS, volume = "11", number = "1", pages = "20--36", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.3162", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05 (65-04)", MRnumber = "86g:65092", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p20-cuyt/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf I.1.m}: Computing Methodologies, ALGEBRAIC MANIPULATION, Miscellaneous.", } @Article{Vitter:1985:RSR, author = "Jeffrey Scott Vitter", title = "Random Sampling with a Reservoir", journal = j-TOMS, volume = "11", number = "1", pages = "37--57", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.3165", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10 (62-04)", MRnumber = "87b:65007", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p37-vitter/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance; theory; verification", reviewer = "Brian Conolly", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems Management, Access methods.", } @Article{Bownds:1985:AFS, author = "John M. Bownds and Lee Appelbaum", title = "{Algorithm 627}: a {FORTRAN} Subroutine for Solving {Volterra} Integral Equations", journal = j-TOMS, volume = "11", number = "1", pages = "58--65", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.214314", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R20", MRnumber = "793 057", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p58-bownds/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "documentation; economics; performance", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Winkler:1985:AAC, author = "F. Winkler and B. Buchberger and F. Lichtenberger and H. Rolletschek", title = "{Algorithm 628}: An Algorithm for Constructing Canonical Bases of Polynomial Ideals", journal = j-TOMS, volume = "11", number = "1", pages = "66--78", month = mar, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3147.214316", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68Q40 (13-04)", MRnumber = "793 058", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p66-winkler/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Atkinson:1985:AIE, author = "Kendall E. Atkinson", title = "{Algorithm 629}: An Integral Equation Program for {Laplace}'s Equation in Three Dimensions", journal = j-TOMS, volume = "11", number = "2", pages = "85--96", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214393", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N30 (65R20)", MRnumber = "86m:65137", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p85-atkinson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", reviewer = "H. Kersten", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Dembo:1985:TPG, author = "R. S. Dembo and T. Steihaug", title = "A Test Problem Generator for Large-Scale Unconstrained Optimization", journal = j-TOMS, volume = "11", number = "2", pages = "97--102", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214394", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "86h:65090", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p97-dembo/", abstract = "A test problem generator for large-scale unconstrained optimization is described. It permits the generation of a poorly or well-conditioned problems of arbitrary size, derived from nonlinear network flow models. An eigenvalue analysis provides bounds on the condition number of the Hessian of the objective function and an example of an efficient preconditioner, using these bounds, is outlined.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; measurement", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf D.2.5}: Software, SOFTWARE ENGINEERING, Testing and Debugging, Test data generators.", } @Article{Buckley:1985:ABE, author = "A. Buckley and A. LeNir", title = "{Algorithm 630}: {BBVSCG}\emdash a Variable Storage Algorithm for Function Minimization", journal = j-TOMS, volume = "11", number = "2", pages = "103--119", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214395; http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p103-buckley/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Buckley:1989:RA}.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Norton:1985:AFB, author = "Victor Norton", title = "{Algorithm 631}: Finding a Bracketed Zero by {Larkin}'s Method of Rational Interpolation", journal = j-TOMS, volume = "11", number = "2", pages = "120--134", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214396", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05 (65D05)", MRnumber = "797 616", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Norton:1986:RFB}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p120-norton/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Martello:1985:APM, author = "Silvano Martello and Paolo Toth", title = "{Algorithm 632}: a Program for the $0-1$ Multiple Knapsack Problem", journal = j-TOMS, volume = "11", number = "2", pages = "135--140", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214397", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:12:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p135-martello/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Liu:1985:MMD, author = "Joseph W. H. Liu", title = "Modification of the Minimum-Degree Algorithm by Multiple Elimination", journal = j-TOMS, volume = "11", number = "2", pages = "141--153", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214398", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65F05)", MRnumber = "86m:65040", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p141-liu/", abstract = "The most widely used ordering scheme to reduce fills and operations in sparse matrix computation is the minimum-degree algorithm. The notion of {\em multiple elimination} is introduced here as a modification to the conventional scheme. The motivation is discussed using the $k$-by-$k$ grid model problem. Experimental results indicate that the modified version retains the fill-reducing property of (and is often better than) the original ordering algorithm and yet requires less computer time. The reduction in ordering time is problem dependent, and for some problems the modified algorithm can run a few times faster than existing implementations of the minimum-degree algorithm. The use of {\em external degree} in the algorithm is also introduced.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "David R. Kincaid", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Gan:1985:NCG, author = "C. T. Gan", title = "A Note on Combination Generators", journal = j-TOMS, volume = "11", number = "2", pages = "154--156", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214401", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p154-gan/", abstract = "A recent study by Akl indicates that Mifsud's algorithm, which involves unnecessary searching operations, is the fastest existing combination generator. A modified Page and Wilson's algorithm, which is essentially similar to Mifsud's algorithm, is presented. A theoretical analysis of the modified algorithm is also given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", } @Article{Ahrens:1985:SRS, author = "J. H. Ahrens and U. Dieter", title = "Sequential Random Sampling", journal = j-TOMS, volume = "11", number = "2", pages = "157--169", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214402", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p157-ahrens/", abstract = "Fast algorithms for selecting a random set of exactly $k$ records from a file of $n$ records are constructed. Selection is sequential: the sample records are chosen in the same order in which they occur in the file. All procedures run in $O(k)$ time. The ``geometric'' method has two versions: with or without $O(k)$ auxiliary space. A further procedure uses hashing techniques and requires $O(k)$ space.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Ward:1985:AAL, author = "R. C. Ward and G. J. Davis and V. E. Kane", title = "{Algorithm 633}: An Algorithm for Linear Dependency Analysis of Multivariate Data", journal = j-TOMS, volume = "11", number = "2", pages = "170--182", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214403", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65U05 (62-04)", MRnumber = "86j:65187", bibdate = "Fri Sep 30 01:12:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p170-ward/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "measurement; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Novotny:1985:RNS, author = "Milan Novotny", title = "Remark on ``{Algorithm} 30: Numerical Solution of the Polynomial Equation''", journal = j-TOMS, volume = "11", number = "2", pages = "183--184", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214404", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ellenberger:1960:NSP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p183-novotny/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Hill:1985:RCS, author = "I. D. Hill and M. C. Pike", title = "Remark on ``{Algorithm} 299: Chi-Squared Integral''", journal = j-TOMS, volume = "11", number = "2", pages = "185--185", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214405; http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p185-hill/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:20:54 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hill:1967:CSI,elLozy:1976:RAC,elLozy:1979:RAS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Preusser:1985:RBI, author = "Albrect Preusser", title = "Remark on ``{Algorithm} 526: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]''", journal = j-TOMS, volume = "11", number = "2", pages = "186--187", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.214407", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1978:ABI,Akima:1979:RBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p186-preusser/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Lawrie:1985:CCC, author = "D. H. Lawrie and A. H. Sameh", title = "Corrections to ``{The} Computation and Communication Complexity of a Parallel Banded System Solver''", journal = j-TOMS, volume = "11", number = "2", pages = "188--188", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.356133", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawrie:1984:CCC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1985:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "11", number = "2", pages = "193--196", month = jun, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214392.356134", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bartels:1985:LSF, author = "Richard H. Bartels and John J. Jezioranski", title = "Least-Squares Fitting Using Orthogonal Multinomials", journal = j-TOMS, volume = "11", number = "3", pages = "201--217", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214410", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D10", MRnumber = "87f:65016", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p201-bartels/", abstract = "Forsythe has given a method for generating basis polynomials in a single variable that are orthogonal with respect to a given inner product. Weisfeld later demonstrated that Forsythe's approach could be extended to polynomials in an arbitrary number of variables. In this paper we sharpen Weisfeld's results and present a method for computing weighted, multinomial, least-squares approximations to given data.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "Wolfgang Boehm", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @Article{Bartels:1985:ACE, author = "Richard H. Bartels and John J. Jezioranski", title = "{Algorithm 634}: {CONSTR} and {EVAL}: Routines for Fitting Multinomials in a Least-Squares Sense", journal = j-TOMS, volume = "11", number = "3", pages = "218--228", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D10", MRnumber = "87f:65017", bibdate = "Sun Sep 4 20:58:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p218-bartels/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "Wolfgang Boehm", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf F.1.2}: Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation.", } @Article{Hull:1985:PRV, author = "T. E. Hull and A. Abrham", title = "Properly Rounded Variable Precision Square Root", journal = j-TOMS, volume = "11", number = "3", pages = "229--237", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214413", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15 (65G05)", MRnumber = "87a:65041", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/; http://www.acm.org/pubs/toc/Abstracts/toms/214413.html", abstract = "The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. {\em Properly rounded} means rounded to the nearest, or to nearest even in case of a tie. It is {\em variable precision} in that it is designed to return a $p$-digit approximation to a $p$-digit argument, for any $ p > 0 $. (Precision $p$ means $p$ decimal digits.) The program and the analysis are valid for all $ p > 0 $, but current implementations place some restrictions on $p$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", catcode = "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0", CRclass = "G.4 Algorithm analysis; G.4 Verification; G.1.0 General; G.1.0 Numerical algorithms; G.1.2 Approximation; G.1.2 Elementary function approximation; G.4 Certification and testing; G.1.0 General; G.1.0 Error analysis", descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification; Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing; Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis", fjournal = "ACM Transactions on Mathematical Software (TOMS)", genterm = "algorithms; verification", guideno = "02789", journal-URL = "https://dl.acm.org/loi/toms", jrldate = "Sept. 1985", keywords = "algorithms; decimal floating-point arithmetic; verification", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Stewart:1985:NCD, author = "G. W. Stewart", title = "A Note on Complex Division", journal = j-TOMS, volume = "11", number = "3", pages = "238--241", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214414", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:15 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrigendum \cite{Stewart:1986:CNC} and the faster and more robust algorithm in \cite{Priest:2004:ESC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/", abstract = "An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; complex arithmetic; computer arithmetic; na", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Streit:1985:AAS, author = "Roy L. Streit", title = "{Algorithm 635}: An Algorithm for the Solution of Systems of Complex Linear Equations in the ${L}_\infty$ Norm with Constraints on the Unknowns", journal = j-TOMS, volume = "11", number = "3", pages = "242--249", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214415", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:59:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p242-streit/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Le:1985:EDF, author = "D. Le", title = "An Efficient Derivative-Free Method for Solving Nonlinear Equations", journal = j-TOMS, volume = "11", number = "3", pages = "250--262", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214416", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05", MRnumber = "87d:65057", bibdate = "Sat Nov 19 13:08:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Le:1989:CED}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p250-le/", abstract = "An algorithm is presented for finding a root of a real function. The algorithm combines bisection with second and third order methods using derivatives estimated from objective function values. Global convergence is ensured and the number of function evaluations is bounded by four times the number needed by bisection. Numerical comparisons with existing algorithms indicate the superiority of the new algorithm in all classes of problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "T. Feagin", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence.", } @Article{Tischer:1985:ESN, author = "P. E. Tischer and G. K. Gupta", title = "An Evaluation of Some New Cyclic Linear Multistep Formulas for Stiff {ODEs}", journal = j-TOMS, volume = "11", number = "3", pages = "263--270", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214417", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "87d:65078", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p263-tischer/", abstract = "We evaluate several sets of cyclic linear multistep formulas (CLMFs). One of these sets was derived by Tischer and Sacks-Davis. Three new sets of formulas have been derived and we present their characteristics.\par The formulas have been evaluated by comparing the performance of four versions of a code which implements CLMFs. The four versions are very similar and each version implements one of the sets of CLMFs being studied. We compare the performance of these codes with that of a widely used code, LSODE. One of the new sets of CLMFs is not only much more efficient in solving stiff problems that have a Jacobian with eigenvalues close to the imaginary axis but is almost as efficient as LSODE in solving other problems. This is a significant improvement over the only other CLMF code available, STINT from Tendler, Bickart, and Picel.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", reviewer = "W. H. Enright", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Johnsson:1985:SNB, author = "S. Lennart Johnsson", title = "Solving Narrow Banded Systems on Ensemble Architectures", journal = j-TOMS, volume = "11", number = "3", pages = "271--288", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214418", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65W05 (65F05)", MRnumber = "86m:65170", bibdate = "Sun Sep 04 21:01:13 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p271-johnsson/", abstract = "We present concurrent algorithms for the solution of narrow banded systems on ensemble architectures, and analyze the communication and arithmetic complexities of the algorithms. The algorithms consist of three phases. In phase 1, a block tridiagonal system of reduced size is produced through largely local operations. Diagonal dominance is preserved. If the original system is positive, definite, and symmetric, so is the reduced system. It is solved in a second phase, and the remaining variables obtained through local back substitution in a third phase. With a sufficient number of processing elements, there is no first and third phase. We investigate the arithmetic and communication complexity of Gaussian elimination and block cyclic reduction for the solution of the reduced system on boolean cubes, perfect shuffle and shuffle-exchange networks, binary trees, and linear arrays.\par With an optimum number of processors, the minimum solution time on a linear array is of an order that ranges from $O(m^{2}Nm)$ to $O(m^{3} + m^{3}\log_{2}(N/m))$ depending on the bandwidth, the dimension of the problem, and the times for communication and arithmetic. For boolean cubes, cube-connected cycles, prefect shuffle and shuffle-exchange networks, and binary trees, the minimum time is $O(m^{3}+m^{3}\log_2(N/m))$ including the communication complexity", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; band matrix; linear system; nla; performance; prll", subject = "{\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Multiple-instruction-stream, multiple-data-stream processors (MIMD). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", } @Article{Hall:1985:ESR, author = "George Hall", title = "Equilibrium States of {Runge Kutta} Schemes", journal = j-TOMS, volume = "11", number = "3", pages = "289--301", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214424", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "87c:65082", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p289-hall/", abstract = "Understanding the behavior of Runge--Kutta codes when stability considerations restrict the stepsize provides useful information for stiffness detection and other implementation details. Analysis of equilibrium states on test problems is presented which provides predictions and insights into this behavior. The implications for global error are also discussed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "Henning Esser", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Ericksen:1985:IPT, author = "Wilhelm S. Ericksen", title = "Inverse Pairs of Test Matrices", journal = j-TOMS, volume = "11", number = "3", pages = "302--304", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214425", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "15A09 (65F35)", MRnumber = "87f:15002", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p302-ericksen/", abstract = "Algorithms that are readily programmable are provided for constructing inverse pairs of matrices with elements in a field, a division ring, or a ring.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "R. Kala", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Condition (and ill-condition). {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Hamilton:1985:RRK, author = "Dennis E. Hamilton", title = "Remark on ``{Algorithm} 620: References and Keywords for {\em {Collected Algorithms} of the {ACM}}''", journal = j-TOMS, volume = "11", number = "3", pages = "305--307", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214426", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Rice:1984:ARK,Hopkins:1990:RRK}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p305-hamilton/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Boisvert:1985:GFM, author = "Ronald F. Boisvert and Sally E. Howe and David K. Kahaner", title = "{GAMS}: a Framework for the Management of Scientific Software", journal = j-TOMS, volume = "11", number = "4", pages = "313--355", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6188", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:06:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p313-boisvert/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "documentation; human factors; management", review = "ACM CR 8702-0100", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, GAMS. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf H.3.5}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Online Information Services. {\bf D.2.7}: Software, SOFTWARE ENGINEERING, Distribution and Maintenance, Documentation.", } @Article{Davenport:1985:PRA, author = "J. H. Davenport and B. M. Trager", title = "On the Parallel {Risch} Algorithm ({II})", journal = j-TOMS, volume = "11", number = "4", pages = "356--362", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6189", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "12H05 (68Q40)", MRnumber = "87d:12010", bibdate = "Sun Sep 04 21:06:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p356-davenport/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory; verification", reviewer = "Michael F. Singer", subject = "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms.", } @Article{Coleman:1985:SES, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "Software for Estimating Sparse {Hessian} Matrices", journal = j-TOMS, volume = "11", number = "4", pages = "363--377", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6190", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65K10)", MRnumber = "828 562", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p363-coleman/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8710-0876", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Coleman:1985:AFS, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "{Algorithm 636}: {FORTRAN} subroutines for estimating sparse {Hessian} matrices", journal = j-TOMS, volume = "11", number = "4", pages = "378--378", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6193", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "378. 65F50 (65-04)", MRnumber = "828 563", bibdate = "Sat Aug 27 14:55:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "The title of this paper incorrectly said Algorithm 649; it should be {Algorithm 636}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p378-coleman/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf E.1}: Data, DATA STRUCTURES, Graphs. {\bf E.2}: Data, DATA STORAGE REPRESENTATIONS, Linked representations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Houstis:1985:CSS, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "Collocation Software for Second-Order Elliptic Partial Differential Equations", journal = j-TOMS, volume = "11", number = "4", pages = "379--412", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6191", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081a", bibdate = "Sun Sep 04 21:07:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p379-houstis/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; measurement; performance", review = "ACM CR 8702-0097", reviewer = "John Stephenson", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods.", } @Article{Houstis:1985:AGC, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "{Algorithm 637}: {GENCOL}: Collocation of General Domains with Bicubic {Hermite} Polynomials", journal = j-TOMS, volume = "11", number = "4", pages = "413--415", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6194", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081b", bibdate = "Sat Aug 27 14:56:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p413-houstis/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "John Stephenson", subject = "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations \\ G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods \\ G.m Mathematics of Computing, MISCELLANEOUS \\ D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN", } @Article{Houstis:1985:AIH, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "{Algorithm 638}: {INTCOL} and {HERMCOL}: Collocation on Rectangular Domains with Bicubic {Hermite} Polynomials", journal = j-TOMS, volume = "11", number = "4", pages = "416--418", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6195", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081c", bibdate = "Sun Sep 04 21:08:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p416-houstis/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "John Stephenson", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Schnabel:1985:MSA, author = "Robert B. Schnabel and John E. Koontz and Barry E. Weiss", title = "A Modular System of Algorithms for Unconstrained Minimization", journal = j-TOMS, volume = "11", number = "4", pages = "419--440", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.6192", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (65-04 90-04 90C30)", MRnumber = "828 567", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p419-schnabel/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8702-0093", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Unconstrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, UNCMIN.", } @Article{Er:1985:RG, author = "M. C. Er", title = "Remark on ``{Algorithm} 246: {Graycode} [{Z}]''", journal = j-TOMS, volume = "11", number = "4", pages = "441--443", month = dec, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6187.356154", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 20:42:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Boothroyd:1964:G,Misra:1975:RG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:1986:FVV, author = "L. F. Shampine and L. S. Baca", title = "Fixed versus Variable Order {Runge--Kutta}", journal = j-TOMS, volume = "12", number = "1", pages = "1--23", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.5964", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:09:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p1-shampine/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", review = "ACM CR 8702-0096", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Lyness:1986:AIS, author = "James Lyness and Gwendolen Hines", title = "{Algorithm 639}: To Integrate Some Infinite Oscillating Tails", journal = j-TOMS, volume = "12", number = "1", pages = "24--25", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.214318", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65D32)", MRnumber = "868 093", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p24-lyness/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation.", } @Article{Laub:1986:AEC, author = "Alan J. Laub", title = "{Algorithm 640}: Efficient Calculation of Frequency Response Matrices from State Space Models", journal = j-TOMS, volume = "12", number = "1", pages = "26--33", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.214319", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p26-laub/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering.", } @Article{Deak:1986:EMG, author = "I. Deak", title = "The Economical Method for Generating Random Samples from Discrete Distributions", journal = j-TOMS, volume = "12", number = "1", pages = "34--36", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.214321", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:11:10 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p34-deak/", abstract = "The idea of the economical method is applied for generating samples from any discrete distribution. In the resulting procedure, the expected number of uniformly distributed random numbers is less than in the alias method (practically 1). A refinement gives a version where in limit just one uniformly distributed number is required at the expense of some storage space.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7183", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Law:1986:NAM, author = "Kincho H. Law and Steven J. Fenives", title = "A Node-Addition Model for Symbolic Factorization", journal = j-TOMS, volume = "12", number = "1", pages = "37--50", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.5963", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F30", MRnumber = "87m:65068", bibdate = "Sun Sep 04 21:11:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p37-law/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; theory; verification", review = "ACM CR 8704-0290", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf E.1}: Data, DATA STRUCTURES.", } @Article{Springer:1986:ESG, author = "J{\"o}rn Springer", title = "Exact Solution of General Integer Systems of Linear Equations", journal = j-TOMS, volume = "12", number = "1", pages = "51--61", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.5961", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F20", MRnumber = "868 095", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p51-springer/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8703-0190", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields.", } @Article{Jansen:1986:HAA, author = "Paul Jansen and Peter Weidner", title = "High-Accuracy Arithmetic Software --- Some Tests of the {ACRITH} Problem-Solving Routines", journal = j-TOMS, volume = "12", number = "1", pages = "62--70", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.5962", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Dxx", MRnumber = "868 096", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/", abstract = "The program package ACRITH (High-Accuracy Arithmetic Subroutine Library) provides FORTRAN subroutines for the solution of several standard mathematical problems. The routines use floating point operations with extended precision and interval arithmetic and are designated especially for the solution of ill-conditioned problems. Test results for most of the routines are presented with emphasis on the practical usability of the package. It turns out that not all routines are of equal high quality and reliability; in the documentation, hints to the implemented numerical algorithms are completely missing, and the error messages are not always concise. Some possible alternatives like symbolic algebra systems or multiple precision packages are mentioned.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8612-1110", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Hanson:1986:RCA, author = "Richard J. Hanson", title = "Remark on ``{Algorithm} 584: {CUBTRI}: Automatic Cubature over a Triangle''", journal = j-TOMS, volume = "12", number = "1", pages = "71--71", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.356162", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 20:57:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Laurie:1982:ACA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Norton:1986:RFB, author = "Victor Norton", title = "Remark on ``{Algorithm} 631: Finding a Bracketed Zero by {Larkin}'s Method of Rational Interpolation''", journal = j-TOMS, volume = "12", number = "1", pages = "72--72", month = mar, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/5960.356163", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "72. 65H05 (65D05)", MRnumber = "868 097", bibdate = "Mon Sep 05 20:41:38 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Norton:1985:AFB}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hull:1986:VPE, author = "T. E. Hull and A. Abrham", title = "Variable Precision Exponential Function", journal = j-TOMS, volume = "12", number = "2", pages = "79--91", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.6498", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15 (65D20)", MRnumber = "863 786", bibdate = "Sun Sep 04 21:17:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/", abstract = "The exponential function presented here returns a result which differs from $e^x$ by less than one unit in the last place, for any representable value of $x$ which is not too close to values for which $e^x$ would overflow or underflow. (For values of $x$ which are not within this range, an error condition is raised.) It is a ``variable precision'' function in that it returns a $p$-digit approximation for a $p$-digit argument, for any $p > 0$ ($p$-digit means $p$-decimal-digit). The program and analysis are valid for all $p > 0$, but current implementations place a restriction on $p$. The program is presented in a Pascal-like programming language called Numerical Turing which has special facilities for scientific computing, including precision control, directed roundings, and built-in functions for getting and setting exponents.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; decimal floating-point arithmetic; theory; verification", review = "ACM CR 8702-0091", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification.", } @Article{Dolk:1986:GMM, author = "Daniel R. Dolk", title = "A Generalized Model Management System for Mathematical Programming", journal = j-TOMS, volume = "12", number = "2", pages = "92--126", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.6501", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:18:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p92-dolk/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "human factors; languages; management", review = "ACM CR 8705-0407", subject = "{\bf H.4.2}: Information Systems, INFORMATION SYSTEMS APPLICATIONS, Types of Systems, Decision support. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Applicative languages. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Nonprocedural languages. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, XMP. {\bf H.2.3}: Information Systems, DATABASE MANAGEMENT, Languages, Query languages. {\bf H.2.4}: Information Systems, DATABASE MANAGEMENT, Systems, Query processing. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, User interfaces. {\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Applications and Expert Systems, GXMP. {\bf I.2.4}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods.", } @Article{Liu:1986:CRS, author = "Joseph W. H. Liu", title = "A Compact Row Storage Scheme for {Cholesky} Factors Using Elimination Trees", journal = j-TOMS, volume = "12", number = "2", pages = "127--148", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.6499", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65F50)", MRnumber = "863 787", bibdate = "Sun Sep 04 21:18:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p127-liu/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; measurement; performance; theory; verification", review = "ACM CR 8703-0191", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory.", } @Article{Springer:1986:AES, author = "J{\"o}rn Springer", title = "{Algorithm 641}: Exact Solution of General Systems of Linear Equations", journal = j-TOMS, volume = "12", number = "2", pages = "149--149", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.356167", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 21:19:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hutchinson:1986:AFP, author = "M. F. Hutchinson", title = "{Algorithm 642}: a Fast Procedure for Calculating Minimum Cross-Validation Cubic Smoothing Splines", journal = j-TOMS, volume = "12", number = "2", pages = "150--153", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.214322", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D10 (65D07)", MRnumber = "863 788", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p150-hutchinson/", abstract = "The procedure CUBGCV is an implementation of a recently developed algorithm for fast $O(n)$ calculation of a cubic smoothing spline fitted to $n$ noisy data points, with the degree of smoothing chosen to minimize the expected mean square error at the data points when the variance of the error associated with the data is known, or, to minimize the generalized cross validation (GCV) when the variance of the error associated with the data is unknown. The data may be unequally spaced and nonuniformly weighted. The algorithm exploits the banded structure of the matrices associated with the cubic smoothing spline problem. Bayesian point error estimates are also calculated in $O(n)$ operations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Mehta:1986:AFF, author = "Cyrus R. Mehta and Nitin R. Patel", title = "{Algorithm 643}: {FEXACT}: {A FORTRAN} Subroutine for {Fisher}'s Exact Test on Unordered $r\times c$ Contingency Tables", journal = j-TOMS, volume = "12", number = "2", pages = "154--161", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.214326", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65U05", MRnumber = "863 789", bibdate = "Tue Mar 9 10:27:54 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Clarkson:1993:RAF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p154-mehta/", abstract = "The computer code for Mehta and Patel's (1983) network algorithm for Fisher's exact test on unordered $r\times c$ contingency tables is provided. The code is written in double precision FORTRAN 77. This code provides the fastest currently available method for executing Fisher's exact test, and is shown to be orders of magnitude superior to any other available algorithm. Many important details of data structures and implementation that have contributed crucially to the success of the network algorithm are recorded here.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{McKeown:1986:IIU, author = "G. P. McKeown", title = "Iterated Interpolation Using a Systolic Array", journal = j-TOMS, volume = "12", number = "2", pages = "162--170", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.6500", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p162-mckeown/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", review = "ACM CR 8703-0161", subject = "{\bf B.6.1}: Hardware, LOGIC DESIGN, Design Styles, Cellular arrays and automata. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Krogh:1986:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "12", number = "2", pages = "171--174", month = jun, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/6497.356171", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:20:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hall:1986:ESR, author = "George Hall", title = "Equilibrium States of {Runge--Kutta} Schemes: {Part II}", journal = j-TOMS, volume = "12", number = "3", pages = "183--192", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.7922", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "88e:65087", bibdate = "Sun Sep 04 21:21:39 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p183-hall/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", reviewer = "Henning Esser", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Enright:1986:IRK, author = "W. H. Enright and K. R. Jackson and S. P. N{\o}rsett and P. G. Thomsen", title = "Interpolants for {Runge--Kutta} Formulas", journal = j-TOMS, volume = "12", number = "3", pages = "193--218", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.7923", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D07 (65L05)", MRnumber = "889 066", bibdate = "Sun Sep 04 21:21:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p193-enright/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8707-0591", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Kallay:1986:PCM, author = "Michael Kallay", title = "Plane Curves of Minimal Energy", journal = j-TOMS, volume = "12", number = "3", pages = "219--222", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.7924", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "53A04 (58E10 73K05)", MRnumber = "89c:53002", bibdate = "Sun Sep 04 21:22:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p219-kallay/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8706-0499", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Skeel:1986:NBL, author = "Robert D. Skeel and Thu V. Vu", title = "Note on Blended Linear Multistep Formulas", journal = j-TOMS, volume = "12", number = "3", pages = "223--224", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.7925", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p223-skeel/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods.", } @Article{Sagie:1986:CAM, author = "Ike Sagie", title = "Computer-Aided Modeling and Planning ({CAMP})", journal = j-TOMS, volume = "12", number = "3", pages = "225--248", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.15667", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p225-sagie/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "economics; languages; management", review = "ACM CR 8710-0893", subject = "{\bf J.6}: Computer Applications, COMPUTER-AIDED ENGINEERING, Computer-aided design (CAD). {\bf H.2.3}: Information Systems, DATABASE MANAGEMENT, Languages. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf H.1.2}: Information Systems, MODELS AND PRINCIPLES, User/Machine Systems, Human factors. {\bf I.6.2}: Computing Methodologies, SIMULATION AND MODELING, Simulation Languages. {\bf I.2.7}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Natural Language Processing.", } @Article{Liu:1986:SRC, author = "Joseph W. H. Liu", title = "On the Storage Requirement in the Out-of-Core Multifrontal Method for Sparse Factorization", journal = j-TOMS, volume = "12", number = "3", pages = "249--264", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.11325", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50", MRnumber = "889 068", bibdate = "Sun Sep 04 21:23:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p249-liu/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", review = "ACM CR 8709-0776", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Amos:1986:APP, author = "D. E. Amos", title = "{Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order", journal = j-TOMS, volume = "12", number = "3", pages = "265--273", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.214331", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "889 069", bibdate = "Tue Mar 09 10:26:27 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/", abstract = "This algorithm is a package of subroutines for Computing Bessel functions $H_{v}^{(1)}(z)$, $H_{v}^{(2)}(z)$, $I_{v}(z)$, $J_{v}(z)$, $K_{v}(z)$, $Y_{v}(z)$ and Airy functions $\mbox{Ai}(z)$, $\mbox{Ai}'(z)$, $\mbox{Bi}(z)$, $\mbox{Bi}'(z)$ for orders $v \geq 0$ and complex $z$ in $-\pi< \mbox{arg} z \leq \pi$. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Nash:1986:AST, author = "J. C. Nash and R. L. C. Wang", title = "{Algorithm 645}: Subroutines for Testing Programs that Compute the Generalized Inverse of a Matrix", journal = j-TOMS, volume = "12", number = "3", pages = "274--277", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.214334", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F20", MRnumber = "889 070", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p274-nash/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Crawford:1986:APR, author = "Charles R. Crawford", title = "{Algorithm 646}: {PDFIND}: a Routine to Find a Positive Definite Linear Combination of Two Real Symmetric Matrices", journal = j-TOMS, volume = "12", number = "3", pages = "278--282", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.214335", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F30", MRnumber = "889 071", bibdate = "Sun Sep 04 21:24:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p278-crawford/", abstract = "PDFIND is a FORTRAN-77 implementation of an algorithm that finds a positive definite linear combination of two symmetric matrices, or determines that such a combination does not exist. The algorithm is designed to be independent of the data structures used to store the matrices. The user must provide a subroutine, CHLSKY, which acts as an interface between PDFIND and the matrix data structures. CHLSKY also provides the user control over the number of iterations of the algorithm. Implementations of CHLSKY are included which call LINPAC routines for full matrices as well as symmetric banded matrices.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; geig; nla; symmetric matrix", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Hake:1986:RCC, author = "J.-Fr. Hake", title = "Remark on ``{Algorithm} 569: {COLSYS}: Collocation Software for Boundary-Value {ODEs} [{D2}]''", journal = j-TOMS, volume = "12", number = "3", pages = "283--284", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.356181", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:16:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ascher:1981:ACC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Stewart:1986:CNC, author = "G. W. Stewart", title = "Corrigendum: ``{A} Note on Complex Division''", journal = j-TOMS, volume = "12", number = "3", pages = "285--285", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.356182", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:17:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Stewart:1985:NCD}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Milovanovic:1986:CEI, author = "G. V. Milovanovi{\'c} and M. S. Petkovi{\'c}", title = "On Computational Efficiency of the Iterative Methods for the Simultaneous Approximation of Polynomial Zeros", journal = j-TOMS, volume = "12", number = "4", pages = "295--306", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.8932", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:39:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p274-milovanovic/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "measurement; performance", review = "ACM CR 8707-0590", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods.", } @Article{Nazareth:1986:IAO, author = "J. L. Nazareth", title = "Implementation Aids for Optimization Algorithms that Solve Sequences of Linear Programs", journal = j-TOMS, volume = "12", number = "4", pages = "307--323", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.22959", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:29:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p307-nazareth/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; languages", review = "ACM CR 8708-0686", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Modules and interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.", } @Article{Cowell:1986:TFD, author = "Wayne R. Cowell and Christopher P. Thompson", title = "Transforming {Fortran DO} Loops to Improve Performance on Vector Architectures", journal = j-TOMS, volume = "12", number = "4", pages = "324--353", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.24035", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:30:12 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p324-cowell/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages; performance", review = "ACM CR 8712-0989", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors.", } @Article{Ostermann:1986:SCP, author = "A. Ostermann and P. Kaps and T. D. Bui", title = "The Solution of a Combustion Problem with {Rosenbrock} Methods", journal = j-TOMS, volume = "12", number = "4", pages = "354--361", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.22722", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:30:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p354-ostermann/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Method of lines.", } @Article{Fox:1986:AIR, author = "Bennett L. Fox", title = "{Algorithm 647}: Implementation and Relative Efficiency of Quasirandom Sequence Generators", journal = j-TOMS, volume = "12", number = "4", pages = "362--376", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.356187", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 10:43:26 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DiDonato:1986:CIG, author = "Armido R. DiDonato and Alfred H. {Morris, Jr.}", title = "Computation of the Incomplete Gamma Function Ratios and Their Inverse", journal = j-TOMS, volume = "12", number = "4", pages = "377--393", month = dec, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/22721.23109", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:31:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p377-didonato/", abstract = "An algorithm is given for computing the incomplete gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $ a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An extensive set of coefficients for the Temme expansions is included.\par An algorithm, employing third-order Schr{\"o}der iteration supported by Newton-Raphson iteration, is provided for computing $x$ when $a$, $ P(a, x) $, and $ Q(a, x) $ are given. Three iterations at most are required to obtain 10 significant digit accuracy for $x$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8709-0775", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Enright:1987:TFP, author = "W. H. Enright and J. D. Pryce", title = "Two {FORTRAN} Packages for Assessing Initial Value Methods", journal = j-TOMS, volume = "13", number = "1", pages = "1--27", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.27645", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Enright:1989:CFP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p1-enright/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", review = "ACM CR 8803-0208", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Enright:1987:ANS, author = "W. H. Enright and J. D. Pryce", title = "{Algorithm 648}: {NSDTST} and {STDTST}: Routines for Assessing the Performance of {IV} Solvers", journal = j-TOMS, volume = "13", number = "1", pages = "28--34", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.214338", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 21:32:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p28-enright/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Alagar:1987:FLS, author = "Vangalur S. Alagar and David K. Probst", title = "A Fast, Low-Space Algorithm for Multiplying Dense Multivariate Polynomials", journal = j-TOMS, volume = "13", number = "1", pages = "35--57", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.27646", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:32:38 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p35-alagar/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", review = "ACM CR 8802-0114", subject = "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", } @Article{Vitter:1987:EAS, author = "Jeffrey Scott Vitter", title = "An Efficient Algorithm for Sequential Random Sampling", journal = j-TOMS, volume = "13", number = "1", pages = "58--67", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.23003", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:32:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p58-vitter/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance", review = "ACM CR 8808-0614", subject = "{\bf F.2.m}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Miscellaneous. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Foley:1987:IIP, author = "Thomas A. Foley", title = "Interpolation with Interval and Point Tension Controls Using Cubic Weighted $v$-Splines", journal = j-TOMS, volume = "13", number = "1", pages = "68--96", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.23004", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D07 (65D05 65D10)", MRnumber = "88h:65023", bibdate = "Sat Nov 19 13:08:26 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Foley:1988:CIP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p68-foley/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8802-0098", reviewer = "K. Jetter", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Giunta:1987:APC, author = "G. Giunta and A. Murli", title = "{Algorithm 649}: a Package for Computing Trigonometric {Fourier} Coefficients Based on {Lyness}'s Algorithm", journal = j-TOMS, volume = "13", number = "1", pages = "97--107", month = mar, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/23002.214339", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p97-giunta/", abstract = "We present a package that allows the computation of the trigonometric Fourier coefficients of a smooth function. The function can be provided as a subprogram or as a data list of function values at equally spaced points.\par The computational cost of the algorithm does not depend on the required number of Fourier coefficients. Numerical results of comparative tests with a standard integrator for oscillatory functions are also reported.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation.", } @Article{Dyksen:1987:IEI, author = "Wayne R. Dyksen and Calvin J. Ribbens", title = "Interactive {ELLPACK}: An Interactive Problem-Solving Environment for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "13", number = "2", pages = "113--132", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328515", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N99 (65V05)", MRnumber = "88g:65127", bibdate = "Sun Sep 04 21:35:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "W. C. Rheinboldt", } @Article{Pardalos:1987:GLS, author = "Panos M. Pardalos", title = "Generation of Large-Scale Quadratic Programs for Use as Global Optimization Test Problems", journal = j-TOMS, volume = "13", number = "2", pages = "133--137", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328516", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "49D40 (90C30 93A15)", MRnumber = "88h:49057", bibdate = "Sun Sep 04 21:35:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "G. Di Pillo", } @Article{Johnson:1987:AES, author = "Kenneth C. Johnson", title = "{Algorithm 650}: Efficient Square Root Implementation on the 68000", journal = j-TOMS, volume = "13", number = "2", pages = "138--151", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328520", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15", MRnumber = "898 489", bibdate = "Sun Sep 4 21:36:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Johnson:1987:CES}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morgan:1987:BBS, author = "Alexander Morgan and Vadim Shapiro", title = "Box-Bisection for Solving Second-Degree Systems and the Problem of Clustering", journal = j-TOMS, volume = "13", number = "2", pages = "152--167", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328521", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "88e:65063", bibdate = "Sat Nov 19 13:08:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Morgan:1987:CBS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Monahan:1987:AGC, author = "John F. Monahan", title = "An Algorithm for Generating Chi Random Variables", journal = j-TOMS, volume = "13", number = "2", pages = "168--172", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328522", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10", MRnumber = "88d:65013", bibdate = "Sat Nov 19 13:08:24 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Liu:1987:PPS, author = "Joseph W. H. Liu", title = "A Partial Pivoting Strategy for Sparse Symmetric Matrix Decomposition", journal = j-TOMS, volume = "13", number = "2", pages = "173--182", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328525", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65F50)", MRnumber = "88f:65046", bibdate = "Sun Sep 04 21:35:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", reviewer = "R. P. Tewarson", } @Article{Krogh:1987:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "13", number = "2", pages = "183--186", month = jun, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/328512.328526", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:35:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kearfott:1987:STG, author = "R. Baker Kearfott", title = "Some Tests of Generalized Bisection", journal = j-TOMS, volume = "13", number = "3", pages = "197--220", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.29862", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "88m:65081", bibdate = "Sat Nov 19 13:08:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Kearfott:1988:CTG}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p197-kearfott/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for.", } @Article{Boisvert:1987:FOA, author = "Ronald F. Boisvert", title = "A Fourth-Order-Accurate {Fourier} Method for the {Helmholtz} Equation in Three Dimensions", journal = j-TOMS, volume = "13", number = "3", pages = "221--234", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.29863", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N05", MRnumber = "88m:65149", bibdate = "Sun Sep 04 21:39:43 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p221-boisvert/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory; verification", review = "ACM CR 8808-0622", reviewer = "Ian Gladwell", subject = "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations \\ G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis", } @Article{Boisvert:1987:AAH, author = "Ronald F. Boisvert", title = "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order Fast-Direct Solution of the {Helmholtz} Equation", journal = j-TOMS, volume = "13", number = "3", pages = "235--249", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.214342", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65V05", MRnumber = "918 578", bibdate = "Sun Sep 4 21:40:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Johnson:1987:CES}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/", abstract = "HFFT is a software package for solving the Helmholtz equation on bounded two- and three-dimensional rectangular domains with Dirichlet, Neumann, or periodic boundary conditions. The software is the result of combining new fourth-order accurate compact finite difference (HODIE) discretizations and a fast-direct solution technique (the Fourier method). In this paper we briefly describe the user interface to HFFT and present an example of its usage and several details of its implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory; verification", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Liu:1987:TPM, author = "Joseph W. H. Liu", title = "On Threshold Pivoting in the Multifrontal Method for Sparse Indefinite Systems", journal = j-TOMS, volume = "13", number = "3", pages = "250--261", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.31331", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65F05)", MRnumber = "88j:65089", bibdate = "Sun Sep 04 21:40:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p250-liu/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; theory", review = "ACM CR 8804-0281", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Corana:1987:MMF, author = "A. Corana and M. Marchesi and C. Martini and S. Ridella", title = "Minimizing Multimodal Functions of Continuous Variables with the {``Simulated Annealing''} Algorithm", journal = j-TOMS, volume = "13", number = "3", pages = "262--280", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.29864", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C30 (65K05)", MRnumber = "88m:90121", bibdate = "Sat Nov 19 13:08:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Corana:1989:CMF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p262-corana/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", review = "ACM CR 8804-0282", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching.", } @Article{Watson:1987:AHS, author = "Layne T. Watson and Stephen C. Billups and Alexander P. Morgan", title = "{Algorithm 652}: {HOMPACK}: a Suite of Codes for Globally Convergent Homotopy Algorithms", journal = j-TOMS, volume = "13", number = "3", pages = "281--310", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.214343", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65V05 (58C30 65H10 90C30)", MRnumber = "918 581", bibdate = "Sun Sep 4 21:41:46 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p281-watson/", abstract = "There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Hanson:1987:ATA, author = "R. J. Hanson and F. T. Krogh", title = "{Algorithm 653}: Translation of {Algorithm} 539: {PC-BLAS Basic Linear Algebra Subprograms} for {FORTRAN} Usage with the {INTEL} 8087, 80287 Numeric Data Processor", journal = j-TOMS, volume = "13", number = "3", pages = "311--317", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.214346", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 23:07:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Louter-Nool:1988:ATA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p311-hanson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DiDonato:1987:AFS, author = "Armido R. DiDonato and Alfred H. {Morris, Jr.}", title = "{Algorithm 654}: {FORTRAN} Subroutines for Computing the Incomplete Gamma Function Ratios and their Inverse", journal = j-TOMS, volume = "13", number = "3", pages = "318--319", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.214348", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 21:43:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/pdf/10.1145/29380.214348", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Johnson:1987:CES, author = "Kenneth C. Johnson", title = "Corrigendum: {``Algorithm 650: efficient square root implementation on the 68000'' [{ACM} Trans. Math. Software {\bf 13} (1987), no. 2, 138--151]}", journal = j-TOMS, volume = "13", number = "3", pages = "320--320", month = sep, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/29380.356210", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "320. 65D15", MRnumber = "918 582", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bar-On:1987:PPA, author = "Ilan Bar-On", title = "A Practical Parallel Algorithm for Solving Band Symmetric Positive Definite Systems of Linear Equations", journal = j-TOMS, volume = "13", number = "4", pages = "323--332", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.35079", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65W05)", MRnumber = "88m:65048", bibdate = "Sun Sep 04 21:45:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p323-bar-on/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Schoenauer:1987:SCB, author = "Willi Sch{\"o}nauer and Eric Schnepf", title = "Software Considerations for the ``Black Box'' Solver {FIDISOL} for Partial Differential Equations", journal = j-TOMS, volume = "13", number = "4", pages = "333--349", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.35080", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p333-schonauer/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", review = "ACM CR 8809-0699", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Parabolic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, FIDOSOL.", } @Article{Ahlfeld:1987:NPG, author = "David P. Ahlfeld and John M. Mulvey and Ron S. Dembo and Stavros A. Zenios", title = "Nonlinear Programming on Generalized Networks", journal = j-TOMS, volume = "13", number = "4", pages = "350--367", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.42181", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C35 (90C30)", MRnumber = "89b:90218", bibdate = "Sun Sep 04 21:47:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p350-ahlfeld/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8810-0796", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems.", } @Article{Haas:1987:MPR, author = "Alexander Haas", title = "The Multiple Prime Random Number Generator", journal = j-TOMS, volume = "13", number = "4", pages = "368--381", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.214349", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10", MRnumber = "89h:65018", bibdate = "Sun Sep 04 21:45:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p368-haas/", abstract = "A new pseudorandom number generator, the Multiple Prime Random Number Generator, has been developed; it is efficient, conceptually simple, flexible, and easy to program. The generator utilizes cycles around prime numbers to guarantee the length of the period, which can easily be programmed to surpass the maximum period of any other presently available random number generator. There are minimum limits placed on the seed values of the variables because the period of the generator is not a function of the initial values of the variables. The generator passes thirteen standard random number generator tests. It requires only about fifteen lines of FORTRAN code to program and utilizes programming language constructs found in most major languages. Finally, it compares very favorably to the fastest of the other available generators.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; economics; experimentation; performance; reliability", reviewer = "Brian Conolly", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf I.6.3}: Computing Methodologies, SIMULATION AND MODELING, Applications. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Economics. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Sociology.", } @Article{Schneider:1987:EEA, author = "Michael H. Schneider", title = "The Expanding Equilibrium Algorithm", journal = j-TOMS, volume = "13", number = "4", pages = "382--398", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.42322", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:48:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p382-schneider/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; economics; performance", review = "ACM CR 8812-0937", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Economics.", } @Article{Elhay:1987:AIF, author = "Sylvan Elhay and Jaroslav Kautsky", title = "{Algorithm 655}: {IQPACK}: {FORTRAN} Subroutines for the Weights of Interpolatory Quadratures", journal = j-TOMS, volume = "13", number = "4", pages = "399--415", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.214351", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 21:49:00 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p399-elhay/", abstract = "We present FORTRAN subroutines that implement the method described in [3] for the stable evaluation of the weights of interpolatory quadratures with prescribed simple or multiple knots. Given a set of knots and their multiplicities, the package generates the weights by using the zeroth moment $\mu_{0}$ of $w$, the weight function in the integrand, and the (symmetric tridiagonal) Jacobi matrix $J$ associated with the polynomials orthogonal on $(a, b)$ with respect to $w$. There are utility routines that generate $\mu_{0}$ and $J$ for classical weight functions, but quadratures can be generated for any $\mu_{0}$ and $J$ supplied by the user. Utility routines are also provided that (1) evaluate a computed quadrature, applied to a user-supplied integrand, (2) check the polynomial order of precision of a quadrature formula, and (3) compute the knots and weights of simple Gaussian quadrature formula.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature.", } @Article{Morgan:1987:CBS, author = "Alexander Morgan and Vadim Shapiro", title = "Corrigendum: ``{Box-Bisection} for Solving Second-Degree Systems and the Problem of Clustering''", journal = j-TOMS, volume = "13", number = "4", pages = "416--416", month = dec, year = "1987", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/35078.356217", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H10", MRnumber = "89a:65088, 88e:65063", bibdate = "Sun Sep 04 21:45:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Morgan:1987:BBS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dongarra:1988:ESF, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Richard J. Hanson", title = "An Extended Set of {FORTRAN Basic Linear Algebra Subprograms}", journal = j-TOMS, volume = "14", number = "1", pages = "1--17", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42291", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Dongarra:1988:CES}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p1-dongarra/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; standardization", review = "ACM CR 8812-0940", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Dongarra:1988:AES, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Richard J. Hanson", title = "{Algorithm 656}: An Extended Set of {Basic Linear Algebra Subprograms}: Model Implementation and Test Programs", journal = j-TOMS, volume = "14", number = "1", pages = "18--32", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42292", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:52:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p18-dongarra/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; BLAS; nla; software; theory; vect", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Sewell:1988:PCS, author = "Granville Sewell", title = "Plotting Contour Surfaces of a Function of Three Variables", journal = j-TOMS, volume = "14", number = "1", pages = "33--41", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42289", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65S05", MRnumber = "89c:65140", bibdate = "Sun Sep 04 21:53:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p33-sewell/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", review = "ACM CR 8810-0795", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Sewell:1988:ASP, author = "Granville Sewell", title = "{Algorithm 657}: Software for Plotting Contour Surfaces of a Function of Three Variables", journal = j-TOMS, volume = "14", number = "1", pages = "42--44", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42290", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 15:08:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Sewell:1990:RSP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p42-sewell/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Leis:1988:SSS, author = "Jorge R. Leis and Mark A. Kramer", title = "The Simultaneous Solution and Sensitivity Analysis of Systems Described by Ordinary Differential Equations", journal = j-TOMS, volume = "14", number = "1", pages = "45--60", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.46156", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65V05)", MRnumber = "89b:65176", bibdate = "Sun Sep 04 21:54:22 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p45-leis/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance; reliability; theory", review = "ACM CR 8903-0152", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Leis:1988:AOO, author = "Jorge R. Leis and Mark A. Kramer", title = "{Algorithm 658}: {ODESSA}: An Ordinary Differential Equation Solver with Explicit Simultaneous Sensitivity Analysis", journal = j-TOMS, volume = "14", number = "1", pages = "61--67", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.214371", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p61-leis/", abstract = "ODESSA is a package of FORTRAN routines for simultaneous solution of ordinary differential equations and the associated first-order parametric sensitivity equations, yielding the ODE solution vector $\underline{y}(t)$ and the first-order sensitivity coefficients with respect to equation parameters $\underline{p}$, $\partial \underline{y}(t)/\partial \underline{p}$. ODESSA is a modification of the widely disseminated initial-value solver LSODE, and retains many of the same operational features. Standard program usage and optional capabilities, installation, and verification considerations are addressed herein.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Butcher:1988:TEI, author = "J. C. Butcher", title = "Towards Efficient Implementation of Singly-Implicit Methods", journal = j-TOMS, volume = "14", number = "1", pages = "68--75", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42341", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "89b:65167", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p68-butcher/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", review = "ACM CR 8812-0938", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Ammann:1988:RCR, author = "Larry Ammann and John {Van Ness}", title = "A Routine for Converting Regression Algorithms into Corresponding Orthogonal Regression Algorithms", journal = j-TOMS, volume = "14", number = "1", pages = "76--87", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42342", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65U05", MRnumber = "944 765", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p76-ammann/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability", review = "ACM CR 8903-0155", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Bratley:1988:AIS, author = "Paul Bratley and Bennett L. Fox", title = "{Algorithm 659}: Implementing {Sobol}'s Quasirandom Sequence Generator", journal = j-TOMS, volume = "14", number = "1", pages = "88--100", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.214372", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p88-bratley/", abstract = "We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol' generator.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Robertazzi:1988:BOF, author = "T. G. Robertazzi and S. C. Schwartz", title = "Best ``Ordering'' for Floating-Point Addition", journal = j-TOMS, volume = "14", number = "1", pages = "101--110", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.42343", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G99 (65V05)", MRnumber = "89b:65117", bibdate = "Sat Nov 19 13:08:22 1994", bibsource = "ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/", acknowledgement = ack-nhfb, affiliation = "State Univ. of New York at Stony Brook, Stony Brook; Princeton Univ., Princeton, NJ", ajournal = "ACM Trans. Math. Softw.", bibno = "42343", catcode = "G.1.0", content = "This paper compares a variety of methods for accumulating a floating-point sum. Wilkinson pointed out that if we compute the $\sum^n_{i = 1} x_i$ in strictly increasing order in magnitude of the $x_i$, then we obtain a better bound on the rounding error than if the sum is computed in random order [1].\par The authors discuss five different accumulation strategies. They compare these accumulation strategies for when the $x_i$ are uniformly distributed and for when they are exponentially distributed. First they compare a random order for summing the $x_i$, summing in decreasing order of magnitude, and summing in increasing order of magnitude. Not surprisingly, summing in increasing order of magnitude is the best and summing in decreasing order of magnitude is the worst. In fact, it is not difficult to show this for any class of distributions where the mean and variance exist.\par The interesting results in the paper concern two other accumulation strategies. Both of these are shown to be better than summing in increasing order of magnitude for both the uniform and exponential distribution. Fortunately, one of these strategies is the tree sum (or fan-in sum) that is often used in parallel computation. The paper calls this strategy the ``adjacency'' ordering.", CRclass = "G.1.0 General; G.1.0 Computer arithmetic", CRnumber = "8810-0794", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic", fjournal = "ACM Transactions on Mathematical Software (TOMS)", genterm = "ALGORITHMS; PERFORMANCE", journal-URL = "https://dl.acm.org/loi/toms", journalabbrev = "ACM Trans. Math. Softw.", keywords = "accurate floating-point summation; algorithms; performance", review = "ACM CR 8810-0794", reviewer = "Jesse L. Barlow", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic", } @Article{Monahan:1988:CAG, author = "John F. Monahan", title = "Corrigendum: ``{An} Algorithm for Generating Chi Random Variables''", journal = j-TOMS, volume = "14", number = "1", pages = "111--111", month = mar, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/42288.356228", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "111. 65C10", MRnumber = "89d:65006, 88d:65013", bibdate = "Fri Mar 28 10:45:16 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Monahan:1987:AGC}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Melhem:1988:MRS, author = "Rami G. Melhem and K. V. S. Ramarao", title = "Multicolor Reordering of Sparse Matrices Resulting from Irregular Grids", journal = j-TOMS, volume = "14", number = "2", pages = "117--138", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.214373", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65D30)", MRnumber = "90b:65084", bibdate = "Mon Dec 08 12:15:02 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p117-melhem/", abstract = "Many iterative algorithms for the solution of large linear systems may be effectively vectorized if the diagonal of the matrix is surrounded by a large band of zeroes, whose width is called the zero stretch. In this paper, a multicolor numbering technique is suggested for maximizing the zero stretch of irregularly sparse matrices. The technique, which is a generalization of a known multicoloring algorithm for regularly sparse matrices, executes in linear time, and produces a zero stretch approximately equal to $n/2\sigma$, where $2\sigma$ is the number of colors used in the algorithm. For triangular meshes, it is shown that $\sigma \leq 3$, and that it is possible to obtain $\sigma=2$ by applying a simple backtracking scheme.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", reviewer = "Stephen W. Brady", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Iterative methods. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Renka:1988:MIL, author = "Robert J. Renka", title = "Multivariate Interpolation of Large Sets of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "139--148", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.45055", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (41A05)", MRnumber = "89d:65009", bibdate = "Sun Sep 04 22:00:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p139-renka/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8903-0148", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1988:AQQa, author = "Robert J. Renka", title = "{Algorithm 660}: {QSHEP2D}: Quadratic {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "149--150", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.356231", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 10:45:50 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:1988:AQQb, author = "Robert J. Renka", title = "{Algorithm 661}: {QSHEP3D}; Quadratic {Shepard} Method for Trivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "151--152", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.214374", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p151-renka/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Wan:1988:AMD, author = "S. J. Wan and S. K. M. Wong and P. Prusinkiewicz", title = "An Algorithm for Multidimensional Data Clustering", journal = j-TOMS, volume = "14", number = "2", pages = "153--162", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.45056", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:00:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p153-wan/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", review = "ACM CR 8912-0911", subject = "{\bf I.5.3}: Computing Methodologies, PATTERN RECOGNITION, Clustering, Algorithms.", } @Article{Garbow:1988:SIW, author = "B. S. Garbow and G. Giunta and J. N. Lyness and A. Murli", title = "Software for an Implementation of {Weeks}' Method for the Inverse {Laplace} Transform", journal = j-TOMS, volume = "14", number = "2", pages = "163--170", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.45057", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R10 (65V05)", MRnumber = "89d:65107", bibdate = "Sun Sep 04 22:01:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p163-garbow/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8903-0153", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Fredholm equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Finite difference methods.", } @Article{Garbow:1988:AFS, author = "B. S. Garbow and G. Giunta and J. N. Lyness and A. Murli", title = "{Algorithm 662}: {A FORTRAN} Software Package for the Numerical Inversion of the {Laplace} Transform Based on {Weeks}' Method", journal = j-TOMS, volume = "14", number = "2", pages = "171--176", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.214375", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 23:29:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Garbow:1990:RFS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p171-garbow/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Louter-Nool:1988:ATA, author = "Margreet Louter-Nool", title = "{Algorithm 663}: Translation of {Algorithm} 539: {Basic Linear Algebra Subprograms} for {FORTRAN} Usage in {FORTRAN} 200 for the {Cyber} 205", journal = j-TOMS, volume = "14", number = "2", pages = "177--195", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.45058", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 23:08:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p177-louter-nool/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", review = "ACM CR 8904-0243", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Diaz:1988:RCA, author = "J. C. Diaz and G. Fairweather and P. Keast", title = "Remark on ``{Algorithm} 603: {COLROW} and {ARCECO}: {FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination''", journal = j-TOMS, volume = "14", number = "2", pages = "196--196", month = jun, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/45054.356237", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 21:59:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Diaz:1983:ACA}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hull:1988:EHS, author = "T. E. Hull and M. S. Cohen and J. T. M. Sawshuk and D. B. Wortman", title = "Exception Handling in Scientific Computing", journal = j-TOMS, volume = "14", number = "3", pages = "201--217", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.44129", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:27:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p201-hull/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; languages", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Specialized application languages. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Run-time environments. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Freeman:1988:DSM, author = "Timothy S. Freeman and Gregory M. Imirzian and Erich Kaltofen and Lakshman Yagati", title = "{Dagwood}: a System for Manipulating Polynomials Given by Straight-Line Programs", journal = j-TOMS, volume = "14", number = "3", pages = "218--240", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.214376", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p218-freeman/", abstract = "We discuss the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations. Our system is capable of performing rational arithmetic on, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials in straight-line format. The straight-line results can also be converted to standard, sparse format. We show by example that our system can handle problems for which conventional methods lead to excessive intermediate expression swell.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; measurement; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", } @Article{Grimes:1988:SLD, author = "Roger G. Grimes and Horst D. Simon", title = "Solution of Large, Dense Symmetric Generalized Eigenvalue Problems Using Secondary Storage", journal = j-TOMS, volume = "14", number = "3", pages = "241--256", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.44130", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F15)", MRnumber = "1 062 476", bibdate = "Sun Sep 04 22:29:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p241-grimes/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", review = "ACM CR 8903-0149", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf D.4.2}: Software, OPERATING SYSTEMS, Storage Management, Secondary storage.", } @Article{Schrauf:1988:AGA, author = "G{\'e}za Schrauf", title = "{Algorithm 664}: {A Gauss} Algorithm to Solve Systems with Large Banded Matrices Using Random-Access Disk Storage", journal = j-TOMS, volume = "14", number = "3", pages = "257--260", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.214379", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p257-schrauf/", abstract = "A FORTRAN 77 implementation of a Gauss algorithm with partial pivoting for banded matrices is described. The algorithm keeps only part of the matrix that is necessary for the actual computation in memory. This allows large systems to be solved on machine without virtual memory, or if the virtual memory is too small for the problem.", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Minh:1988:GGV, author = "Do Le Minh", title = "Generating Gamma Variates", journal = j-TOMS, volume = "14", number = "3", pages = "261--266", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.214382", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65U05)", MRnumber = "1 062 477", bibdate = "Sun Sep 04 22:30:10 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p261-minh/", abstract = "An algorithm to generate variates having a gamma distribution with shape parameter greater than one is presented in this paper. This algorithm is faster than Schmeiser and Lal's G4PE, which is the fastest one currently available, yet is equally simple and easy to implement.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7672", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Duff:1988:RIN, author = "Iain S. Duff and Torbj{\"o}rn Wiberg", title = "Remarks on Implementation of ${O}(n^{1/2}\tau)$ Assignment Algorithms", journal = j-TOMS, volume = "14", number = "3", pages = "267--287", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.44131", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 062 478", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p267-duff/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8904-0244", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Cormack:1988:RTP, author = "R. S. Cormack and I. D. Hill", title = "Remark on ``{Algorithm} 346: ${F}$-Test Probabilities''", journal = j-TOMS, volume = "14", number = "3", pages = "288--289", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.356244", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Morris:1969:TP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:1988:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "14", number = "3", pages = "290--293", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.356245", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Foley:1988:CIP, author = "Thomas A. Foley", title = "Corrigendum: ``{Interpolation} with Interval and Point Tension Controls Using Cubic Weighted $v$-Splines''", journal = j-TOMS, volume = "14", number = "3", pages = "297--297", month = sep, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/44128.356246", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:26:45 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Foley:1987:IIP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cody:1988:AMS, author = "W. J. Cody", title = "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically Determine Machine Parameters", journal = j-TOMS, volume = "14", number = "4", pages = "303--311", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.51907", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:33:58 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/", acknowledgement = ack-nj # " and " # ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @Article{Vrahatis:1988:SSN, author = "Michael N. Vrahatis", title = "Solving Systems of Nonlinear Equations Using the Nonzero Value of the Topological Degree", journal = j-TOMS, volume = "14", number = "4", pages = "312--329", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.214384", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65H10 90C30)", MRnumber = "91g:65006", bibdate = "Sun Sep 04 22:34:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p312-vrahatis/", abstract = "Two algorithms are described here for the numerical solution of a system of nonlinear equations $F(X) = \Theta, Q=(0,0,\ldots,0)$ in $R$, and $F$ is a given continuous mapping of a region $D$ in $R^{n}$ into $R^{n}$. The first algorithm locates at least one root of the sy stem within $n$-dimensional polyhedron, using the nonzero value of the topological degree of $F$ at [theta] relative to the polyhedron; the second algorithm applies a new generalized bisection method in order to compute an approximate solution to the system. The size of the original $n$-dimensional polyhedron is arbitrary, and the method is globally convergent in a residual sense.\par These algorithms, in the various function evaluations, only make use of the algebraic sign of $F$ and do not require computations of the topological degree. Moreover, they can be applied to nondifferentiable continuous functions $F$ and do not involve derivatives of $F$ or approximations of such derivatives.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Vrahatis:1988:ACM, author = "Michael N. Vrahatis", title = "{Algorithm 666}: {CHABIS}: a Mathematical Software Package for Locating and Evaluating Roots of Systems of Nonlinear Equations", journal = j-TOMS, volume = "14", number = "4", pages = "330--336", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.51906", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (90C30)", MRnumber = "91g:65007", bibdate = "Sat Aug 27 15:08:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p330-vrahatis/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations.", } @Article{Garavelli:1988:AMS, author = "John S. Garavelli", title = "An Algorithm for the Multiplication of Symmetric Polynomials", journal = j-TOMS, volume = "14", number = "4", pages = "337--344", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.214385; http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p337-garavelli/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "05-04 (68Q40)", MRnumber = "91f:05002", bibdate = "Sun Sep 04 22:34:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Although the cycle index polynomial for a permutation group can often be easily determined, expansion of the figure counting series in a P{\'o}lya enumeration presents computational difficulties for object sets with higher degrees of symmetry and more than modest size. An algorithm that does not require algebraic symbol manipulation is derived for multiplying symmetric polynomials represented by partitions. Because the repetitive identification and collection of common terms are eliminated and storage requirements reduced, this algorithm is useful in rapidly expanding the figure counting series in such P{\'o}lya enumeration problems as the counting of chemical isomers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", reviewer = "Kevin Lawrence McAvaney", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @Article{Aluffi-Pentini:1988:GOA, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "A Global Optimization Algorithm Using Stochastic Differential Equations", journal = j-TOMS, volume = "14", number = "4", pages = "345--365", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.50064", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65K05 90C30)", MRnumber = "1 062 482", bibdate = "Sun Sep 04 22:36:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p345-aluffi-pentini/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages; theory; verification", review = "ACM CR 8907-0480", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Aluffi-Pentini:1988:ASE, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "{Algorithm 667}: {SIGMA}\emdash a Stochastic-Integration Global Minimization Algorithm", journal = j-TOMS, volume = "14", number = "4", pages = "366--380", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.51908", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (90C30)", MRnumber = "1 062 483", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p366-aluffi-pentini/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Higham:1988:AFC, author = "Nicholas J. Higham", title = "{Algorithm 674}: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation", journal = j-TOMS, volume = "14", number = "4", pages = "381--396", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.214386", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F35)", MRnumber = "1 062 484", bibdate = "Sat Aug 27 15:05:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Higham:1989:CFC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/", abstract = "FORTRAN 77 codes SONEST and CONEST are presented for estimating the 1-norm ( or the infinity-norm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, $A$, is not required; instead, matrix-vector products $Ax$ and $A^Tx$ are computed by the calling program via a reverse communication interface. The algorithms are based on a convex optimization method for estimating the 1-norm of a real matrix devised by Hager. We derive new results concerning the behavior of Hager's method, extend it to complex matrices, and make several algorithmic modifications in order to improve the reliability and efficiency.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; condition estimation; nla; software", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Kachitvichyanukul:1988:AHS, author = "Voratas Kachitvichyanukul and Bruce W. Schmeiser", title = "{Algorithm 668}: {H2PEC}: Sampling from the Hypergeometric Distribution", journal = j-TOMS, volume = "14", number = "4", pages = "397--398", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.214387", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 4 22:37:31 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p397-kachitvichyanukul/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Dongarra:1988:CES, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Richard J. Hanson", title = "Corrigenda: ``{An} Extended Set of {FORTRAN Basic Linear Algebra Subprograms}''", journal = j-TOMS, volume = "14", number = "4", pages = "399--399", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.356256", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 10:48:38 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Dongarra:1988:ESF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kearfott:1988:CTG, author = "R. Baker Kearfott", title = "Corrigenda: ``{Some} Tests of Generalized Bisection''", journal = j-TOMS, volume = "14", number = "4", pages = "399--399", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.356257", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "399 (1989). 65H10", MRnumber = "1 062 485, 88m:65081", bibdate = "Sat Nov 19 13:04:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Kearfott:1987:STG}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anonymous:1988:FCA, author = "Anonymous", title = "Five-Year Cumulative Author Index (Vol. 10--14. 1984--1988)", journal = j-TOMS, volume = "14", number = "4", pages = "403--411", month = dec, year = "1988", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/50063.356247", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "00A15", MRnumber = "1 062 486", bibdate = "Fri Mar 28 10:56:10 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:1989:SMT, author = "Iain S. Duff and Roger G. Grimes and John G. Lewis", title = "Sparse Matrix Test Problems", journal = j-TOMS, volume = "15", number = "1", pages = "1--14", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.62043", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:42:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p1-duff/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "measurement; performance", review = "ACM CR 9002-0143", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1989:BRK, author = "J. R. Cash", title = "A Block 6(4) {Runge--Kutta} Formula for Nonstiff Initial Value Problems", journal = j-TOMS, volume = "15", number = "1", pages = "15--28", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.62042", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:42:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p15-cash/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", review = "ACM CR 8909-0672", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Cash:1989:ABF, author = "J. R. Cash", title = "{Algorithm 669}: {BRKF45}: {A FORTRAN} Subroutine for Solving First-Order Systems of Nonstiff Initial Value Problems for Ordinary Differential Equations", journal = j-TOMS, volume = "15", number = "1", pages = "29--30", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.214388", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:44:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Higham:1991:RBF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p29-cash/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Brankin:1989:ARK, author = "R. W. Brankin and I. Gladwell and J. R. Dormand and P. J. Prince and W. L. Seward", title = "{Algorithm 670}: a {Runge--Kutta--Nystr{\"o}m} code", journal = j-TOMS, volume = "15", number = "1", pages = "31--40", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.69650", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p31-brankin/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Cody:1989:PEP, author = "W. J. Cody and L. Stoltz", title = "Performance Evaluation of Programs for Certain {Bessel} Functions", journal = j-TOMS, volume = "15", number = "1", pages = "41--48", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.62039", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:43:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p41-cody/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability; verification", review = "ACM CR 8911-0825", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Shanno:1989:NES, author = "David F. Shanno and Kang Hoh Phua", title = "Numerical Experience with Sequential Quadratic Programming Algorithms for Equality Constrained Nonlinear Programming", journal = j-TOMS, volume = "15", number = "1", pages = "49--63", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.62040", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C30 (90B20)", MRnumber = "91c:90104", bibdate = "Sun Sep 04 22:44:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p49-shanno/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 8909-0670", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization.", } @Article{Chang:1989:IPS, author = "Michael D. Chang and Chou-Hong J. Chen and Michael Engquist", title = "An Improved Primal Simplex Variant for Pure Processing Networks", journal = j-TOMS, volume = "15", number = "1", pages = "64--78", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.62041", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p64-chang/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance; theory", review = "ACM CR 8909-0669", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Preusser:1989:AFF, author = "Albrecht Preusser", title = "{Algorithm 671}: {FARB-E-2D}: Fill Area with Bicubics on Rectangles\emdash a Contour Plot Program", journal = j-TOMS, volume = "15", number = "1", pages = "79--89", month = mar, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/62038.69651", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:46:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p79-preusser/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Morgan:1989:FAI, author = "Alexander P. Morgan and Andrew J. Sommese and Layne T. Watson", title = "Finding All Isolated Solutions to Polynomial Systems Using {HOMPACK}", journal = j-TOMS, volume = "15", number = "2", pages = "93--122", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.64124", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (58C30 65H10)", MRnumber = "91g:65003", bibdate = "Sun Sep 04 22:46:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p93-morgan/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 8912-0895", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, HOMPACK. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for.", } @Article{Patterson:1989:AGIa, author = "T. N. L. Patterson", title = "An Algorithm for Generating Interpolatory Quadrature Rules of the Highest Degree of Precision with Preassigned Nodes for General Weight Functions", journal = j-TOMS, volume = "15", number = "2", pages = "123--136", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.63523", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D32)", MRnumber = "91g:65004", bibdate = "Sun Sep 04 22:46:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p123-patterson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 9006-0500", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @Article{Patterson:1989:AGIb, author = "T. N. L. Patterson", title = "{Algorithm 672}: Generation of Interpolatory Quadrature Rules of the Highest Degree of Precision with Preassigned Nodes for General Weight Functions", journal = j-TOMS, volume = "15", number = "2", pages = "137--143", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.69649", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04", MRnumber = "91g:65005", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p137-patterson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1989:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Exponential Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "15", number = "2", pages = "144--157", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.214389", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:47:40 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/", abstract = "Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.", acknowledgement = ack-nj, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Vitter:1989:ADH, author = "Jeffrey Scott Vitter", title = "{Algorithm 673}: Dynamic {Huffman} Coding", journal = j-TOMS, volume = "15", number = "2", pages = "158--167", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.214390", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:47:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Novoselsky:2016:RAD}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p158-vitter/", abstract = "We present a Pascal implementation of the one-pass algorithm for constructing dynamic Huffman codes that is described and analyzed in a companion paper. The program runs in real time; that is, the processing time for each letter of the message is proportional to the length of its codeword. The number of bits used to encode a message of $t$ letters is less than $t$ bits more than that used by the well-known two-pass algorithm. This is best possible for any one-pass Huffman scheme. In practice, it uses fewer bits than all other Huffman schemes. The algorithm has applications in file compression and network transmission.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance; theory", subject = "{\bf C.2.0}: Computer Systems Organization, COMPUTER-COMMUNICATION NETWORKS, General, Data communications. {\bf E.1}: Data, DATA STRUCTURES, Trees. {\bf E.4}: Data, CODING AND INFORMATION THEORY, Data compaction and compression. {\bf E.4}: Data, CODING AND INFORMATION THEORY, Nonsecret encoding schemes. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf H.1.1}: Information Systems, MODELS AND PRINCIPLES, Systems and Information Theory, Value of information.", } @Article{Higham:1989:CFC, author = "Nicholas J. Higham", title = "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation''", journal = j-TOMS, volume = "15", number = "2", pages = "168--168", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.214391", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:18:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Higham:1988:AFC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/", abstract = "We omitted giving this article an ACM algorithm number when it was first published in its entirety in the December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp. 381-396. To correct this, we do so here, and reprint the title as a pointer to the original article.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Krogh:1989:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "15", number = "2", pages = "169--172", month = jun, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/63522.356273", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 10:56:42 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ribbens:1989:FAG, author = "Calvin J. Ribbens", title = "A Fast Adaptive Grid Scheme for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "15", number = "3", pages = "179--197", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.66889", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:50:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p179-ribbens/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 9006-0506", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", } @Article{Liu:1989:GPA, author = "Joseph W. H. Liu", title = "A Graph Partitioning Algorithm by Node Separators", journal = j-TOMS, volume = "15", number = "3", pages = "198--219", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.66890", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (05-04 05C70 65F50)", MRnumber = "1 062 491", bibdate = "Sun Sep 04 22:51:08 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p198-liu/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 9003-0235", subject = "{\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Mahdavi-Amiri:1989:CNL, author = "Nezam Mahdavi-Amiri and Richard H. Bartels", title = "Constrained Nonlinear Least Squares: An Exact Penalty Approach with Projected Structured Quasi-{Newton} Updates", journal = j-TOMS, volume = "15", number = "3", pages = "220--242", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.66891", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 062 492", bibdate = "Sun Sep 04 22:51:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p220-mahdavi-amiri/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", review = "ACM CR 9004-0320", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations.", } @Article{Vanbegin:1989:AFS, author = "Michel Vanbegin and Paul {Van Dooren} and Michel Verhaegen", title = "{Algorithm 675}: {FORTRAN} Subroutines for Computing the Square Root Covariance Filter and Square Root Information Filter in Dense or {Hessenberg} Forms", journal = j-TOMS, volume = "15", number = "3", pages = "243--256", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.69647", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:52:41 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p243-vanbegin/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Dadurkevicius:1989:RA, author = "Virgis Dadurkevi{\v{c}}ius", title = "Remark on ``{Algorithm} 587: Two Algorithms for the Linearly Constrained Least Squares Problem''", journal = j-TOMS, volume = "15", number = "3", pages = "257--261", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.77344", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 20:52:30 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hanson:1982:ATA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p257-dadurkevicius/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Buckley:1989:RA, author = "A. Buckley", title = "Remark on {Algorithm 630}", journal = j-TOMS, volume = "15", number = "3", pages = "262--274", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.69648", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:53:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Buckley:1985:ABE}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p262-buckley/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Domich:1989:RHN, author = "Paul D. Domich", title = "Residual {Hermite} Normal Form Computations", journal = j-TOMS, volume = "15", number = "3", pages = "275--286", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.66892", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "15A21 (15-04 15A36 65-04 65F05)", MRnumber = "91d:15020", bibdate = "Sun Sep 04 22:53:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p275-domich/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 9007-0597", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Corana:1989:CMF, author = "A. Corana and M. Marchesi and C. Martini and S. Ridella", title = "Corrigenda: ``{Minimizing} Multimodal Functions of Continuous Variables with the `Simulated Annealing' Algorithm''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.356281", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "287. 90C30 (65K05)", MRnumber = "1 062 494, 88m:90121", bibdate = "Sat Feb 24 09:58:06 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Corana:1987:MMF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Enright:1989:CFP, author = "W. H. Enright and J. D. Pryce", title = "Corrigenda: ``{Two FORTRAN} Packages for Assessing Initial Value Methods''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.356282", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 10:57:50 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Enright:1987:TFP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Le:1989:CED, author = "D. Le", title = "Corrigenda: ``{An} Efficient Derivative-Free Method for Solving Nonlinear Equations''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/66888.356283", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "287. 65H05", MRnumber = "1 062 495, 87d:65057", bibdate = "Fri Mar 28 10:57:46 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Le:1985:EDF}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ashcraft:1989:IRS, author = "Cleve Ashcraft and Roger Grimes", title = "The Influence of Relaxed Supernode Partitions on the Multifrontal Method", journal = j-TOMS, volume = "15", number = "4", pages = "291--309", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76910", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:58:46 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p291-ashcraft/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Liu:1989:MMP, author = "Joseph W. H. Liu", title = "The Multifrontal Method and Paging in Sparse {Cholesky} Factorization", journal = j-TOMS, volume = "15", number = "4", pages = "310--325", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76911", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 22:59:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p310-liu/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; experimentation; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf D.4.2}: Software, OPERATING SYSTEMS, Storage Management, Virtual memory. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Mitchell:1989:CAR, author = "William F. Mitchell", title = "A Comparison of Adaptive Refinement Techniques for Elliptic Problems", journal = j-TOMS, volume = "15", number = "4", pages = "326--347", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76912", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65N99 (65-04)", MRnumber = "1 062 496", bibdate = "Sun Sep 04 22:59:21 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p326-mitchell/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "experimentation", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Boggs:1989:AOS, author = "Paul T. Boggs and Janet R. Donaldson and Richard h. Byrd and Robert B. Schnabel", title = "{Algorithm 676}: {ODRPACK}: Software for Weighted Orthogonal Distance Regression", journal = j-TOMS, volume = "15", number = "4", pages = "348--364", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76913", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 15:09:23 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p348-boggs/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Montefusco:1989:ASI, author = "Laura Bacchelli Montefusco and Giulio Casciola", title = "{Algorithm 677}: ${C}^1$ Surface Interpolation", journal = j-TOMS, volume = "15", number = "4", pages = "365--374", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76914", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:22:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://doi.acm.org/10.1145/76909.76914; http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p365-montefusco/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Corliss:1989:IIV, author = "George Corliss and Gary Krenz", title = "Indefinite Integration with Validation", journal = j-TOMS, volume = "15", number = "4", pages = "375--393", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76915", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65-04)", MRnumber = "1 062 497", bibdate = "Sun Sep 04 23:01:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", review = "ACM CR 9007-0598", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory.", } @Article{Kachitvichyanukul:1989:ABS, author = "Voratas Kachitvichyanukul and Bruce W. Schmeiser", title = "{Algorithm 678}: {BTPEC}: Sampling from the Binomial Distribution", journal = j-TOMS, volume = "15", number = "4", pages = "394--397", month = dec, year = "1989", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/76909.76916", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p394-kachitvichyanukul/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation.", } @Article{Dongarra:1990:SLB, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Iain Duff", title = "A Set of Level 3 {Basic Linear Algebra Subprograms}", journal = j-TOMS, volume = "16", number = "1", pages = "1--17", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.79170", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 19:10:43 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p1-dongarra/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; reliability; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Dongarra:1990:ASL, author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven Hammarling and Iain Duff", title = "{Algorithm 679}: a Set of Level 3 {Basic Linear Algebra Subprograms}: Model Implementation and Test Programs", journal = j-TOMS, volume = "16", number = "1", pages = "18--28", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77627", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 17:29:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p18-dongarra/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; reliability; verification", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 8X. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cody:1990:PEP, author = "W. J. Cody", title = "Performance Evaluation of Programs for the Error and Complementary Error Functions", journal = j-TOMS, volume = "16", number = "1", pages = "29--37", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77628", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65G05)", MRnumber = "1 073 407", bibdate = "Tue Oct 09 09:29:47 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html", abstract = "This paper presents methods for performance evaluation of computer programs for the functions ${\rm erf}(x)$, ${\rm erfc}(x)$, and $e^{x^2} {\rm erfc}(x)$. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of ${\rm erfc}(x)$. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.", acknowledgement = ack-nhfb, affiliation = "Argonne Nat. Lab., IL, USA", ajournal = "ACM Trans. Math. Softw.", classification = "B0290B (Error analysis in numerical methods); B0290F (Interpolation and function approximation); C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Complementary error functions; Computer programs; FORTRAN; Power series expansions; Repeated integrals; Robustness; Test program", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", thesaurus = "Error analysis; Function approximation; Performance evaluation", } @Article{Poppe:1990:MEC, author = "G. P. M. Poppe and C. M. J. Wijers", title = "More Efficient Computation of the Complex Error Function", journal = j-TOMS, volume = "16", number = "1", pages = "38--46", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77629", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G05 (65D20)", MRnumber = "91h:65068a", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.", } @Article{Poppe:1990:AEC, author = "G. P. M. Poppe and C. M. J. Wijers", title = "{Algorithm 680}: Evaluation of the Complex Error Function", journal = j-TOMS, volume = "16", number = "1", pages = "47--47", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77630", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "47. 65G05 (65-04)", MRnumber = "91h:65068b", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Zaghloul:2019:RO}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.", } @Article{Arney:1990:AMM, author = "David C. Arney and Joseph E. Flaherty", title = "An Adaptive Mesh-Moving and Local Refinement Method for Time-Dependent Partial Differential Equations", journal = j-TOMS, volume = "16", number = "1", pages = "48--71", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77631", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65M50", MRnumber = "91f:65154", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p48-arney/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Schryer:1990:DSO, author = "N. L. Schryer", title = "Designing Software for One-Dimensional Partial Differential Equations", journal = j-TOMS, volume = "16", number = "1", pages = "72--85", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77632", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65P05)", MRnumber = "1 073 411", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p72-schryer/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems.", } @Article{Hansen:1990:PES, author = "Eldon R. Hansen and Merrell L. Patrick and Richard L. C. Wang", title = "Polynomial Evaluation with Scaling", journal = j-TOMS, volume = "16", number = "1", pages = "86--93", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77633", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Y10", MRnumber = "1 073 412", bibdate = "Fri Aug 26 23:38:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p86-hansen/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", xxnote = "Original article has incorrect ``Merell'' instead of ``Merrell''.", } @Article{Snow:1990:WGO, author = "Dennis M. Snow", title = "{Weyl} Group Orbits", journal = j-TOMS, volume = "16", number = "1", pages = "94--108", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.77634", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "20G99 (22E15)", MRnumber = "91j:20115", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p94-snow/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", reviewer = "V. L. Popov", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Sewell:1990:RSP, author = "Granville Sewell", title = "Remark on ``{Algorithm 657}: Software for Plotting Contour Surfaces of a Function of Three Variables''", journal = j-TOMS, volume = "16", number = "1", pages = "109--109", month = mar, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/77626.356300", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:03:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Sewell:1988:ASP}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zenios:1990:INO, author = "Stavros A. Zenios", title = "Integrating Network Optimization Capabilities into a High-Level Modeling Language", journal = j-TOMS, volume = "16", number = "2", pages = "113--142", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78929", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p113-zenios/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; experimentation; languages; performance; theory", subject = "{\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf C.2.1}: Computer Systems Organization, COMPUTER-COMMUNICATION NETWORKS, Network Architecture and Design. {\bf C.4}: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Modeling techniques.", } @Article{Meintjes:1990:CES, author = "Keith Meintjes and Alexander P. Morgan", title = "Chemical Equilibrium Systems as Numerical Test Problems", journal = j-TOMS, volume = "16", number = "2", pages = "143--151", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78930", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p143-meintjes/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry.", } @Article{Kearfott:1990:AIP, author = "R. Baker Kearfott and Manuel {Novoa III}", title = "{Algorithm 681}: {INTBIS}, a Portable Interval {Newton}\slash Bisection Package", journal = j-TOMS, volume = "16", number = "2", pages = "152--157", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78931", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p152-kearfott/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Murli:1990:ATM, author = "A. Murli and M. Rizzardi", title = "{Algorithm 682}: {Talbot}'s Method for the {Laplace} Inversion Problem", journal = j-TOMS, volume = "16", number = "2", pages = "158--168", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78932", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p158-murli/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Equal interval integration. {\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Fredholm equations.", } @Article{Amos:1990:CEI, author = "Donald E. Amos", title = "Computation of Exponential Integrals of a Complex Argument", journal = j-TOMS, volume = "16", number = "2", pages = "169--177", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78933", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "92k:65025", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p169-amos/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous.", } @Article{Amos:1990:APF, author = "Donald E. Amos", title = "{Algorithm 683}: a Portable {FORTRAN} Subroutine for Exponential Integrals of a Complex Argument", journal = j-TOMS, volume = "16", number = "2", pages = "178--182", month = jun, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/78928.78934", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (65Y10)", MRnumber = "92k:65026", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p178-amos/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Tang:1990:AET, author = "Ping Tak Peter Tang", title = "Accurate and Efficient Testing of the Exponential and Logarithm Functions", journal = j-TOMS, volume = "16", number = "3", pages = "185--200", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79506", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65G99)", MRnumber = "1 070 797", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/", abstract = "Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Cash:1990:VOR, author = "J. R. Cash and Alan H. Karp", title = "A Variable Order {Runge--Kutta} Method for Initial Value Problems with Rapidly Varying Right-Hand Sides", journal = j-TOMS, volume = "16", number = "3", pages = "201--222", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79507", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "1 070 798", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p201-cash/", abstract = "Explicit Runge--Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of nonstiff, initial value problems. However, high-order Runge--Kutta methods require more function evaluations per integration step than, for example, Adams methods used in PECE mode, and so, with RKMs, it is especially important to avoid rejected steps. Steps are often rejected when certain derivatives of the solutions are very large for part of the region of integration. This corresponds, for example, to regions where the solution has a sharp front or, in the limit, some derivative of the solution is discontinuous. In these circumstances the assumption that the local truncation error is changing slowly is invalid, and so any step-choosing algorithm is likely to produce an unacceptable step. In this paper we derive a family of explicit Runge--Kutta formulas. Each formula is very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains imbedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge--Kutta step have been computed. We can then either accept a lower order solution or abort the step, depending on which course of action seems appropriate. The efficiency of the new algorithm is demonstrated on the DETEST test set as well as on some difficult test problems with sharp fronts or discontinuities.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Weiss:1990:SSC, author = "Shlomo Weiss and James E. Smith", title = "A Study of Scalar Compilation Techniques for Pipelined Supercomputers", journal = j-TOMS, volume = "16", number = "3", pages = "223--245", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79508", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p223-weiss/", abstract = "This paper studies two compilation techniques for enhancing scalar performance in high-speed scientific processors: software pipelining and loop unrolling. We study the impact of the architecture (size of the register file) and of the hardware (size of instruction buffer) on the efficiency of loop unrolling. We also develop a methodology for classifying software pipelining techniques. For loop unrolling, a straightforward scheduling algorithm is shown to produce near-optimal results when not inhibited by recurrences or memory hazards. Our study indicates that the performance produced with a modified CRAY-1S scalar architecture and a code scheduler utilizing loop unrolling is comparable to the performance achieved by the CRAY-1S with a vector unit and the CFT vectorizing compiler.\par Finally, we show that the combination of loop unrolling and dynamic software pipelining, as implemented by a decoupled computer, substantially outperforms the vector CRAY-1S.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; experimentation; performance", subject = "{\bf C.1.1}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Single Data Stream Architectures, Pipeline processors. {\bf C.4}: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Performance attributes. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf C.5.1}: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and Medium (``Mainframe'') Computers.", } @Article{Preusser:1990:EFB, author = "Albrecht Preusser", title = "Efficient Formulation of a Bivariate Nonic ${C}^2$-{Hermite} Polynomial on Triangles", journal = j-TOMS, volume = "16", number = "3", pages = "246--252", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79509", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "1 070 799", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p246-preusser/", abstract = "Bivariate polynomials over triangular domains are widely in use for the definition of surfaces that are continuously differentiable across a set of triangles. A description is given of how explicit formulas for the coefficients of bivariate nonic polynomials can be found with the help of a computer algebra system. A linear system with 55 equations and 45 nonzero right hand sides must be solved algebraically. The interpolant is twice differentiable across triangle sides and based on function values and partial derivatives up to fourth order at the nodes. Horner's scheme for evaluating polynomials can be applied directly, leading to optimal efficiency during the evaluation phase (54 additions and multiplications for one point). Starting with transformed nodal data, the calculation of one set of coefficients takes about 350 additions, the same number of multiplications, and 30 divisions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Preusser:1990:AIT, author = "Albrecht Preusser", title = "{Algorithm 684}: ${C}^1$- and ${C}^2$-Interpolation on Triangles with Quintic and Nonic Bivariate Polynomials", journal = j-TOMS, volume = "16", number = "3", pages = "253--257", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79510", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D05)", MRnumber = "1 070 800", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p253-preusser/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Shacham:1990:FBD, author = "Orit Shacham and Mordechai Shacham", title = "Finding Boundaries of the Domain of Definition for Functions Along a One-Dimensional Ray", journal = j-TOMS, volume = "16", number = "3", pages = "258--268", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79511", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D99)", MRnumber = "1 070 801", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p258-shacham/", abstract = "A program for finding boundaries of function domains along a one-dimensional ray has been developed. The program decomposes the function into subexpressions which are recursively tested for intervals where they are undefined, negative, or fractional, or points where they equal zero. The intervals in which the subexpressions are undefined are then united to create the boundaries of the domain of definition of the whole function. The advantages of the use of such a program in solution of systems of nonlinear algebraic equations and nonlinear optimization are demonstrated.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Nair:1990:IAO, author = "K. Aiyappan Nair", title = "An Improved Algorithm for Ordered Sequential Random Sampling", journal = j-TOMS, volume = "16", number = "3", pages = "269--274", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.356313", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10", MRnumber = "1 070 802", bibdate = "Sat Aug 27 15:57:03 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Palacios-Velez:1990:DHS, author = "Oscar Palacios-V{\'e}lez and Baltazar Cuevas Renaud", title = "A Dynamic Hierarchical Subdivision Algorithm for Computing {Delaunay} Triangulations and Other Closest-Point Problems", journal = j-TOMS, volume = "16", number = "3", pages = "275--292", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.79512", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04", MRnumber = "1 070 803", bibdate = "Sat Aug 27 15:57:45 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p275-palacios-velez/", abstract = "A new, dynamic, hierarchical subdivision and recursive algorithm for computing Delaunay triangulations is presented. The algorithm has four main steps: (1) location of the already formed triangle that contains the point (2) identification of other adjoining triangles whose circumcircle contains the point (3) formation of the new triangles, and (4) database update. Different search procedures are analyzed. It is shown that the ``oriented walk'' search, when the total number of points is less than 417 or when the points are presorted by distance or coordinates. The algorithm has point-deletion capabilities which are discussed in detail.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages, and systems. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Hierarchy and geometric transformations. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching.", } @Article{Krogh:1990:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "16", number = "3", pages = "293--296", month = sep, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/79505.356315", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:14:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pothen:1990:CBT, author = "Alex Pothen and Chin-Ju Fan", title = "Computing the Block Triangular Form of a Sparse Matrix", journal = j-TOMS, volume = "16", number = "4", pages = "303--324", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98287", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50", MRnumber = "91k:65075", bibdate = "Sat Aug 27 15:58:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p303-pothen/", abstract = "We consider the problem of permuting the rows and columns of a rectangular or square, unsymmetric sparse matrix to compute its block triangular form. This block triangular form is based on a canonical decomposition of bipartite graphs induced by a maximum matching and was discovered by Dulmage and Mendelsohn. We describe implementations of algorithms to compute the block triangular form and provide computational results on sparse matrices from test collections. Several applications of the block triangular form are also included.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; perm; sparse", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Permutations and combinations. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory.", } @Article{Kaufman:1990:APS, author = "Linda Kaufman and Daniel D. Warner", title = "{Algorithm 685}: a Program for Solving Separable Elliptic Equations", journal = j-TOMS, volume = "16", number = "4", pages = "325--351", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98289", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:21:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p325-kaufman/", abstract = "This paper presents a program SERRG2 that solves separable elliptic equations on a rectangle. The program uses a matrix decomposition technique to directly solve the linear system arising from a Rayleigh--Ritz--Galerkin approach with tensor product B-splines to solve the separable partial differential equation. This approach permits high-order discretizations, variable meshes, and multiple knots.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Higham:1990:EFM, author = "Nicholas J. Higham", title = "Exploiting Fast Matrix Multiplication Within the Level 3 {BLAS}", journal = j-TOMS, volume = "16", number = "4", pages = "352--368", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98290", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F99)", MRnumber = "1 095 133", bibdate = "Sun Sep 04 23:21:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "Describes algorithms based on Strassen's method which are asymptotically faster than the standard ${N}^3$ algorithm, and in practice, faster for ${N}\approx100$, and examines their numerical stability. See \cite{Dongarra:1990:ASL,Demmel:1992:SBA,Dayde:1994:PBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/", abstract = "The Level 3 BLAS (BLAS3) are a set of specifications of FORTRAN 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple right-hand sides. They are intended to provide efficient and portable building blocks for linear algebra algorithms on high-performance computers. We describe algorithms for the BLAS3 operations that are asymptotically faster than the conventional ones. These algorithms are based on Strassen's method for fast matrix multiplication, which is now recognized to be a practically useful technique once matrix dimensions exceed about 100. We pay particular attention to the numerical stability of these ``fast BLAS3.'' Error bounds are given and their significance is explained and illustrated with the aid of numerical experiments. Our conclusion is that the fast BLAS3, although not as strongly stable as conventional implementations, are stable enough to merit careful consideration in many applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Reichel:1990:AFS, author = "L. Reichel and W. B. Gragg", title = "{Algorithm 686}: {FORTRAN} Subroutines for Updating the {QR} Decomposition", journal = j-TOMS, volume = "16", number = "4", pages = "369--377", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98291", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:25:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p369-reighel/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Gram--Schmidt algorithm; nla; qrd; software; updating", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1990:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Logarithm Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "16", number = "4", pages = "378--400", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98294", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:26:09 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/", abstract = "Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.", acknowledgement = ack-nj, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance; reliability; standardization; theory; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Hopkins:1990:RRK, author = "Tim Hopkins and David Morse", title = "Remark on ``{Algorithm 620}: References and Keywords for {\em {Collected Algorithms} of the {ACM}}''", journal = j-TOMS, volume = "16", number = "4", pages = "401--403", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98297", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 24 09:58:26 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Rice:1984:ARK,Hamilton:1985:RRK}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p401-hopkins/", abstract = "The authors report on an enhanced version of the database originally reported in `Algorithm 620: references and keywords for collected algorithms from ACM', J. R. Rice and R. J. Hanson, ACM Trans Math. Soft. vol. 10, no. 4, p. 359-360 (1984). In this new version they have included all the information necessary to generate full bibliographic references. Extra information includes the author's name (including any accents), the page range of the original reference (rather than just the starting page), the month and year of publication and an abbreviated journal name. The programming language used to code the algorithm is also given. Any mathematical notation used within the algorithm title and accents in the author's name have been defined using {\TeX}. Following the practice used with Bib{\TeX}, all letters within the title that need to remain capitalized in a printed version of the reference (e.g. Fortran, Bessel) are enclosed in braces. (3 Refs.)", acknowledgement = ack-nhfb, affiliation = "Kent Univ., UK", ajournal = "ACM Trans. Math. Softw.", classification = "C4100 (Numerical analysis); C7250C (Bibliographic systems); C7310 (Mathematics)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Abbreviated journal name; Algorithm title; algorithms; Bibliographic references; BibTeX; Mathematical notation; TeX", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", thesaurus = "Bibliographic systems; Mathematics computing; Numerical methods", } @Article{Amos:1990:RPP, author = "D. E. Amos", title = "Remark on ``{Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order''", journal = j-TOMS, volume = "16", number = "4", pages = "404--404", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98299", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:26:24 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Garbow:1990:RFS, author = "B. S. Garbow and J. N. Lyness", title = "Remark on ``{Algorithm 662}: {A FORTRAN} Software Package for the Numerical Inversion of the {Laplace} Transform Based on {Weeks}' Method''", journal = j-TOMS, volume = "16", number = "4", pages = "405--406", month = dec, year = "1990", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/98267.98302", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:21:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Garbow:1988:AFS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p405-garbow/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Addison:1991:ADT, author = "C. A. Addison and W. H. Enright and P. W. Gaffney and I. Gladwell and P. M. Hanson", title = "{Algorithm 687}: a Decision Tree for the Numerical Solution of Initial Value Ordinary Differential Equations", journal = j-TOMS, volume = "17", number = "1", pages = "1--10", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103148", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p1-addison/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Shampine:1991:RSS, author = "L. F. Shampine and I. Gladwell and R. W. Brankin", title = "Reliable Solutions of Special Event Location Problems for {ODEs}", journal = j-TOMS, volume = "17", number = "1", pages = "11--25", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103149", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L05", MRnumber = "92e:65093", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p11-shampine/", abstract = "Computing the solution of the initial value problem in ordinary differential equations (ODEs) may be only part of a larger task. One such task is finding where an algebraic function of the solution (an event function) has a root (an event occurs). This is a task which is difficult both in theory and in software practice. For certain useful kinds of event functions, it is possible to avoid two fundamental difficulties. It is described how to achieve the reliable solutions of such problems in a way that allows the capability to be grafted onto popular codes for the initial value problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; theory", reviewer = "H. Shintani", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Gal:1991:AEM, author = "Shmuel Gal and Boris Bachelis", title = "An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard", journal = j-TOMS, volume = "17", number = "1", pages = "26--45", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103151", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (65-04 65D15)", MRnumber = "92a:65069", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/", abstract = "The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.\par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.", } @Article{Cody:1991:PEP, author = "W. J. Cody", title = "Performance Evaluation of Programs Related to the Real Gamma Function", journal = j-TOMS, volume = "17", number = "1", pages = "46--54", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103153", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (65Y20)", MRnumber = "91m:65052", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/", abstract = "Methods are presented for evaluating the performance of programs for the functions $\Gamma(x)$, $\ln \Gamma(x)$, and $\psi(x)$. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "measurement; performance; reliability", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Cody:1991:UTS, author = "W. J. Cody and L. Stoltz", title = "The Use of {Taylor} Series to Test Accuracy of Function Programs", journal = j-TOMS, volume = "17", number = "1", pages = "55--63", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103154", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20 (65Y20)", MRnumber = "91m:65053", bibdate = "Sun Sep 04 23:36:36 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/", abstract = "This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Dax:1991:CAB, author = "Achiya Dax", title = "On Computational Aspects of Bounded Linear Least Squares Problems", journal = j-TOMS, volume = "17", number = "1", pages = "64--73", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103155", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10", MRnumber = "91m:65179", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p64-dax/", abstract = "The paper describes numerical experiments with active set methods for solving bounded linear least squares problems. It concentrates on two problems that arise in the implementation of the active set method. One problem is the choice of a good starting point. The second problem is how to move out of a ``{\em dead point}.'' The paper investigates the use of simple iterative methods to solve these problems. The results of our experiments indicate that the use of Gauss--Seidel iterations to obtain a starting point is likely to provide large gains in efficiency. Another interesting conclusion is that dropping one constraint at a time is advantageous to dropping several constraints at a time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Pardalos:1991:CTP, author = "Panos M. Pardalos", title = "Construction of Test Problems in Quadratic Bivalent Programming", journal = j-TOMS, volume = "17", number = "1", pages = "74--87", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103156", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K05", MRnumber = "92c:65075", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p74-pardalos/", abstract = "A method of constructing test problems for constrained bivalent quadratic programming is presented. For any feasible integer point for a given domain, the method generates quadratic functions whose minimum over the given domain occurs at the selected point.\par Certain properties of unconstrained quadratic zero-one programs that determine the difficulty of the test problems are also discussed. In addition, a standardized random test problem generator for unconstrained quadratic zero-one programming is given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance", reviewer = "P. K. Subramanian", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Klier:1991:FCB, author = "Peter Klier and Richard J. Fateman", title = "On Finding the Closest Bitwise Matches in a Fixed Set", journal = j-TOMS, volume = "17", number = "1", pages = "88--97", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103157", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68Q20", MRnumber = "1 103 630", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p88-klier/", abstract = "In a given large fixed table of bit-vectors, we would like to find, as rapidly as possible, those bit-vectors which have the least Hamming distances from a newly-presented arbitrary bit-vector.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Pattern matching. {\bf E.2}: Data, DATA STORAGE REPRESENTATIONS. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching. {\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Search process.", } @Article{LEcuyer:1991:IRN, author = "Pierre L'Ecuyer and Serge C{\^o}t{\'e}", title = "Implementing a Random Number Package with Splitting Facilities", journal = j-TOMS, volume = "17", number = "1", pages = "98--111", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103158", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65C10", MRnumber = "91m:65016", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p98-lecuyer/", abstract = "A portable set of software tools is described for uniform random variates generation. It provides for multiple generators running simultaneously, and each generator has its sequence of numbers partitioned into many long (disjoint) substreams. Simple procedure calls allow the user to make any generator ``jump'' ahead to the beginning of its next substream, back to the beginning of its current substream, or back to the beginning of its first substream\ldots. Implementation issues are discussed\ldots. A Pascal implementation for 32-bit computers is described.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Liu:1991:GEM, author = "Joseph W. H. Liu", title = "A Generalized Envelope Method for Sparse Factorization by Rows", journal = j-TOMS, volume = "17", number = "1", pages = "112--129", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103159", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50", MRnumber = "92b:65037", bibdate = "Sun Sep 04 23:43:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p112-liu/", abstract = "A generalized form of the envelope method is proposed for the solution of large sparse symmetric and positive definite matrices by rows. The method is demonstrated to have practical advantages over the conventional column-oriented factorization using compressed column storage or the multifrontal method using full frontal submatrices.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; functional algorithm", reviewer = "R. P. Tewarson", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Mohideen:1991:RCG, author = "Saleem Mohideen and Vladimir Cherkassky", title = "On Recursive Calculation of the Generalized Inverse of a Matrix", journal = j-TOMS, volume = "17", number = "1", pages = "130--147", month = mar, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/103147.103160", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F10 (65F20)", MRnumber = "92c:65042", bibdate = "Sun Sep 04 23:33:02 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p130-mohideen/", abstract = "The generalized inverse of a matrix is an extension of the ordinary square matrix inverse which applies to any matrix (e.g., singular, rectangular). The generalized inverse has numerous important applications such as regression analysis, filtering, optimization and, more recently, linear associative memories. In this latter application known as Distributed Associative Memory, stimulus vectors are associated with response vectors and the result of many associations is spread over the entire memory matrix, which is calculated as the generalized inverse. Addition/deletion of new associations requires recalculation of the generalized inverse, which becomes computationally costly for large systems. A better solution is to calculate the generalized inverse recursively. The proposed algorithm is a modification of the well known algorithm due to Rust et al. [2], originally introduced for nonrecursive computation. We compare our algorithm with Greville's recursive algorithm and conclude that our algorithm provides better numerical stability at the expense of little extra computation time and additional storage.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Pseudoinverses. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Keast:1991:AEM, author = "P. Keast and P. H. Muir", title = "{Algorithm 688}: {EPDCOL}: a More Efficient {PDECOL} Code", journal = j-TOMS, volume = "17", number = "2", pages = "153--166", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108558", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p153-keast/", abstract = "The software package PDECOL [7] is a popular code among scientists wishing to solve systems of nonlinear partial differential equations. The code is based on a method-of-lines approach, with collocation in the space variable to reduce the problem to a system of ordinary differential equations. There are three principal components: the basis functions employed in the collocation; the method used to solve the system of ordinary differential equations; and the linear equation solver which handles the linear algebra. This paper will concentrate on the third component, and will report on the improvement in the performance of PDECOL resulting from replacing the current linear algebra modules of the code by modules which take full advantage of the special structure of the equations which arise. Savings of over 50 percent in total execution time can be realized.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Blom:1991:ADC, author = "J. G. Blom and H. Brunner", title = "{Algorithm 689}: Discretized Collocation and Iterated Collocation for Nonlinear {Volterra} Integral Equations of the Second Kind", journal = j-TOMS, volume = "17", number = "2", pages = "167--177", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108562", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p167-blom/", abstract = "This paper describes a FORTRAN code for calculating approximate solutions to systems of nonlinear Volterra integral equations of the second kind. The algorithm is based on polynomial spline collocation, with the possibility of combination with the corresponding iterated collocation. It exploits certain local superconvergence properties for the error estimation and the stepsize strategy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Volterra equations. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berzins:1991:ACP, author = "M. Berzins and P. M. Dew", title = "{Algorithm 690}: {Chebyshev} Polynomial Software for Elliptic-Parabolic Systems of {PDEs}", journal = j-TOMS, volume = "17", number = "2", pages = "178--206", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108566", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p178-berzins/", abstract = "PDECHEB is a FORTRAN 77 software package that semidiscretizes a wide range of time-dependent partial differential equations in one space variable. The software implements a family of spacial discretization formulas, based on piecewise Chebyshev polynomial expansions with $C^{0}$ continuity. The package has been designed to be used in conjunction with a general integrator for initial value problems to provide a powerful software tool for the solution of parabolic-elliptic PDEs with coupled differential algebraic equations. Examples are provided to illustrate the use of the package with the DASSL d.a.e integrator of Petzold [18].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Parabolic equations.", } @Article{Favati:1991:IIF, author = "Paola Favati and Grazia Lotti and Francesco Romani", title = "Interpolatory Integration Formulas for Optimal Composition", journal = j-TOMS, volume = "17", number = "2", pages = "207--217", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108571", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "92k:65035", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p207-favati/", abstract = "A set of symmetric, closed, interpolatory integration formulas on the interval [-1, 1] with positive weights and increasing degree of precision is introduced. These formulas, called recursive monotone stable (RMS) formulas, allow applying higher order or compound rules without wasting previously computed functional values. An exhaustive search shows the existence of 27 families of RMS formulas, stemming from the simple trapezoidal rule.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Favati:1991:AIQ, author = "Paola Favati and Grazia Lotti and Francesco Romani", title = "{Algorithm 691}: Improving {QUADPACK} Automatic Integration Routines", journal = j-TOMS, volume = "17", number = "2", pages = "218--232", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108580", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65Y10)", MRnumber = "92k:65036", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p218-favati/", abstract = "Two automatic adaptive integrators from QUADPACK (namely, QAG, and QAGS) are modified by substituting the Gauss--Kronrod rules used for local quadrature with recursive monotone stable (RMS) formulas. Extensive numerical tests, both for one-dimensional and two-dimensional integrals, show that the resulting programs are faster, perform less functional evaluations, and are more suitable", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berntsen:1991:EEA, author = "Jarle Berntsen and Terje O. Espelid", title = "Error Estimation in Automatic Quadrature Routines", journal = j-TOMS, volume = "17", number = "2", pages = "233--252", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108575", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G99 (65D20 65Y10)", MRnumber = "92m:65067", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p233-berntsen/", abstract = "A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule approximations. These null rule approximations are then used to produce an estimate of the local error. The algorithm allows us to take advantage of the degree of precision of the basic quadrature rule. In the experiments we show that the algorithm works satisfactorily for a selection of different quadrature rules on all test families of integrals.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Dodson:1991:SEF, author = "David S. Dodson and Roger G. Grimes and John G. Lewis", title = "Sparse Extensions to the {FORTRAN Basic Linear Algebra Subroutines}", journal = j-TOMS, volume = "17", number = "2", pages = "253--263", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108577", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p253-dodson/", abstract = "This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extension is targeted at sparse vector operations, with the goal of providing efficient, but portable, implementations of algorithms for high-performance computers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; standardization", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Dodson:1991:AMI, author = "David S. Dodson and Roger G. Grimes and John G. Lewis", title = "{Algorithm 692}: Model Implementation and Test Package for the Sparse {Basic Linear Algebra Subroutines}", journal = j-TOMS, volume = "17", number = "2", pages = "264--272", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108582", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p264-dodson/", abstract = "This paper describes a model implementation and test software for the Sparse Basic Linear Algebra Subprograms (Sparse BLAS). The Sparse BLAS perform vector operations common in sparse linear algebra, with the goal of providing efficient, but portable, implementations of algorithms for high performance computers. The model implementation provides a portable set of FORTRAN 77 Sparse BLAS for the use on machines where specially tuned implementations do not exist or are not required. The test software is designed to verify that tuned implementations meet the specifications of the Sparse BLAS and that implementations are correctly installed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Smith:1991:AFP, author = "David M. Smith", title = "{Algorithm 693}: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic", journal = j-TOMS, volume = "17", number = "2", pages = "273--283", month = jun, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/108556.108585", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Dec 13 18:36:25 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/", abstract = "FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.", acknowledgement = ack-nhfb, affiliation = "Loyola Marymount Univ., Los Angeles, CA, USA", ajournal = "ACM Trans. Math. Softw.", classification = "C4130 (Interpolation and function approximation); C5230 (Digital arithmetic methods); C7310 (Mathematics)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Accuracy; Elementary functions; Floating-point multiple-precision arithmetic; FM; FORTRAN-77 routines; Mathematical library; Portable software; Rounding off", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", thesaurus = "Digital arithmetic; Function approximation; Mathematics computing; Software packages; Subroutines", } @Article{Higham:1991:ACT, author = "Nicholas J. Higham", title = "{Algorithm 694}: a Collection of Test Matrices in {MATLAB}", journal = j-TOMS, volume = "17", number = "3", pages = "289--305", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116805", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Eskow:1991:ASN, author = "Elizabeth Eskow and Robert B. Schnabel", title = "{Algorithm 695}: Software for a New Modified {Cholesky} Factorization", journal = j-TOMS, volume = "17", number = "3", pages = "306--312", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116806", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p306-eskow/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Rothberg:1991:ESM, author = "Edward Rothberg and Anoop Gupta", title = "Efficient Sparse Matrix Factorization on High-Performance Workstations\emdash Exploiting the Memory Hierarchy", journal = j-TOMS, volume = "17", number = "3", pages = "313--334", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116809", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p313-rothberg/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; experimentation; performance", subject = "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design Styles, Cache memories. {\bf C.5.3}: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Microcomputers, Workstations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Schrauf:1991:AIR, author = "G{\'e}za Schrauf", title = "{Algorithm 696}: An Inverse {Rayleigh} Iteration for Complex Band Matrices", journal = j-TOMS, volume = "17", number = "3", pages = "335--340", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116807", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p335-schrauf/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Akima:1991:MUI, author = "Hiroshi Akima", title = "A Method for Univariate Interpolation that Has the Accuracy of a Third-Degree Polynomial", journal = j-TOMS, volume = "17", number = "3", pages = "341--366", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116810", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p341-akima/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation.", } @Article{Akima:1991:AUI, author = "Hiroshi Akima", title = "{Algorithm 697}: Univariate Interpolation that Has the Accuracy of a Third-Degree Polynomial", journal = j-TOMS, volume = "17", number = "3", pages = "367--367", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116808", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p367-akima/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation.", } @Article{Higham:1991:HCR, author = "D. J. Higham", title = "Highly Continuous {Runge--Kutta} Interpolants", journal = j-TOMS, volume = "17", number = "3", pages = "368--386", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.103150", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L06", MRnumber = "92m:65092", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p368-higham/", abstract = "To augment the discrete Runge--Kutta solution to the minimal value problem, piecewise Hermite interpolants have been used to provide a continuous approximation with a continuous first derivative. We show that it is possible to construct interpolants with arbitrarily many continuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpolants. We also show that the usual truncation coefficient analysis can be applied to these new interpolants, allowing their accuracy to be examined in more detail. As an illustration, we present some globally $C^2$ interpolants for use with a popular 4th and 5th order Runge--Kutta pair of Dormand and Prince, and we compare them theoretically and numerically with existing interpolants.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Sharp:1991:NCS, author = "P. W. Sharp", title = "Numerical Comparisons of Some Explicit {Runge--Kutta} Pair of Orders 3 Through 8", journal = j-TOMS, volume = "17", number = "3", pages = "387--409", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116811", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p387-sharp/", abstract = "We performed numerical testing of six explicit Runge--Kutta pairs ranging in order from a (3,4) pair to a (7,8) pair. All the test problems had smooth solutions and we assumed dense output was not required. The pairs were implemented in a uniform way. In particular, the stepsize selection for all pairs was based on the locally optimal formula. We tested the efficiency of the pairs, to what extent tolerance proportionality held, the accuracy of the local error estimate and stepsize prediction, and the performance on mildly stiff problems. We also showed, for these pairs, how the performance could be altered noticeably by making simple changes to the stepsize selection strategy. As part of the work, we demonstrated new ways of presenting numerical comparisons.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Ziv:1991:FEE, author = "Abraham Ziv", title = "Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit", journal = j-TOMS, volume = "17", number = "3", pages = "410--423", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116813", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Sep 1 10:15:31 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/", acknowledgement = ack-nj, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; standardization; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Higham:1991:RBF, author = "Desmond J. Higham", title = "Remark on ``{Algorithm 669}: {BRKF45}: {A FORTRAN} Subroutine for Solving First-Order Systems of Nonstiff Initial Value Problems for Ordinary Differential Equations''", journal = j-TOMS, volume = "17", number = "3", pages = "424--426", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.116814", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Cash:1989:ABF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p424-higham/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Krogh:1991:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "17", number = "3", pages = "427--430", month = sep, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/114697.356357", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Berntsen:1991:AAA, author = "Jarle Berntsen and Terje O. Espelid and Alan Genz", title = "An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals", journal = j-TOMS, volume = "17", number = "4", pages = "437--451", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210233", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D30)", MRnumber = "1 140 034", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p437-berntsen/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berntsen:1991:ADA, author = "Jarle Berntsen and Terje O. Espelid and Alan Genz", title = "{Algorithm 698}: {DCUHRE}: An Adaptive Multidimensional Integration Routine for a Vector of Integrals", journal = j-TOMS, volume = "17", number = "4", pages = "452--456", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210234", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D30)", MRnumber = "1 140 035", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p452-berntsen/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Krogh:1991:ANR, author = "Fred T. Krogh and W. Van Snyder", title = "{Algorithm 699}: a New Representation of {Patterson}'s Quadrature Formulae", journal = j-TOMS, volume = "17", number = "4", pages = "457--461", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210235", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:54:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p457-krogh/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Broughan:1991:SHL, author = "Kevin A. Broughan", title = "{SENAC}: a High-Level Interface for the {NAG} Library", journal = j-TOMS, volume = "17", number = "4", pages = "462--480", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210236", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p462-broughan/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; languages; performance; theory", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.2.2}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming.", } @Article{Marletta:1991:CAN, author = "Marco Marletta", title = "Certification of {Algorithm 700}: Numerical Tests of the {SLEIGN} Software for {Sturm--Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "481--490", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210237", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p481-marletta/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS.", } @Article{Bailey:1991:EEC, author = "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper and Anton Zettl", title = "Eigenvalue and Eigenfunction Computations for {Sturm--Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "491--499", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210238", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L15", MRnumber = "1 140 036", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p491-bailey/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Bailey:1991:AFS, author = "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper and Anton Zettl", title = "{Algorithm 700}: {A FORTRAN} Software Package for {Sturm--Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "500--501", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210239", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L15", MRnumber = "1 140 037", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p500-bailey/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Alfeld:1991:EAS, author = "Peter Alfeld and David J. Eyre", title = "The Exact Analysis of Sparse Rectangular Linear Systems", journal = j-TOMS, volume = "17", number = "4", pages = "502--518", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210240", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 140 038", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p502-alfeld/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "measurement; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Alfeld:1991:AGE, author = "Peter Alfeld and David J. Eyre", title = "{Algorithm 701}: {Goliath}\emdash a Software System for the Exact Analysis of Rank-Deficient Sparse Rational Linear Systems", journal = j-TOMS, volume = "17", number = "4", pages = "519--532", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210241", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 140 039", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p519-alfeld/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Gustafsson:1991:CTT, author = "Kjell Gustafsson", title = "Control Theoretic Techniques for Stepsize Selection in Explicit {Runge--Kutta} Methods", journal = j-TOMS, volume = "17", number = "4", pages = "533--554", month = dec, year = "1991", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210232.210242", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65L06)", MRnumber = "1 140 040", bibdate = "Sun Sep 04 23:59:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p533-gustafsson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Boubez:1992:PED, author = "Toufic I. Boubez and Andy M. Froncioni and Richard L. Peskin", title = "A Prototyping Envelope for Differential Equations", journal = j-TOMS, volume = "18", number = "1", pages = "1--10", month = mar, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/128745.128746", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 08:43:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p1-boubez/", abstract = "A system is presented to allow end users to solve nonlinear differential equations without need to write computer programs. The system treats $n$th order space (one dimensional), first order time systems with initial and/or two point boundary value specification. Users of the system need only enter the problem in direct mathematical notation, and output is automatically presented as a solution graph. The system allows the user to alter this equations, in-situ, that is to computationally steer his model. Thus the system is suited for model prototyping. Implementation is based on an object-oriented paradigm, well established and robust numerical procedures, and distributed computing to supported needed resources for numerically intensive tasks.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; experimentation; languages", subject = "{\bf D.2.6}: Software, SOFTWARE ENGINEERING, Programming Environments. {\bf D.2.m}: Software, SOFTWARE ENGINEERING, Miscellaneous. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Smalltalk.", } @Article{Lucks:1992:ASM, author = "Michael Lucks and Ian Gladwell", title = "Automated Selection of Mathematical Software", journal = j-TOMS, volume = "18", number = "1", pages = "11--34", month = mar, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/128745.128747", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 08:43:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p11-lucks/", abstract = "Current approaches to recommending mathematical software are qualitative and categorical. These approaches are unsatisfactory when the problem to be solved has features that can ``trade-off'' in the recommendation process. A quantitative system is proposed that permits tradeoffs and can be built and modified incrementally. This quantitative approach extends other knowledge-engineering techniques in its knowledge representation and aggregation facilities. The system is demonstrated on the domain of ordinary differential equation initial value problems. The results are significantly superior to an existing qualitative (decision tree) system.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.2.4}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods, Representation languages.", } @Article{Olszewski:1992:FTA, author = "Jan Olszewski", title = "A Flexible Thinning Algorithm Allowing Parallel, Sequential, and Distributed Application", journal = j-TOMS, volume = "18", number = "1", pages = "35--45", month = mar, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/128745.128748", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:54:33 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p35-olszewski/", abstract = "A parallel thinning algorithm for digital patterns is presented. This algorithm can also be used for sequential thinning without the simulation of parallel computation. The mathematical background of the algorithm bases on the notion of the Euler characteristic. The proposed algorithm is simple and particularly faster than other parallel algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf I.5.2}: Computing Methodologies, PATTERN RECOGNITION, Design Methodology. {\bf I.4.1}: Computing Methodologies, IMAGE PROCESSING, Digitization. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming.", } @Article{Schlick:1992:TETa, author = "Tamar Schlick and Aaron Fogelson", title = "{TNPACK}\emdash a Truncated {Newton} Minimization Package for Large-Scale Problems: {I}. Algorithm and Usage", journal = j-TOMS, volume = "18", number = "1", pages = "46--70", month = mar, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/128745.150973", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 10 08:50:20 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p46-schlick/", abstract = "We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner $M$ is factored in PCG using a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we briefly describe the method and provide details for program usage.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Schlick:1992:TETb, author = "Tamar Schlick and Aaron Fogelson", title = "{TNPACK}\emdash a Truncated {Newton} Minimization Package for Large-Scale Problems: {II}. Implementation Examples", journal = j-TOMS, volume = "18", number = "1", pages = "71--111", month = mar, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/128745.150975", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 10 08:50:15 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p71-schlick/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf I.6.3}: Computing Methodologies, SIMULATION AND MODELING, Applications. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING. {\bf J.3}: Computer Applications, LIFE AND MEDICAL SCIENCES.", } @Article{Hanson:1992:QTM, author = "R. J. Hanson and Fred T. Krogh", title = "A Quadratic-Tensor Model Algorithm for Nonlinear Least-Squares Problems with Linear Constraints", journal = j-TOMS, volume = "18", number = "2", pages = "115--133", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146857", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Y10 (49M30)", MRnumber = "1 167 883", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p115-hanson/", abstract = "A new algorithm is presented for solving nonlinear least-squares and nonlinear equation problems. The algorithm is based on approximating the nonlinear functions using the quadratic-tensor model proposed by Schnabel and Frank. The problem statement may include simple bounds or more general linear constraints on the unknowns. The algorithm uses a trust-region defined by a box containing the current values of the unknowns. The objective function (Euclidean length of the functions) is allowed to increase at intermediate steps. These increases are allowed as long as our predictor indicates that a new set of best values exists in the trust-region. There is logic provided to retreat to the current best values, should that be required. The computations for the model-problem require a constrained nonlinear least-squares solver. This is done using a simpler version of the algorithm. In its present form the algorithm is effective for problems with linear constraints and dense Jacobian matrices. Results on standard test problems are presented in the Appendix. The new algorithm appears to be efficient in terms of function and Jacobian evaluations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Gurwitz:1992:TCE, author = "Chaya Gurwitz", title = "A Test for Cancellation Errors In Quasi-{Newton} Methods", journal = j-TOMS, volume = "18", number = "2", pages = "134--140", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146876", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "1 167 884", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p134-gurwitz/", abstract = "It has recently been shown that cancellation errors in a quasi-Newton method can increase without bound as the method converges. A simple test is presented to determine when cancellation errors could lead to significant contamination of the approximating matrix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Schlick:1992:ATE, author = "Tamar Schlick and Aaron Fogelson", title = "{Algorithm 702}: {TNPACK}\emdash a Truncated {Newton} Minimization Package for Large-Scale Problems: {I}. Algorithm and Usage", journal = j-TOMS, volume = "18", number = "2", pages = "141--141", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146921; http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p141-schlick/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 10 08:50:33 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Xie:1999:RAU}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Cash:1992:MCS, author = "J. R. Cash and S. Considine", title = "An {MEBDF} Code for Stiff Initial Value Problems", journal = j-TOMS, volume = "18", number = "2", pages = "142--155", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146922", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65L06)", MRnumber = "1 167 885", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p142-cash/", abstract = "In two recent papers one of the present authors has proposed a class of modified extended backward differentiation formulae for the numerical integration of stiff initial value problems. In this paper we describe a code based on this class of formulae and discuss its performance on a large set of stiff test problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Multistep methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1992:AMF, author = "J. R. Cash and S. Considine", title = "{Algorithm 703}: {MEBDF}: {A FORTRAN} Subroutine for Solving First-Order Systems of Stiff Initial Value Problems for Ordinary Differential Equations", journal = j-TOMS, volume = "18", number = "2", pages = "156--158", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146923", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D05 (65L06)", MRnumber = "1 167 886", bibdate = "Sat Jan 27 07:37:25 MST 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p156-cash/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Multistep methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Neidinger:1992:EMN, author = "Richard D. Neidinger", title = "An Efficient Method for the Numerical Evaluation of Partial Derivatives of Arbitrary Order", journal = j-TOMS, volume = "18", number = "2", pages = "159--173", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146924", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D25 (65Y10)", MRnumber = "93b:65040", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p159-neidinger/", abstract = "For any typical multivariable expression $f$, point $a$ in the domain of $f$, and positive integer maxorder, this method produces the numerical values of all partial derivatives at $a$ up through order maxorder. By the technique known as automatic differentiation, theoretically exact results are obtained using numerical (as opposed to symbolic) manipulation. The key ideas are a hyperpyramid data structure and a generalized Leibniz's rule. Any expression in $n$ variables corresponds to a hyperpyramid array, in $n$-dimensional space, containing the numerical values of all unique partial derivatives (not wasting space on different permutations of derivatives). The arrays for simple expressions are combined by hyperpyramid operators to form the arrays for more complicated expressions. These operators are facilitated by a generalized Leibniz's rule which, given a product of multivariable functions, produces any partial derivative by forming the minimum number of products (between two lower partials) together with a product of binomial coefficients. The algorithms are described in abstract pseudo-code. A section on implementation shows how these ideas can be converted into practical and efficient programs in a typical computing environment. For any specific problem, only the expression itself would require recoding.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Edwards:1992:EEN, author = "John A. Edwards", title = "Exact Equations of the Nonlinear Spline", journal = j-TOMS, volume = "18", number = "2", pages = "174--192", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146925", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "41A15 (65D05 65D07 65K10 65Y25)", MRnumber = "93c:41018", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p174-edwards/", abstract = "We define the spline interpolating function, and obtain in directly computable form the elementary set of nonlinear equations describing nonlinear spline curves. Using Newton's and Newton-like methods, we solve typical spline configurations, and hence infer that the procedure will reliably yield precise extremum-energy solutions to nonlinear splines of arbitrary (but presumably reasonable) size and complexity.\par In order to distinguish between stable and unstable states of spline equilibria, we evaluate the energy change resulting from a perturbation, and we briefly discuss aspects of spline existence and uniqueness in relation to the solved examples. We demonstrate the abrupt transition which occurs at the threshold between spline existence and nonexistence, and conclude that proof of a spline's existence is implicit in the solution set of constants yielded by the method.\par The procedure may be regarded on the one hand as a precise and efficient research instrument for investigating the properties of true splines and elastica, and on the other as an everyday method for obtaining ``the smoothest interpolating curve of all''.\par Contact is always maintained with the physical analogue to the curve, the thin uniform elastic beam, since the four assignable parameters used in each spline interval comprise the necessary and sufficient three angles and one length dimension of the actual physical spline.\par On an historical note, the method may be seen to offer progress in the search, begun in the late 17th century, for a definitive solution to the elastica problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Splines. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics.", } @Article{Majaess:1992:SAB, author = "Fouad Majaess and Patrick Keast and Graeme Fairweather and Karin R. Bennett", title = "The Solution of Almost Block Diagonal Linear Systems Arising in Spline Collocation at {Gaussian} Points with Monomial Basis Functions", journal = j-TOMS, volume = "18", number = "2", pages = "193--204", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146926", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65D15 65F05)", MRnumber = "93a:65002", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p193-majaess/", abstract = "Numerical techniques based on piecewise polynomial (that is, spline) collation at Gaussian points are exceedingly effective for the approximate solution of boundary value problems, both for ordinary differential equations and for time dependent partial differential equations. There are several widely available computer codes based on this approach, all of which have at their core a particular choice of basis representation for the piecewise polynomials used to approximate the solutions. Until recently, the most popular approach was to use a B-spline representation, but it has been shown that the B-spline basis is inferior, both in operation counts and conditioning, to a certain monomial basis, and the latter has come more into favor. In this paper, we describe a linear algebraic equations which arise in spline collocation at Gaussian points with such a monomial basis. It is shown that the new package, which implements an alternate column and row pivoting algorithm, is a distinct improvement over existing packages from the points of view of speed and storage requirements. In addition, we describe a second package, an important special case of the first, for solving the almost block diagonal systems which arise when condensation is applied to the systems arising in spline collocation at Gaussian points, and also in other methods for solving two-point boundary value problems, such as implicit Runge--Kutta methods and multiple shooting.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Majaess:1992:AAA, author = "Fouad Majaess and Patrick Keast and Graeme Fairweather and Karin R. Bennett", title = "{Algorithm 704}: {ABDPACK} and {ABBPACK}\emdash {FORTRAN} Programs for the Solution of Almost Block Diagonal Linear Systems Arising in Spline Collocation at {Gaussian} Points with Monomial Basis Functions", journal = j-TOMS, volume = "18", number = "2", pages = "205--210", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146927", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F05)", MRnumber = "93a:65003", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p205-majaess/", abstract = "ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point boundary value problems with separated boundary conditions. The package ABBPACK is designed to handle a subclass of such linear systems which have what may be called an almost block bidiagonal structure. Such systems result, for example, when condensation is applied to the full spline collocation linear system. This package may also be used to solve the almost block bidiagonal systems arising in multiple shooting techniques and implicit Runge--Kutta methods for solving two-point boundary value problems. The algorithms implemented in the package are based on an alternate column and row pivoting scheme which avoids most of the fill-in introduced by more commonly used techniques.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; standardization", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1992:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the {{\tt Expm1}} Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "18", number = "2", pages = "211--222", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146928", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D15", MRnumber = "1 167 891", bibdate = "Sat Feb 24 15:01:45 MST 1996", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See independent analysis and accuracy confirmation of this algorithm in \cite{Kramer:1998:PWC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/", abstract = "Algorithms and implementation details for the function $e^x - 1$ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Gardiner:1992:SSM, author = "Judith D. Gardiner and Alan J. Laub and James J. Amato and Cleve B. Moler", title = "Solution of the {Sylvester} Matrix Equation {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}", journal = j-TOMS, volume = "18", number = "2", pages = "223--231", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146929", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65-04 65F10 65F35)", MRnumber = "1 167 892", bibdate = "Mon Sep 05 08:48:51 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p223-gardiner/", abstract = "A software package has been developed to solve efficiently the Sylvester-type matrix equation $AXB^{T} + CXD^{T} = E$. A transformation method is used which employs the QZ algorithm to structure the equation in such a way that it can be solved columnwise by a back substitution technique. The algorithm is an extension of the Bartels--Stewart method and the Hessenberg--Schur method. The numerical performance of the algorithms and software is demonstrated by application to near-singular systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Gardiner:1992:AFS, author = "Judith D. Gardiner and Matthew R. Wette and Alan J. Laub and James J. Amato and Cleve B. Moler", title = "{Algorithm 705}: {A FORTRAN-77} Software Package for Solving the {Sylvester} Matrix Equation {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}", journal = j-TOMS, volume = "18", number = "2", pages = "232--238", month = jun, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/146847.146930", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65-04 65F10 65F35)", MRnumber = "1 167 893", bibdate = "Tue Mar 14 17:31:30 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrections \cite{Hopkins:2002:RAF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p232-gardiner/", abstract = "This paper documents a software package for solving the Sylvester matrix equation (1) $AXB^{T} + CXD^{T} = E$.\par All quantities are real matrices; $A$ and $C$ are $m \times n$; $B$ and $D$ are $m \times n$; and $X$ and $E$ are $m \times n$. The unknown is $X$. Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2) $AXE^{T} + EXA^{T} + C = 0$ and the discrete time equation (3) $AXA^{T} + C = 0$, for which $A$, $E$, and $C$ is symmetric. The software also provides a means for estimating the condition number of these three equations. The algorithms employed are more fully described in an accompanying paper [3].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Weerawarana:1992:PCG, author = "Sanjiva Weerawarana and Paul S. Wang", title = "A Portable Code Generator for {CRAY FORTRAN}", journal = j-TOMS, volume = "18", number = "3", pages = "241--255", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131767", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p241-weerawarana/", abstract = "One way to combine the powers of symbolic computing with numeric computing is to automatically derive and produce numeric code. This approach has important applications in science and engineering. Once the desired formulas and procedures are derived in a symbolic manipulation system, they can be translated into a target numeric language by a {\em code generator}. GENCRAY is a code generator written in the C language for portability. GENCRAY defines a LISP-style input language that is translated into either FORTRAN 77 or CRAY FORTRAN. By defining its own input syntax, GENCRAY becomes a free-standing code translator that can be made to work with any symbolic manipulation system. GENCRAY is portable to any computer system with a standard C compiler. Input to GENCRAY can come from a file or directly from a symbolic system through a pipe. On UNIX systems with Berkeley networking, GENCRAY also runs as a network server. The input syntax is customizable to allow both Common and Franz LISP input styles. In addition to generating easily vectorizable CRAY FORTRAN code, GENCRAY also provides high-level, easy-to-use parallel programming macros to produce parallel code for the multiprocessor CRAY systems. The features, applications, usage, and implementation of GENCRAY are described. Techniques for producing parallel codes are discussed and illustrated by a substantial example contained in the Appendix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; theory", subject = "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf D.1.2}: Software, PROGRAMMING TECHNIQUES, Automatic Programming. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf I.1.4}: Computing Methodologies, ALGEBRAIC MANIPULATION, Applications. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C.", } @Article{Hansen:1992:FSG, author = "Per Christian Hansen and Tony F. Chan", title = "{FORTRAN} Subroutines for General {Toeplitz} Systems", journal = j-TOMS, volume = "18", number = "3", pages = "256--273", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131768", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Hansen:1994:CAF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p256-hansen/", abstract = "This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen [7, 8] for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do not have many {\em consecutive} ill-conditioned leading principal submatrices, and also produce estimates of the algorithm and matrix condition numbers. In contrast, the classical Levinson algorithm is only guaranteed to be numerically stable for symmetric positive definite Toeplitz matrices, and no condition estimate is produced.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Demmel:1992:SBA, author = "James W. Demmel and Nicholas J. Higham", title = "Stability of Block Algorithms with Fast Level-3 {BLAS}", journal = j-TOMS, volume = "18", number = "3", pages = "274--291", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131769", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:27:16 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/", abstract = "Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar, they have a higher level of granularity than point algorithms, and this makes them well suited to high-performance computers. The numerical stability of the block algorithms in the new linear algebra program library LAPACK is investigated here. It is shown that these algorithms have backward error analyses in which the backward error bounds are commensurate with the error bounds for the underlying level-3 BLAS (BLAS3). One implication is that the block algorithms are as stable as the corresponding point algorithms when conventional BLAS3 are used. A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing {\em LU} factorization, it is shown that fixed precision iterative refinement helps to mitigate the effect of the larger error constants. Despite the positive results presented here, not all plausible block algorithms are stable; we illustrate this with the example of {\em LU} factorization with block triangular factors and describe how to check a block algorithm for stability without doing a full error analysis.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Ammar:1992:IDC, author = "G. S. Ammar and L. Reichel and D. C. Sorensen", title = "An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem", journal = j-TOMS, volume = "18", number = "3", pages = "292--307", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131770", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:42 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Ammar:1994:CAI}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p292-ammar/", abstract = "We present a FORTRAN implementation of a divide-and-conquer method for computing the spectral resolution of a unitary upper Hessenberg matrix $H$. Any such matrix $H$ of order $n$, normalized so that its subdiagonal elements are nonnegative, can be written as a product of $n-1$ Givens matrices and a diagonal matrix. This representation, which we refer to as the Schur parametric form of $H$, arises naturally in applications such as in signal processing and in the computation of Gauss--Szeg{\H{o}} quadrature rules. Our programs utilize the Schur parametrization to compute the spectral decomposition of $H$ without explicitly forming the elements of $H$. If only the eigenvalues and first components of the eigenvectors are desired, as in the applications mentioned above, the algorithm requires only $O(n^{2})$ arithmetic operations. Experimental results presented indicate that the algorithm is reliable and competitive with the general QR algorithm applied to this problem. Moreover, the algorithm can be easily adapted for parallel implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; reliability", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Toint:1992:LFS, author = "Ph. L. Toint and D. Tuyttens", title = "{LSNNO}, {A FORTRAN} Subroutine for Solving Large-Scale Nonlinear Network Optimization Problems", journal = j-TOMS, volume = "18", number = "3", pages = "308--328", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131771", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:27:49 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p308-toint/", abstract = "The implementation and testing of LSNNO, a new FORTRAN subroutine for solving large-scale nonlinear network optimization problems is described. The implemented algorithm applies the concepts of partial separability and partitioned quasi-Newton updating to high-dimensional nonlinear network optimization problems. Some numerical results on both academic and practical problems are reported.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Berntsen:1992:ADA, author = "Jarle Berntsen and Terje O. Espelid", title = "{Algorithm 706}: {DCUTRI}: An Algorithm for Adaptive Cubature Over a Collection of Triangles", journal = j-TOMS, volume = "18", number = "3", pages = "329--342", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:18:59 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Espelid:1998:RAD}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p329-berntsen/", abstract = "An adaptive algorithm for computing an approximation to the integral of each element in a vector function $f(x,y)$ over a two-dimensional region made up of triangles is presented. A FORTRAN implementation of the algorithm is included. The basic cubature rule used over each triangle is a 37-point symmetric rule of degree 13. Based on the same evaluation points the local error for each element in the approximation vector and for each triangle is computed using a sequence of null rule evaluations. A sophisticated error-estimation procedure tries, in a cautious manner, to decide whether we have asymptotic behavior locally for each function. Different actions are taken depending on that decision, and the procedure takes advantage of the basic rule's polynomial degree when computing the error estimate in the asymptotic case.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Hopkins:1992:RPG, author = "Tim Hopkins", title = "Remark on ``{Algorithm 540}: {PDECOL}, General Collocation Software for Partial Differential Equations [{D3}]''", journal = j-TOMS, volume = "18", number = "3", pages = "343--344", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131773", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:27:53 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Madsen:1979:APG}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p343-hopkins/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Nardin:1992:ACN, author = "Mark Nardin and W. F. Perger and Atul Bhalla", title = "{Algorithm 707}: {CONHYP}: a Numerical Evaluator of the Confluent Hypergeometric Function for Complex Arguments of Large Magnitudes", journal = j-TOMS, volume = "18", number = "3", pages = "345--349", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:28:04 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p345-nardin/", abstract = "A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer's series is presented. Extended precision subroutines using large arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to 13 significant figures, and on rare occasion accurate to only 9 for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow; however, the evaluator remains valuable as a benchmark even in such cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Schweikard:1992:RZI, author = "Achim Schweikard", title = "Real Zero Isolation for Trigonometric Polynomials", journal = j-TOMS, volume = "18", number = "3", pages = "350--359", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131775", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65H05 (65D15)", MRnumber = "93g:65066", bibdate = "Fri Sep 30 01:28:05 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p350-schweikard/", abstract = "An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. The method is based on zero isolation techniques for algebraic polynomials. An efficient method for the calculation of the coefficients of a corresponding algebraic polynomial is stated. The complexity of trigonometric zero isolation depending on the degree and the coefficient size of the given trigonometric polynomial is analyzed. In an experimental evaluation, the performance of the method is compared to the performance of recently developed numeric techniques for the approximate determination of all roots of trigonometric polynomials. The case of exponential or hyperbolic polynomials is treated in an appendix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{DiDonato:1992:ASD, author = "Armido R. DiDonato and Alfred H. {Morris, Jr.}", title = "{Algorithm 708}: Significant Digit Computation of the Incomplete Beta Function Ratios", journal = j-TOMS, volume = "18", number = "3", pages = "360--373", month = sep, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/131766.131776", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:14:47 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Brown:1994:CAS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/", abstract = "An algorithm is given for evaluating the incomplete beta function ratio $I_{x}(a,b)$ and its complement $1 - I^{x}(a,b)$. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Buckley:1992:ATA, author = "A. G. Buckley", title = "{Algorithm 709}: Testing Algorithm Implementations", journal = j-TOMS, volume = "18", number = "4", pages = "375--391", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138378", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:52:09 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p375-buckley/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; experimentation", subject = "{\bf D.2.5}: Software, SOFTWARE ENGINEERING, Testing and Debugging, Monitors. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Dongarra:1992:AFS, author = "J. J. Dongarra and G. A. Geist and C. H. Romine", title = "{Algorithm 710}: {FORTRAN} Subroutines for Computing the Eigenvalues and Eigenvectors of a General Matrix by Reduction to General Tridiagonal Form", journal = j-TOMS, volume = "18", number = "4", pages = "392--400", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138352", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:52:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p392-dongarra/", abstract = "This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, to compute the eigenvalues of the tridiagonal matrix, to improve the accuracy of an eigenvalue, and to compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense nonsymmetric matrix faster and more accurately than previous methods. The performance and accuracy of the new routines are compared to two EISPACK paths: RG and HQR-INVIT. The results show that the new routines are more accurate and also faster if less than 20 percent of the eigenpairs are needed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Fisher:1992:DTO, author = "M. E. Fisher and L. S. Jennings", title = "Discrete-Time Optimal Control Problems with General Constraints", journal = j-TOMS, volume = "18", number = "4", pages = "401--413", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138356", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "49M05 (65K99)", MRnumber = "1 199 848", bibdate = "Fri Sep 30 00:52:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p401-fisher/", abstract = "This paper presents a computational procedure for solving combined discrete-time optimal control and optimal parameter selection problems subject to general constraints. The approach adopted is to convert the problem into a nonlinear programming problem which can be solved using standard optimization software. The main features of the procedure are the way the controls are parametrized and the conversion of all constraints into a standard form suitable for computation. The software is available commercially as a FORTRAN program DMISER3 together with a companion program MISER3 for solving continuous-time problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Nash:1992:ABS, author = "Stephen G. Nash and Ariela Sofer", title = "{Algorithm 711}: {BTN}: Software for Parallel Unconstrained Optimization", journal = j-TOMS, volume = "18", number = "4", pages = "414--448", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138359", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:53:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p414-nash/", abstract = "BTN is a collection of FORTRAN subroutines for solving unconstrained nonlinear optimization problems. It currently runs on both Intel hypercube computers (distributed memory) and Sequent computers (shared memory), and can take advantage of vector processors if they are available. The software can also be run on traditional computers to simulate the performance of a parallel computer. BTN is a general-purpose algorithm, capable of solving problems with a large numbers of variables and suitable for users inexperienced with parallel computing. It is designed to be as easy to use as traditional algorithms for this problem, requiring only that a (scalar) subroutine be provided to evaluate the objective function and its gradient vector of first derivatives. The algorithm is based on a block truncated-Newton method. Truncated-Newton methods obtain the search direction by approximately solving the Newton equations via some iterative method. The particular method used in BTN is a block version of the Lanczos method, which is numerically stable for nonconvex problems. In addition to the optimization software, a parallel derivative checker is also provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; documentation", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Leva:1992:FNR, author = "Joseph L. Leva", title = "A Fast Normal Random Number Generator", journal = j-TOMS, volume = "18", number = "4", pages = "449--453", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138364", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:53:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p449-leva/", abstract = "A method is presented for generating pseudorandom numbers with a normal distribution. The technique uses the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves. An optimized quadratic fit reduces the expected number of logarithm evaluations to 0.012 per normal deviate. The method gives a theoretically correct distribution and can be implemented in 15 lines of FORTRAN. Timing and source size comparisons are made with other methods for generating normal deviates. The proposed algorithm compares favorably with some of the better algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; theory", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Leva:1992:ANR, author = "Joseph L. Leva", title = "{Algorithm 712}: a Normal Random Number Generator", journal = j-TOMS, volume = "18", number = "4", pages = "454--455", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138367", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:53:35 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p454-leva/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Boisvert:1992:PVS, author = "Ronald F. Boisvert and Bonita V. Saunders", title = "Portable Vectorized Software for {Bessel} Function Evaluation", journal = j-TOMS, volume = "18", number = "4", pages = "456--469", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138370", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:53:41 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Boisvert:1993:CPV}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p456-boisvert/", abstract = "A suite of computer programs for the evaluation of Bessel functions and modified Bessel functions of orders zero and one for a vector of real arguments is described. Distinguishing characteristics of these programs are that (a) they are portable across a wide range of machines, and (b) they are vectorized in the case when multiple function evaluations are to be performed. The performance of the new programs are compared with software from the FNLIB collection of Fullerton on which the new software is based.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Drezner:1992:CMN, author = "Zvi Drezner", title = "Computation of the Multivariate Normal Integral", journal = j-TOMS, volume = "18", number = "4", pages = "470--480", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138375", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:39 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Drezner:1993:CAC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p470-drezner/", abstract = "This paper presents a direct computation of the multivariate normal integral by the Gauss Quadrature method. An error control method is given. Results are presented for multivariate integrals consisting of up to twelve normal distributions. A computer program in FORTRAN is given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature.", } @Article{Aberth:1992:PCU, author = "Oliver Aberth and Mark J. Schaefer", title = "Precise Computation Using Range Arithmetic, via {C++}", journal = j-TOMS, volume = "18", number = "4", pages = "481--491", month = dec, year = "1992", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/138351.138377", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:53:58 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p481-aberth/", abstract = "An arithmetic is described that can replace floating-point arithmetic for programming tasks requiring assured accuracy. A general explanation is given of how the arithmetic is constructed with C++, and a programming example in this language is supplied. Times for solving representative problems are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++.", } @Article{Cody:1993:ACP, author = "W. J. Cody", title = "{Algorithm 714}: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions", journal = j-TOMS, volume = "19", number = "1", pages = "1--21", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151272", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 20 18:24:35 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/; http://www.acm.org/pubs/toc/Abstracts/toms/151272.html", abstract = "This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.", abstract-2 = "The author discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions. CELEFUNT is a collection of test programs for the complex floating-point elementary functions required by the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG, CEXP, CSIN/CCOS, and the complex power function.", acknowledgement = ack-nhfb, affiliation = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA", ajournal = "ACM Trans. Math. Softw.", classification = "C4100 (Numerical analysis); C5230 (Digital arithmetic methods); C7310 (Mathematics)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex elementary functions; Complex power function; CSIN/CCOS; CSQRT; Floating-point elementary functions; Fortran programs; measurement; performance; Portable test package", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", thesaurus = "Conformance testing; Digital arithmetic; FORTRAN; Mathematics computing; Numerical analysis; Program testing; Software packages", } @Article{Cody:1993:ASE, author = "W. J. Cody", title = "{Algorithm 715}: {SPECFUN}\emdash a Portable {FORTRAN} Package of Special Function Routines and Test Drivers", journal = j-TOMS, volume = "19", number = "1", pages = "22--32", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151273", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:23:18 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Price:1996:RA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/", abstract = "SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Wu:1993:ACH, author = "Trong Wu", title = "An Accurate Computation of the Hypergeometric Distribution Function", journal = j-TOMS, volume = "19", number = "1", pages = "33--43", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151274", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p33-wu/", abstract = "The computation of the cumulative hypergeometric distribution function is of interest to many researchers who are working in the computational sciences and related areas. Presented here is a new method for computing this function that applies prime number factorization to the factorials. We also apply cancellation to the numerator and denominator to reduce the computational complexity of the initial, the tail end, or weighted probabilities to achieve maximum accuracy. The new method includes two algorithms, one using recursion and the other using iteration. These two algorithms are machine independent; precision is arbitrary, subject to storage limitation. The development of the algorithms is discussed, and some test results and the comparison of these two algorithms are given. To implement both algorithms, we use the Ada programming language that is an American National Standard Institute standardized language. The language has special features such as {\em exception handling} and {\em tasks}. {\em Exception handling} is used to make programming easier and to prevent overflow or underflow conditions during the execution of the program. {\em Tasks} are used to compute the numerator and denominator concurrently, and to maximize the possible number of integer multiplications in the numerator and denominator. All of the computations can be done on currently available machines, and the time consumed by these computations remains reasonably small.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; languages", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Ada. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures.", } @Article{Kamel:1993:OES, author = "M. S. Kamel and K. S. Ma and W. H. Enright", title = "{ODEXPERT}: An Expert System to Select Numerical Solvers for Initial Value {ODE} Systems", journal = j-TOMS, volume = "19", number = "1", pages = "44--62", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151275", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p44-kamel/", abstract = "ODEXPERT is a prototype knowledge-based system which selects the appropriate numerical solvers for initial value ordinary differential equations. It is capable of deriving some knowledge about the input problem by performing automated tests to detect properties and structures in the problem which guide the selection process.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Applications and Expert Systems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1993:MAM, author = "J. R. Cash and S. Semnani", title = "A Modified {Adams} Method for {NonStiff} and Mildly Stiff Initial Value Problems", journal = j-TOMS, volume = "19", number = "1", pages = "63--80", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151276", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p63-cash/", abstract = "Adams predictor-corrector methods, and explicit Runge--Kutta formulas, have been widely used for the numerical solution of nonstiff initial value problems. Both of these classes of methods have certain drawbacks, however, and it has long been the aim of numerical analysts to derive a class of formulas that has the advantages of both Adams and Runge--Kutta methods and the disadvantages of neither! In this paper we derive a class of modified Adams formulas that attempts to achieve this aim. When used in a certain precisely defined predictor-corrector mode, these new formulas require three function evaluations per step, but have much better stability than Adams formulas. This improved stability makes the modified Adams formulas particularly effective for mildly stiff problems, and some numerical evidence of this is given. We also consider the performance of the new class of methods on the well-known DETEST test set to show their potential on general nonstiff initial value problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Renka:1993:ATT, author = "R. J. Renka", title = "{Algorithm 716}: {TSPACK}: Tension Spline Curve-Fitting Package", journal = j-TOMS, volume = "19", number = "1", pages = "81--94", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151277; http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p81-renka/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 18:57:35 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Testa:1999:RA}.", abstract = "The primary purpose of TSPACK is to construct a smooth function which interpolates a discrete set of data points. The function may be required to have either one or two continuous derivatives. If the accuracy of the data does not warrant interpolation, a smoothing function (which does not pass through the data points) may be constructed instead. The fitting method is designed to avoid extraneous inflection points (associated with rapidly varying data values) and preserve local shape properties of the data (monotonicity and convexity), or to satisfy the more general constraints of bounds on function values or first derivatives. The package also provides a parametric representation for construction general planar curves and space curves.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Snow:1993:CTP, author = "Dennis M. Snow", title = "Computing Tensor Product Decompositions", journal = j-TOMS, volume = "19", number = "1", pages = "95--108", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151278", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "22-04 (17B10 22E47)", MRnumber = "94e:22001", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p95-snow/", abstract = "An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreducible components. The algorithm uses a known formula which expresses the multiplicities of the highest weight vectors in the decomposition as an alternating sum indexed by the Weyl group. This sum is accomplished with minimal memory requirements using techniques developed previously by the author for efficiently computing Weyl group orbits. Examples are given for each of the exceptional Lie groups.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; measurement; performance; theory", reviewer = "Jeffrey Adams", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems.", } @Article{Bunch:1993:ASM, author = "David S. Bunch and David M. Gay and Roy E. Welsch", title = "{Algorithm 717}: Subroutines for Maximum Likelihood and Quasi-Likelihood Estimation of Parameters in Nonlinear Regression Models", journal = j-TOMS, volume = "19", number = "1", pages = "109--130", month = mar, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/151271.151279", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p109-bunch/", abstract = "We present FORTRAN 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least-squares, maximum likelihood, maximum quasi-likelihood, generalized nonlinear least-squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (``nonlinear GLIM''), and probabilistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least-squares, employs a model/trust-region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between a Gauss--Newton and an augmented Hessian approximation. Gauss--Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Boisvert:1993:CPV, author = "Ronald F. Boisvert and Bonita V. Saunders", title = "Corrigendum: ``{Algorithm 713}: Portable Vectorized Software for {Bessel} Function Evaluation''", journal = j-TOMS, volume = "19", number = "1", pages = "131--131", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:33:37 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Boisvert:1992:PVS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Boisvert:1993:E, author = "Ronald F. Boisvert", title = "Editorial", journal = j-TOMS, volume = "19", number = "2", pages = "135--135", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Duff:1993:CSE, author = "I. S. Duff and J. A. Scott", title = "Computing Selected Eigenvalues of Sparse Unsymmetric Matrices Using Subspace Iteration", journal = j-TOMS, volume = "19", number = "2", pages = "137--159", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152614", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (65F15)", MRnumber = "96c:65078", bibdate = "Tue Nov 14 09:56:28 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Duff:1995:CCS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p137-duff/", abstract = "This paper discusses the design and development of a code to calculate the eigenvalues of a large sparse real unsymmetric matrix that are the rightmost, leftmost, or are of the largest modulus. A subspace iteration algorithm is used to compute a sequence of sets of vectors that converge to an orthonormal basis for the invariant subspace corresponding to the required eigenvalues. This algorithm is combined with Chebychev acceleration if the rightmost or leftmost eigenvalues are sought, or if the eigenvalues of largest modulus are known to be the rightmost or leftmost eigenvalues. An option exists for computing the corresponding eigenvectors. The code does not need the matrix explicitly since it only requires the user to multiply sets of vectors by the matrix. Sophisticated and novel iteration controls, stopping criteria, and restart facilities are provided. The code is shown to be efficient and competitive on a range of test problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Demmel:1993:GSDa, author = "James Demmel and Bo K{\aa}gstr{\"o}m", title = "The Generalized {Schur} Decomposition of an Arbitrary Pencil {$A-\lambda{B}$}: Robust Software with Error Bounds and Applications. {Part I}: {Theory} and Algorithms", journal = j-TOMS, volume = "19", number = "2", pages = "160--174", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152615", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15 (65-04)", MRnumber = "96d:65060a", bibdate = "Fri Aug 26 23:38:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p160-demmel/", abstract = "Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil $A - \lambda B$ (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of $A - \lambda I$ to matrix pencils and reveals the Kronecker structure of a singular pencil. Since computing the Kronecker structure of a singular pencil is a potentially ill-posed problem, it is important to be able to compute rigorous and reliable error bounds for the computed features. The error bounds rely on perturbation theory for reducing subspaces and generalized eigenvalues of singular matrix pencils. The first part of this two-part paper presents the theory and algorithms for the decomposition and its error bounds, while the second part describes the computed generalized Schur decomposition and the software, and presents applications and an example of its use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; geig; generalized Schur decomposition; matrix pencil; nla; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf F.4.1}: Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Demmel:1993:GSDb, author = "James Demmel and Bo K{\aa}gstr{\"o}m", title = "The Generalized {Schur} Decomposition of an Arbitrary Pencil {$A-\lambda B$}: {Robust} Software with Error Bounds and Applications. {Part II}: {Software} and Applications", journal = j-TOMS, volume = "19", number = "2", pages = "175--201", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152616", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15 (65-04)", MRnumber = "96d:65060b", bibdate = "Mon Sep 05 09:34:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p175-demmel/", abstract = "Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil $A - \lambda B$ (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of $A - \lambda I$ to matrix pencils and reveals the Kronecker structure of a singular pencil. The second part of this two-part paper describes the computed generalized Schur decomposition in more detail and the software, and presents applications and an example of its use. Background theory and algorithms for the decomposition and its error bounds are presented in Part I of this paper.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; geig; generalized Schur decomposition; matrix pencil; nla; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf F.4.1}: Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Bai:1993:CCN, author = "Z. Bai and J. Demmel and A. McKenney", title = "On Computing Condition Numbers for the Nonsymmetric Eigenproblem", journal = j-TOMS, volume = "19", number = "2", pages = "202--223", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152617", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F35 (65-04 65F15)", MRnumber = "96c:65074", bibdate = "Mon Sep 05 09:34:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p202-bai/", abstract = "We review the theory of condition numbers for the nonsymmetric eigenproblem and give a tabular summary of bounds for eigenvalues, means of clusters of eigenvalues, eigenvectors, invariant subspaces, and related quantities. We describe the design of new algorithms for estimating these condition numbers. Fortran subroutines implementing these algorithms are in the LAPACK library [1].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; reliability", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Miminis:1993:AFS, author = "George Miminis and Michael Reid", title = "{Algorithm 718}: {A FORTRAN} Subroutine to Solve the Eigenvalues Allocation Problem for Single-Input Systems", journal = j-TOMS, volume = "19", number = "2", pages = "224--232", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152618", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p224-miminis/", abstract = "An efficient implementation of an algorithm for the eigenvalue allocation (pole placement) problem of single-input linear systems using state feedback is given in this paper. The implementation uses the BLAS level-1 [2] subroutines when possible for better performance. A brief description of the algorithm along with some computational details is also given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Greenberg:1993:EAC, author = "Harvey J. Greenberg", title = "Enhancements of {ANALYZE}: a Computer-Assisted Analysis System for Linear Programming", journal = j-TOMS, volume = "19", number = "2", pages = "233--256", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152619", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p233-greenberg/", abstract = "This describes enhancements to provide more advanced computer-assisted analysis of instances of linear programming models. Three categories of enhancements are described: views, engines for obtaining information, and rule-based advising. Examples of their uses include redundancy and infeasibility diagnoses.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; experimentation; languages; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, ANALYZE. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf I.6.2}: Computing Methodologies, SIMULATION AND MODELING, Simulation Languages. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis.", } @Article{Fishman:1993:GSC, author = "George S. Fishman and L. Stephen Yarberry", title = "Generating a Sample from a $k$-Cell Table with Changing Probabilities in {$O(\log_2k)$} Time", journal = j-TOMS, volume = "19", number = "2", pages = "257--261", month = jun, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/152613.152621", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 00:48:36 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p257-fishman/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS.", } @Article{Bentley:1993:TDI, author = "Jon L. Bentley and Mary F. Fernandez and Brian W. Kernighan and Norman L. Schryer", title = "Template-Driven Interfaces for Numerical Subroutines", journal = j-TOMS, volume = "19", number = "3", pages = "265--287", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155757", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p265-bentley/", abstract = "This paper describes a set of interfaces for numerical subroutines. Typing a short (often one-line) description allows one to solve problems in application domains including least-squares data fitting, differential equations, minimization, root finding, and integration. Our approach of ``template-driven programming'' makes it easy to build such an interface: a simple one takes a few hours to construct, while a few days suffice to build the most complex program we describe.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "awk; design; experimentation; Fortran; languages; Maple; UNIX shell", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, User interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.2.m}: Software, SOFTWARE ENGINEERING, Miscellaneous, Reusable software.", } @Article{Bailey:1993:AMT, author = "David H. Bailey", title = "{Algorithm 719}: Multiprecision Translation and Execution of {FORTRAN} Programs", journal = j-TOMS, volume = "19", number = "3", pages = "288--319", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155767", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Dec 13 18:37:31 1995", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/", abstract = "This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose.\par The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls.\par This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.", abstract-2 = "The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA", ajournal = "ACM Trans. Math. Softw.", classification = "C5230 (Digital arithmetic methods); C6120 (File organisation); C6140D (High level languages); C6150C (Compilers, interpreters and other processors); C7310 (Mathematics)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithm 719; Arithmetic operations; Array space; Complex data types; Computational expressions; Floating point numbers; Fortran programs; Fortran subroutines; Fortran utilities; Fortran-77 intrinsics; Mixed mode operations; Multiprecision computation; Multiprecision data types; Multiprecision subroutine calls; Multiprecision translation; Operator precedence; Source directives; Transcendental functions; Translator program", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems; G.1.0 [Numerical Analysis]: General; G.1.2 [Numerical Analysis]; Approximation", thesaurus = "Data structures; Digital arithmetic; FORTRAN; Mathematics computing; Program interpreters; Subroutines", } @Article{Berntsen:1993:AAA, author = "Jarle Berntsen and Ronald Cools and Terje O. Espelid", title = "{Algorithm 720}: An Algorithm for Adaptive Cubature Over a Collection of $3$-Dimensional Simplices", journal = j-TOMS, volume = "19", number = "3", pages = "320--332", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155785; http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p320-berntsen/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An adaptive algorithm for computing an approximation to the integral of each element in a vector of functions over a 3-dimensional region covered by simplices is presented. The algorithm is encoded in FORTRAN 77.\par Locally, a cubature formula of degree 8 with 43 points is used to approximate an integral. The local error estimate is based on the same evaluation points. The error estimation procedure tries to decide whether the approximation for each function has asymptotic behavior, and different actions are taken depending on that decision.\par The simplex with the largest error is subdivided into 8 simplices. The local procedure is then applied to each new region. This procedure is repeated until convergence.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; automatic integration; cubature; cubature rules; error estimation; null rules; reliability; symmetry; tetrahedrons", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- adaptive quadrature; multiple quadrature; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; reliability and robustness", } @Article{Duffy:1993:NIL, author = "Dean G. Duffy", title = "On the Numerical Inversion of {Laplace} Transforms: Comparison of Three New Methods on Characteristic Problems from Applications", journal = j-TOMS, volume = "19", number = "3", pages = "333--359", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155788", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p333-duffy/", abstract = "Three frequently used methods for numerically inverting Laplace transforms are tested on complicated transforms taken from the literature. The first method is a straightforward application of the trapezoidal rule to Bromwich's integral. The second method, developed by Weeks [22], integrates Bromwich's integral by using Laguerre polynomials. The third method, devised by Talbot [18], deforms Bromwich's contour so that the integrand of Bromwich's integral is small at the beginning and end of the contour. These methods are also applied to joint Laplace-Fourier transform problems. All three methods give satisfactory results; Talbot's, however, has an accurate method for choosing required parameters.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; theory", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems", } @Article{Pruess:1993:MSS, author = "Steven Pruess and Charles T. Fulton", title = "Mathematical Software for {Sturm--Liouville} Problems", journal = j-TOMS, volume = "19", number = "3", pages = "360--376", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155791", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p360-pruess/", abstract = "Software is described for the Sturm--Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The underlying algorithms are briefly described, and several examples are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; approximating the coefficients; eigenfunctions; performance; shooting methods; spectral classification; spectral density functions; Sturm--Liouville eigenvalues", subject = "G.1.7 [Numerical Analysis]: Ordinary Differential Equations -- boundary value problems; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis", } @Article{Shirts:1993:CES, author = "Randall B. Shirts", title = "The Computation of Eigenvalues and Solutions of {Mathieu}'s Differential Equation for Noninteger Order", journal = j-TOMS, volume = "19", number = "3", pages = "377--390", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155796", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p377-shirts/", abstract = "Two algorithms for calculating the eigenvalues and solutions of Mathieu's differential equation for noninteger order are described. In the first algorithm, Leeb's method is generalized, expanding the Mathieu equation in Fourier series and diagonalizing the symmetric tridiagonal matrix that results. Numerical testing was used to parameterize the minimum matrix dimension that must be used to achieve accuracy in the eigenvalue of one part in $10^{12}$. This method returns a set of eigenvalues below a given order and their associated solutions simultaneously. A second algorithm is presented which uses approximations to the eigenvalues (Taylor series and asymptotic expansions) and then iteratively corrects the approximations using Newton's method until the corrections are less than a given tolerance. A backward recursion of the continued fraction expansion is used. The second algorithm is faster and is optimized to obtain accuracy of one part in $10^{14}$, but has only been implemented for orders less than 10.5.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; eigenvalues; Floquet solutions; Mathieu equation; noninteger order; numerical software; ordinary differential equations; performance", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms", } @Article{Shirts:1993:AMM, author = "Randall B. Shirts", title = "{Algorithm 721}: {MTIEU1} and {MTIEU2}: Two Subroutines to Compute Eigenvalues and Solutions to {Mathieu}'s Differential Equation for Noninteger and Integer Order", journal = j-TOMS, volume = "19", number = "3", pages = "391--406", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155847", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p391-shirts/", abstract = "Two FORTRAN routines are described which calculate eigenvalues and eigenfunctions of Mathieu's differential equation for noninteger as well as integer order, MTIEU1 uses standard matrix techniques with dimension parameterized to give accuracy in the eigenvalue of one part in $10^{12}$. MTIEU2 used continued fraction techniques and is optimized to give accuracy in the eigenvalue of one part in $10^{14}$. The limitations of the algorithms are also discussed and illustrated.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; eigenvalues; Floquet solutions; FORTRAN; Mathieu equation; noninteger order; numerical software; ordinary differential equations; performance", subject = "G.1.0 [General Numerical Analysis]", } @Article{Haag:1993:QLA, author = "J. B. Haag and D. S. Watkins", title = "{QR}-Like Algorithms for the Nonsymmetric Eigenvalue Problem", journal = j-TOMS, volume = "19", number = "3", pages = "407--418", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.155849", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p407-haag/", abstract = "Hybrid codes that combine elements of the QR and LR algorithms are described. The codes can calculate the eigenvalues and, optionally, eigenvectors of real, nonsymmetric matrices. Extensive tests are presented as evidence that, for certain choices of parameters, the hybrid codes possess the same high reliability as the QR algorithm and are significantly faster. The greatest success has been achieved with the codes that calculate eigenvalues only. These can do the task in 15\% to 50\% less time than the QR algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; chasing the bulge; eigenvalue; eigenvector; experimentation; GR algorithm; LR algorithm; measurement; performance; QR algorithm; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems.", } @Article{Chang:1993:ICR, author = "S. Frank Chang and S. Thomas McCormick", title = "Implementation and Computational Results for the Hierarchical Algorithm for Making Sparse Matrices Sparser", journal = j-TOMS, volume = "19", number = "3", pages = "419--441", month = sep, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/155743.152620", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p419-chang/", abstract = "If A is the (sparse) coefficient matrix of linear-equality constraints, for what nonsingular $T$ is A = TA as sparse as possible, and how can it be efficiently computed? An efficient algorithm for this {\em Sparsity Problem} (SP) would be a valuable preprocessor for linearly constrained optimization problems. In a companion paper we developed a two-pass approach to solve SP called the {\em Hierarchical Algorithm}. In this paper we report on how we implemented the Hierarchical Algorithm into a code called HASP, and our computational experience in testing HASP on the NETLIB linear-programming problems. We found that HASP substantially outperformed a previous code for SP and that it produced a net savings in optimization time on the NETLIB problems. The results allow us to give guidelines for its use in practice.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance; verification", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems -- computations on matrices; G.1.6 [Numerical Analysis]: Optimization -- linear programming; G.4 [Mathematics of Computing]: Mathematical Software -- algorithms analysis; efficiency", } @Article{Cody:1993:AFS, author = "W. J. Cody and Jerome T. Coonen", title = "{Algorithm 722}: Functions to Support the {IEEE} Standard for Binary Floating-Point Arithmetic", journal = j-TOMS, volume = "19", number = "4", pages = "443--451", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168185", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Feb 24 15:01:45 MST 1996", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/", abstract = "This paper describes C programs for the support functions {\em copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x)}, and {\em isnan(x)} recommended in the Appendix to the {\em IEEE Standard for Binary Floating-Point Arithmetic.} In the case of {\em logb}, the modified definition given in the later {\em IEEE Standard for Radix-Independent Floating-Point Arithmetic} is followed. These programs should run without modification on most systems conforming to the binary standard.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliation = "Argonne Nat. Lab., IL, USA", ajournal = "ACM Trans. Math. Softw.", classification = "C5230 (Digital arithmetic methods); C6130 (Data handling techniques); C7310 (Mathematics)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "C programs; Copysign(x,y); Finite(x); IEEE Standard for Binary Floating-point arithmetic; Isnan(x); Logb(x); Nextafter(x,y); Numerical software; Scalb(x,n)", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.4 [Numerical Analysis]: Mathematical Software -- certification and testing", thesaurus = "Data handling; Digital arithmetic; Mathematics computing; Standards", } @Article{Snyder:1993:AFI, author = "W. Van Snyder", title = "{Algorithm 723}: {Fresnel} Integrals", journal = j-TOMS, volume = "19", number = "4", pages = "452--456", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168193", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:24:56 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/", abstract = "An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; special functions", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Ribbens:1993:TPM, author = "Calvin J. Ribbens and Layne T. Watson and Colin Desa", title = "Toward Parallel Mathematical Software for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "19", number = "4", pages = "457--473", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168383", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p457-ribbens/", abstract = "Three approaches to parallelizing important components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing precompiler, and a two-level approach based on extensive use of a set of low level computational kernels. The focus is on shared memory architectures. Each approach to parallelization is described in detail, along with a discussion of the effort involved. Performance on a test problem, using up to sixteen processors of a Sequent Symmetry S81, is reported and discussed. Implications for the parallelization of a broad class of mathematical software are drawn.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "G.1.0 [Numerical Analysis]: General -- parallel algorithms; G.1.8 [Numerical Analysis]: Partial Differential Equations -- elliptic equations; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; portability", } @Article{Abernathy:1993:ASE, author = "Roger W. Abernathy and Robert P. Smith", title = "Applying Series Expansion to the Inverse Beta Distribution to Find Percentiles of the ${F}$-Distribution", journal = j-TOMS, volume = "19", number = "4", pages = "474--480", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168387", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p474-abernathy/", abstract = "Let $0 <= 1$ and $F$ be the cumulative distribution function (cdf) of the $F$-Distribution. We wish to find $x_{p}$ such that $F(x_{p}|n_{1}, n_{2}) = p$, where $n_{1}$ and $n_{2}$ are the degrees of freedom. Traditionally, $x_{p}$ is found using a numerical root-finding method, such as Newton's method. In this paper, a procedure based on a series expansion for finding $x_{p}$is given. The series expansion method has been applied to the normal, chi-square, and $t$ distributions, but because of computational difficulties, it has not been applied to the $F$-Distribution. These problems have been overcome by making the standard transformation to the beta distribution.\par The procedure is explained in Sections 3 and 4. Empirical results of a comparison of CPU times are given in Section 5. The series expansion is compared to some of the standard root-finding methods. A table is given for $p = 0.90$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; cumulative distribution function; cumulative distribution function (cdf); distribution function; F-distribution; Newton's method; performance; root-finding methods; Taylor series", subject = "G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations; G.3 [Probability and Statistics]", } @Article{Abernathy:1993:APC, author = "Roger W. Abernathy and Robert P. Smith", title = "{Algorithm 724}: Program to Calculate $ {F} $-Percentiles", journal = j-TOMS, volume = "19", number = "4", pages = "481--483", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168405", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/sgml.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p481-abernathy/", abstract = "Let $ 0 < p < 1 $ be given and let $F$ be the cumulative distribution function of the $F$-Distribution with $ (M, N) $, degrees of freedom. This FORTRAN 77 routine is a complement to [1] where a method was presented to find the inverse of the $F$-Distribution function, FINV($ M, N, P $ ), using a series expansion technique to find the inverse for the Beta Distribution function.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; cumulative distribution function (cdf); distribution function; experimentation; F-distribution; Newton's method; root-finding methods; Taylor series; theory", subject = "G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations", } @Article{Clarkson:1993:RAF, author = "Douglas B. Clarkson and Yuan-an Fan and Harry Joe", title = "A Remark on {Algorithm 643}: {FEXACT}: An Algorithm for Performing {Fisher}'s Exact Test in $r\times{c}$ Contingency Tables", journal = j-TOMS, volume = "19", number = "4", pages = "484--488", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Mehta:1986:AFF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p484-clarkson/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; measurement; performance; theory", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Hormann:1993:PRN, author = "Wolfgang H{\"o}rmann and G. Deflinger", title = "A Portable Random Number Generator Well Suited for the Rejection Method", journal = j-TOMS, volume = "19", number = "4", pages = "489--495", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168414", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p489-hormann/", abstract = "Up to now, all known efficient portable implementations of linear congruential random number generators with modulus $ 2^{31} - 1 $ have worked only with multipliers that are small compared with the modulus. We show that for nonuniform distributions, the rejection method may generate random numbers of bad qualify if combined with a linear congruential generator with small multiplier. A method is described that works for any multiplier smaller than $ 2^{30} $. It uses the decomposition of multiplier and seed in high-order and low-order bits to compute the upper and lower half of the product. The sum of the two halves gives the product of multiplier and seed modulo $ 2^{21} - 1 $. Coded in ANSI-C and FORTRAN77 the method results in a portable implementation of the linear congruential generator that is as fast or faster than other portable methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; linear congruential generator; portability; quality of nonuniform random numbers; rejection method; uniform random number generator", subject = "G.3 [Mathematics of Computation]: Probability and Statistics -- random number generation", } @Article{Grassmann:1993:REC, author = "Winifred K. Grassmann", title = "Rounding Errors in Certain Algorithms Involving {Markov} Chains", journal = j-TOMS, volume = "19", number = "4", pages = "496--508", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168416", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 07 16:38:26 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p496-grassmann/", abstract = "A number of algorithms involving Markov chains contain no subtractions. This property makes the analysis of rounding errors particularly simple. To show this, some principles for analyzing the propagation and generation of rounding errors in algorithms containing no subtraction are discussed first. These principles are then applied in the context of a simple recursive algorithm involving the transient solution of discrete-time Markov chains, Jensen's algorithm, and state reduction. Jensen's algorithm, also known as randomization or uniformization, is an algorithm for finding transient solutions of continuous-time Markov chains. State reduction is a method for finding equilibrium probabilities for discrete-time or continuous-time Markov chains.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Khoury:1993:TPG, author = "B. N. Khoury and P. M. Pardalos and D.-Z. Du", title = "A Test Problem Generator for the {Steiner} Problem in Graphs", journal = j-TOMS, volume = "19", number = "4", pages = "509--522", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168420", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Nov 06 07:19:45 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p509-khoury/", abstract = "In this paper we present a new binary-programming formulation for the Steiner problem in graphs (SPG), which is well known to be NP-hard. We use this formulation to generate test problems with known optimal solutions. The technique uses the KKT optimality conditions on the corresponding quadratically constrained optimization problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; integer programming; performance; Steiner problem in graphs; test problems", subject = "G.1.6 [Numerical Analysis]: Optimization -- integer programming; G.4 [Mathematics of Computing]: Mathematical Software -- certification and testing; efficiency", } @Article{Joe:1993:ILM, author = "Stephen Joe and Ian H. Sloan", title = "Implementation of a Lattice Method for Numerical Multiple Integration", journal = j-TOMS, volume = "19", number = "4", pages = "523--545", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168425", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:08:44 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Joe:1994:CIL}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p523-joe/", abstract = "An implementation of a method for numerical multiple integration based on a sequence of imbedded lattice rules is given. Besides yielding an approximation to the integral, this implementation also provides an error estimate which does not require much extra computation. The results of some numerical experiments conclude the paper.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; lattice rules; performance", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature", } @Article{Drezner:1993:CAC, author = "Zvi Drezner", title = "Corrigendum: ``{Algorithm 725}. Computation of the Multivariate Normal Integral''", journal = j-TOMS, volume = "19", number = "4", pages = "546--546", month = dec, year = "1993", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/168173.168428", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:05:07 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Drezner:1992:CMN}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p546-drezner/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; multivariate normal probability", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature.", } @Article{Boisvert:1994:CST, author = "Ronald F. Boisvert", title = "Charter and Scope: Transactions on Mathematical Software ({TOMS})", journal = j-TOMS, volume = "20", number = "1", pages = "1--2", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Renka:1994:CSC, author = "Robert J. Renka", title = "Charter and Scope: Collected Algorithms ({CALGO})", journal = j-TOMS, volume = "20", number = "1", pages = "3--3", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Neusius:1994:NTA, author = "Christian Neusius and Jan Olszewski", title = "A Noniterative Thinning Algorithm", journal = j-TOMS, volume = "20", number = "1", pages = "5--20", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174604", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68U10", MRnumber = "96h:68221", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p5-neusius/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:1994:ACP, author = "Walter Gautschi", title = "{Algorithm 726}: {ORTHPOL}\emdash a Package of Routines for Generating Orthogonal Polynomials and {Gauss}-Type Quadrature Rules", journal = j-TOMS, volume = "20", number = "1", pages = "21--62", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174605", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:16:24 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Gautschi:1998:RAO}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p21-gautschi/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pennington:1994:NNL, author = "S. V. Pennington and M. Berzins", title = "New {NAG} Library Software for First-Order Partial Differential Equations", journal = j-TOMS, volume = "20", number = "1", pages = "63--99", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.155272", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p63-pennington/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hashem:1994:AQE, author = "Sherif Hashem and Bruce Schmeiser", title = "{Algorithm 727}: Quantile Estimation Using Overlapping Batch Statistics", journal = j-TOMS, volume = "20", number = "1", pages = "100--102", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p100-hashem/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Calamai:1994:GQB, author = "Paul H. Calamai and Luis N. Vicente", title = "Generating Quadratic Bilevel Programming Test Problems", journal = j-TOMS, volume = "20", number = "1", pages = "103--119", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174411", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 368 021", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p103-calamai/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Calamai:1994:AFS, author = "Paul H. Calamai and Luis N. Vicente", title = "{Algorithm 728}: {FORTRAN} Subroutines for Generating Quadratic Bilevel Programming Test Problems", journal = j-TOMS, volume = "20", number = "1", pages = "120--123", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174410", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 368 022", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p120-calamai/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jeffrey:1994:ETI, author = "D. J. Jeffrey and A. D. Rich", title = "The Evaluation of Trigonometric Integrals Avoiding Spurious Discontinuities", journal = j-TOMS, volume = "20", number = "1", pages = "124--135", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174409", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30 (65-04)", MRnumber = "96h:65034", bibdate = "Tue Sep 06 19:02:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p124-jeffrey/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Matstoms:1994:SQF, author = "Pontus Matstoms", title = "Sparse {QR} Factorization in {MATLAB}", journal = j-TOMS, volume = "20", number = "1", pages = "136--159", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174408", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:18 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p136-matstoms/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "multfr; qrd; sparse", } @Article{Hansen:1994:CAF, author = "Per Christian Hansen and Tony F. Chan", title = "Corrigendum: ``{Algorithm 729}: {FORTRAN} Subroutines for General {Toeplitz} Systems''", journal = j-TOMS, volume = "20", number = "1", pages = "160--160", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174407", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:10:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hansen:1992:FSG}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p160-hansen/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ammar:1994:CAI, author = "G. S. Ammar and L. Reichel and D. C. Sorensen", title = "Corrigendum: ``{Algorithm 730}: An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem''", journal = j-TOMS, volume = "20", number = "1", pages = "161--161", month = mar, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/174603.174406", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:05:32 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Ammar:1992:IDC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p161-ammar/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Salvy:1994:GMP, author = "Bruno Salvy and Paul Zimmerman", title = "{GFUN}: a {Maple} Package for the Manipulation of Generating and Holonomic Functions in One Variable", journal = j-TOMS, volume = "20", number = "2", pages = "163--177", month = jun, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/178365.178368", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:27:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p163-salvy/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; computer algebra; generating functions; linear differential equations; linear recurrences", subject = "G.2.1 [Discrete Mathematics]: Combinatorics--generating functions; recurrences and difference equations; I.1.2 [Algebraic Manipulation]: Algorithms", } @Article{Dayde:1994:PBI, author = "Michael J. Dayd{\'e} and Iain S. Duff and Antoine Petitet", title = "A Parallel Block Implementation of Level-3 {BLAS} for {MIMD} Vector Processors", journal = j-TOMS, volume = "20", number = "2", pages = "178--193", month = jun, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/178365.174413", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 09 13:52:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p178-dayde/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Level-3 BLAS; matrix-matrix kernels; measurement; parallelization; performance; vectorization", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems--computations on matrices; G.1.0 [Numerical Analysis]: General--numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and iterative methods); G.4 [Mathematics of Computing]: Mathematical Software--certification and testing; efficiency; portability; reliability and robustness; verification", } @Article{Blom:1994:AMG, author = "J. G. Blom and P. A. Zegeling", title = "{Algorithm 731}: a Moving-Grid Interface for Systems of One-Dimensional Time-Dependent Partial Differential Equations", journal = j-TOMS, volume = "20", number = "2", pages = "194--214", month = jun, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/178365.178391", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:27:31 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p194-blom/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Lagrangian methods; mathematical software; method of lines; moving grids; partial differential equations; performance; reliability; time-dependent problems", subject = "G.1.0 [Numerical Analysis]: General; G.1.8 [Numerical Analysis]: Partial Differential Equations; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Hull:1994:ICE, author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang", title = "Implementing Complex Elementary Functions Using Exception Handling", journal = j-TOMS, volume = "20", number = "2", pages = "215--244", month = jun, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/178365.178404", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 21 15:10:29 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See correction \cite{Anonymous:1994:C}, and improved analysis, tightened bounds, and exhibition of worst cases for complex square roots \cite{Jeannerod:2017:REC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/", abstract = "Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; complex elementary functions; design; implementation", subject = "G.1.0 [Numerical Analysis]: General--error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation--elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software--algorithm analysis; reliability and robustness; verification", } @Article{Joe:1994:CIL, author = "Stephen Joe and Ian H. Sloan", title = "Corrigendum: ``{Implementation} of a Lattice Method for Numerical Multiple Integration''", journal = j-TOMS, volume = "20", number = "2", pages = "245--245", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 13:05:52 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Joe:1993:ILM}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Cummins:1994:ASS, author = "Patrick F. Cummins and Geoffrey K. Vallis", title = "{Algorithm 732}: Solvers for Self-Adjoint Elliptic Problems in Irregular Two-Dimensional Domains", journal = j-TOMS, volume = "20", number = "3", pages = "247--261", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192118", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 12:53:13 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p247-cummins/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; capacitance iteration; capacitance matrix; elliptic equations; fast Poisson solvers; Green's function", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.8 [Numerical Analysis]: Partial Differential Equations -- elliptic equations", } @Article{Kraft:1994:ATF, author = "Dieter Kraft", title = "{Algorithm 733}: {TOMP}---{Fortran} Modules for Optimal Control Calculations", journal = j-TOMS, volume = "20", number = "3", pages = "262--281", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192124", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 09:25:54 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p262-kraft/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; boundary value problems; manipulators; optimal control; robotics; shooting method", subject = "G.1.6 [Numerical Analysis]: Optimization; G.1.7 [Numerical Analysis]: Ordinary Differential Equations; G.4 [Mathematics of Computing]: Mathematical Software; I.2.9 [Artificial Intelligence]: Robotics", } @Article{Averbukh:1994:RA, author = "Victoria Z. Averbukh and Samuel Figueroa and Tamar Schlick", title = "Remark on {Algorithm 566}", journal = j-TOMS, volume = "20", number = "3", pages = "282--285", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192128", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{More:1981:AFS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p282-averbukh/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Hessian subroutines; performance", subject = "D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; enhancement; G.1.6 [Numerical Analysis]: Optimization -- nonlinear programming", } @Article{More:1994:LSA, author = "Jorge J. Mor{\'e} and David J. Thuente", title = "Line Search Algorithms With Guaranteed Sufficient Decrease", journal = j-TOMS, volume = "20", number = "3", pages = "286--307", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192132", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C30 (65K05)", MRnumber = "96k:90074", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p286-more/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; conjugate gradient algorithms; line search algorithms; nonlinear optimization; truncated Newton algorithms; variable metric algorithms", reviewer = "K. Schittkowski", subject = "G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; gradient methods; nonlinear programming; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; reliability and robustness", } @Article{Buckley:1994:CFC, author = "A. G. Buckley", title = "Conversion to {Fortran 90}: a Case Study", journal = j-TOMS, volume = "20", number = "3", pages = "308--353", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192139", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p308-buckley/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "conversion; Fortran 90; new features; overview", } @Article{Buckley:1994:AFC, author = "A. G. Buckley", title = "{Algorithm 734}: a {Fortran} 90 Code for Unconstrained Nonlinear Minimization", journal = j-TOMS, volume = "20", number = "3", pages = "354--372", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192146", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p354-buckley/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; conversion; Fortran 90; limited memory; new features; nonlinear optimization; quasi-Newton", subject = "G.1.6 [Numerical Analysis]: Optimization -- gradient methods", } @Article{Kim:1994:PNA, author = "K. Kim and J. L. Nazareth", title = "A Primal Null-Space Affine-Scaling Method", journal = j-TOMS, volume = "20", number = "3", pages = "373--392", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192153", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C05 (65-04 65K05)", MRnumber = "1 367 801", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p373-kim/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; conjugate gradients; diagonal preconditioning; interior-point algorithm; null-space affine scaling; primal method", subject = "G.1.6 [Numerical Analysis]: Optimization -- linear programming", } @Article{Brown:1994:CAS, author = "Barry W. Brown and Lawrence Levy", title = "Certification of {Algorithm 708}: Significant Digit Computation of the Incomplete Beta", journal = j-TOMS, volume = "20", number = "3", pages = "393--397", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192155", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{DiDonato:1992:ASD}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; continued fractions; F-distribution", subject = "G.1.2 [Numerical Analysis]: Approximation", } @Article{Taswell:1994:AWT, author = "Carl Taswell and Kevin C. McGill", title = "{Algorithm 735}: Wavelet Transform Algorithms for Finite-Duration Discrete-Time Signals", journal = j-TOMS, volume = "20", number = "3", pages = "398--412", month = sep, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/192115.192156", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 09:25:55 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p398-taswell/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; multiresolution analysis; signal processing; waveform analysis; wavelet transform; wavelets", subject = "G.1.2 [Numerical Analysis]: Approximations; G.4 [Mathematics of Computing]: Mathematical Software; I.4.5 [Image Processing]: Reconstruction", } @Article{Dunkl:1994:CHI, author = "Charles F. Dunkl and Donald E. Ramirez", title = "Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids", journal = j-TOMS, volume = "20", number = "4", pages = "413--426", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198430", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "1 368 024", bibdate = "Tue Mar 14 16:16:49 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics", } @Article{Dunkl:1994:AHI, author = "Charles F. Dunkl and Donald E. Ramirez", title = "{Algorithm 736}: Hyperelliptic Integrals and the Surface Measure of Ellipsoids", journal = j-TOMS, volume = "20", number = "4", pages = "427--435", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198431", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D30", MRnumber = "1 368 025", bibdate = "Tue Mar 14 16:16:51 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics", } @Article{Fruchtl:1994:NAE, author = "H. Fr{\"u}chtl and P. Otto", title = "A New Algorithm for the Evaluation of the Incomplete Gamma Function on Vector Computers", journal = j-TOMS, volume = "20", number = "4", pages = "436--446", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198432", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:16:52 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Incomplete Gamma Function; quantum chemistry; two-electron integrals", subject = "C.1.2 [Processor Architectures]: Multiple Data Stream Architectures -- array and vector processors; G.1.2 [Numerical Analysis]: Approximation -- rational approximation; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; J.2 [Computer Applications]: Physical Sciences and Engineering -- chemistry", } @Article{Kearfott:1994:AIP, author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu", title = "{Algorithm 737}: {INTLIB}: a Portable {Fortran-77} Elementary Function Library", journal = j-TOMS, volume = "20", number = "4", pages = "447--459", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198433", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:22:20 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See companion interval arithmetic package \cite{Kearfott:1996:IFM}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p447-kearfott/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic; operator overloading; standard functions", subject = "D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation", } @Article{Peters:1994:EAE, author = "J{\"o}rg Peters", title = "Evaluation and Approximate Evaluation of the Multivariate {Bernstein--B{\'e}zier} Form on a Regularly Partitioned Simplex", journal = j-TOMS, volume = "20", number = "4", pages = "460--480", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198434", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D17 (65-04)", MRnumber = "1 368 026", bibdate = "Tue Mar 14 16:28:34 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p460-peters/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernstein--B{\'e}zier form; evaluation; multivariate; power form; subdivision", subject = "G.1.2 [Numerical Analysis]: Approximation; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling", } @Article{Li:1994:RSA, author = "Kim-Hung Li", title = "Reservoir Sampling Algorithms of Time Complexity {$O(n(1+\log(N/n)))$}", journal = j-TOMS, volume = "20", number = "4", pages = "481--493", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198435", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:16:57 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p481-li/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "analysis of algorithms; random sampling; reservoir", subject = "G.3 [Mathematics of Computing]: Probability and Statistics -- probabilistic algorithms; random number generation; statistical software; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis", } @Article{Bratley:1994:APG, author = "Paul Bratley and Bennett L. Fox and Harald Niederreiter", title = "{Algorithm 738}: {Programs} to Generate {Niederreiter}'s Low-discrepancy Sequences", journal = j-TOMS, volume = "20", number = "4", pages = "494--495", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198436", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 10 15:51:40 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p494-bratley/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "low-discrepancy sequences; quasi-Monte Carlo; quasirandom sequences", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation; I.6 [Computing Methodologies]: Simulation and Modeling", } @Article{Gustafsson:1994:CTT, author = "Kjell Gustafsson", title = "Control Theoretic Techniques for Stepsize Selection in Implicit {Runge--Kutta} Methods", journal = j-TOMS, volume = "20", number = "4", pages = "496--517", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198437", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65L06", MRnumber = "1 368 027", bibdate = "Tue Mar 14 16:17:00 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p496-gustafsson/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "control theory; numerical integration; Runge--Kutta methods; stability; stepsize selection", subject = "G.1.7 [Numerical Analysis]: Ordinary Differential Equations -- initial value problems; single step methods; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; reliability and robustness", } @Article{Chow:1994:ASP, author = "Ta-Tung Chow and Elizabeth Eskow and Robert B. Schnabel", title = "{Algorithm 739}: a Software Package for Unconstrained Optimization using Tensor Methods", journal = j-TOMS, volume = "20", number = "4", pages = "518--530", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198438", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 10 15:51:48 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p518-chow/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "higher-order model; tensor method; unconstrained optimization", subject = "G.1.6 [Numerical Analysis]: Optimization -- Gradient methods; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; reliability and robustness", } @Article{Pinar:1994:DPL, author = "Mustafa Pinar and Stavros A. Zenios", title = "Data-level Parallel Linear-quadratic Penalty Algorithm for Multicommodity Network Flows", journal = j-TOMS, volume = "20", number = "4", pages = "531--552", month = dec, year = "1994", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/198429.198439", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:27:42 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p531-pinar/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "massively parallel algorithms; multicommodity network problems; parallel optimization", subject = "D.1.3 [Programming Techniques]: Concurrent Programming -- parallel programming; E.1 [Data]: Data Structures; G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; nonlinear programming; G.2.2 [Discrete Mathematics]: Graph Theory -- network problems", } @Article{Anonymous:1994:C, author = "Anonymous", title = "Corrigenda", journal = j-TOMS, volume = "20", number = "4", pages = "553--553", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:03 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Hull:1994:ICE}", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Boisvert:1995:PST, author = "Ronald F. Boisvert", title = "Purpose and Scope: {TOMS}", journal = j-TOMS, volume = "21", number = "1", pages = "1--2", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:05 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Hopkins:1995:PSC, author = "Tim R. Hopkins", title = "Purpose and Scope: {CALGO}", journal = j-TOMS, volume = "21", number = "1", pages = "3--3", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:06 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Jones:1995:IIC, author = "Mark T. Jones and Paul E. Plassmann", title = "An Improved Incomplete {Cholesky} Factorization", journal = j-TOMS, volume = "21", number = "1", pages = "5--17", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200981", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F10 (65F50)", MRnumber = "1 365 810", bibdate = "Tue Mar 14 16:17:12 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p5-jones/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "incomplete Cholesky; incomplete factorization; preconditioners; sparse matrices", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems; sparse and very large systems", } @Article{Jones:1995:AFS, author = "Mark T. Jones and Paul E. Plassmann", title = "{Algorithm 740}: {Fortran} Subroutines to Compute Improved Incomplete {Cholesky} Factorizations", journal = j-TOMS, volume = "21", number = "1", pages = "18--19", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200986", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:13 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p18-jones/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "incomplete Cholesky; incomplete factorization; preconditioners; sparse matrices", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems; sparse and very large systems", } @Article{Ray:1995:ALS, author = "Richard D. Ray", title = "{Algorithm 741}: Least Squares Solution of a Linear Bordered, Block-diagonal System of Equations", journal = j-TOMS, volume = "21", number = "1", pages = "20--25", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200987", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:14 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p20-ray/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bordered block-diagonal equations; least-squares solutions; sparse systems", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems (direct and iterative methods); G.1.6 [Numerical Analysis]: Optimization -- least squares methods; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Fateman:1995:FFP, author = "Richard J. Fateman and Kevin A. Broughan and Diane K. Willcock and Duane Rettig", title = "Fast Floating Point Processing in {Common Lisp}", journal = j-TOMS, volume = "21", number = "1", pages = "26--62", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200989", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:20:50 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Reid:1996:RFF}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/", acknowledgement = ack-nhfb # " and " # ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "C programming language; Common Lisp; compiler optimization; floating-point arithmetic; Fortran; Lisp; numerical algorithms; symbolic computation", subject = "D.3.4 [Programming Languages]: Processors --- compilers; interpreters; optimization; G.4 [Mathematics of Computing]: Mathematical Software --- efficiency; portability", } @Article{Kearfott:1995:FER, author = "R. Baker Kearfott", title = "A {Fortran} 90 Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization", journal = j-TOMS, volume = "21", number = "1", pages = "63--78", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200991", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat May 20 15:54:41 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p63-kearfott/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; Fortran 90; global optimization; nonlinear algebraic systems; symbolic computation", subject = "D.3.3 [Programming Languages]: Language Constructs; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations; G.1.6 [Numerical Analysis]: Optimization; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Dongarra:1995:SDX, author = "Jack Dongarra and Tom Rowan and Reed Wade", title = "Software Distribution using {XNETLIB}", journal = j-TOMS, volume = "21", number = "1", pages = "79--88", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.200995", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:18 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p79-dongarra/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Netlib; software repositories", subject = "C.2.3 [Computer-Communication Networks]: Network Operations -- public networks; D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; user interfaces; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.4 [Mathematics of Computing]: Mathematical Software -- portability; H.3.0 [Information Systems Applications]: Communications Applications; H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval -- search process; selection process; H.3.5 [Information Storage and Retrieval]: Online Information Services -- databank sharing; H.5.2 [Information Interfaces and Presentation]: User Interfaces -- windowing systems; K.6.3 [Management of Computing and Information Systems]: Software Management -- software development; software maintenance; software selection", } @Article{Grosse:1995:RM, author = "Eric Grosse", title = "Repository Mirroring", journal = j-TOMS, volume = "21", number = "1", pages = "89--97", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.201000", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:20 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p89-grosse/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "C.2.4 [Computer-Communication Networks]: Distributed Systems -- distributed databases", subject = "archives; checksum; distributed administration; electronic distribution; ftp", } @Article{Demetriou:1995:ALF, author = "I. C. Demetriou", title = "{Algorithm 742}: {L2CXFT}: {A Fortran} Subroutine for Least Squares Data Fitting with Nonnegative Second Divided Differences", journal = j-TOMS, volume = "21", number = "1", pages = "98--110", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.201039", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:22 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p98-demetriou/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "B-splines; convex approximation; data fitting; divided difference", subject = "G.1.2 [Numerical Analysis]: Approximation -- least squares approximation; G.1.6 [Numerical Analysis]: Optimization -- quadratic programming", } @Article{Weber:1995:AIG, author = "Kenneth Weber", title = "The Accelerated Integer {GCD} Algorithm", journal = j-TOMS, volume = "21", number = "1", pages = "111--122", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.201042", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68Q20 (68M07)", MRnumber = "96h:68084", bibdate = "Tue Mar 14 16:17:23 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p111-weber/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "GCD; integer greatest common divisor; number-theoretic computations", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems", } @Article{Bongartz:1995:CCU, author = "I. Bongartz and A. R. Conn and Nick Gould and Ph.L. Toint", title = "{CUTE}: Constrained and Unconstrained Testing Environment", journal = j-TOMS, volume = "21", number = "1", pages = "123--160", month = mar, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/200979.201043", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 14 16:17:24 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p123-bongartz/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", subject = "D.2.2 [Software Engineering]: Tools and Techniques -- modules and interfaces; G.1.6 [ Numerical Analysis]: Optimization -- constrained", } @Article{Barry:1995:RVW, author = "D. A. Barry and P. J. Culligan-Hensley and S. J. Barry", title = "Real Values of the {W}-Function", journal = j-TOMS, volume = "21", number = "2", pages = "161--171", month = jun, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/203082.203084", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "1 342 353", bibdate = "Tue Oct 10 15:50:28 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p161-barry/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "W-function", subject = "G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations-iterative methods", } @Article{Barry:1995:AWF, author = "D. A. Barry and S. J. Barry and P. J. Culligan-Hensley", title = "{Algorithm 743}: {WAPR}: {A Fortran} Routine for Calculating Real Values of the {W}-Function", journal = j-TOMS, volume = "21", number = "2", pages = "172--181", month = jun, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/203082.203088", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "1 342 354", bibdate = "Tue Oct 10 15:50:30 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p172-barry/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "W-function", subject = "G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations -- iterative methods", } @Article{Hormann:1995:RTS, author = "Wolfgang H{\"o}rmann", title = "A Rejection Technique for Sampling from {T}-Concave Distributions", journal = j-TOMS, volume = "21", number = "2", pages = "182--193", month = jun, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/203082.203089", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65D20", MRnumber = "96b:65018", bibdate = "Tue Oct 10 15:50:31 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p182-hormann/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Log-concave distributions; rejection method; universal method", subject = "G.3 [Probability and Statistics]: Random Number Generation", } @Article{Rabinowitz:1995:ASA, author = "F. Michael Rabinowitz", title = "{Algorithm 744}: a Stochastic Algorithm for Global Optimization with Constraints", journal = j-TOMS, volume = "21", number = "2", pages = "194--213", month = jun, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/203082.203090", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Oct 10 15:50:33 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p194-rabinowitz/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Constrained optimization; global optimization; stochastic optimization; test functions", subject = "G.1.6 [Numerical Analysis]: Optimization -- nonlinear programming; G.3 [Mathematics of Computing]: Probability and Statistics -- probabilistic algorithms (including Monte Carlo); G.4 [Mathematics of Computing]: Mathematical Software -- certification and testing", } @Article{Goano:1995:ACC, author = "Michele Goano", title = "{Algorithm 745}: Computation of the Complete and Incomplete {Fermi--Dirac} Integral", journal = j-TOMS, volume = "21", number = "3", pages = "221--232", month = sep, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210089.210090", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:19:43 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Goano:1997:RA7}", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "asymptotic expansions; confluent hypergeometric functions; convergence acceleration; e[k] transforms; epsilon algorithm; Euler transformation; Fermi--Dirac integral; incomplete Fermi--Dirac integral; incomplete gamma function; Levin's u transform; Riemann's zeta function", subject = "G.1.2 [Mathematics of Computing]: Approximation; G.4 [Mathematics of Computing]: Mathematical Software; J.2 [Computer Applications]: Physical Sciences and Engineering", } @Article{Dobmann:1995:APF, author = "M. Dobmann and M. Liepelt and K. Schittkowski", title = "{Algorithm 746}: {PCOMP}: {A Fortran} Code for Automatic Differentiation", journal = j-TOMS, volume = "21", number = "3", pages = "233--266", month = sep, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210089.210091", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p233-dobmann/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; forward accumulation; reverse accumulation", subject = "D.1.2 [Programming Techniques]: Automatic Programming; D.3.4 [Programming Languages]: Processors - code generation; G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Sullivan:1995:NAU, author = "Stephen J. Sullivan and Benjamin G. Zorn", title = "Numerical Analysis Using Nonprocedural Paradigms", journal = j-TOMS, volume = "21", number = "3", pages = "267--298", month = sep, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210089.210093", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p267-sullivan/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "benchmarks; experimental languages; Gaussian elimination; linear algebra; programming languages; sparse matrices", subject = "G.1 [Mathematics of Computing]: Numerical Analysis", } @Article{Miminis:1995:AFS, author = "George Miminis and Helmut Roth", title = "{Algorithm 747}: {A Fortran} Subroutine to Solve the Eigenvalue Assignment Problem for Multiinput Systems Using State Feedback", journal = j-TOMS, volume = "21", number = "3", pages = "299--326", month = sep, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210089.210094", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p299-miminis/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "deflation; double steps; eigenvalue assignment; numerical efficiency; pole assignment", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems - computations on matrices; G.1.0 [Numerical Analysis]: General - numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra - eigenvalues; J.2 [Computer Applications]: Physical Sciences and Engineering - aerospace; engineering; J.4 [Computer Applications]: Social and Behavioral Sciences - economics", } @Article{Alefeld:1995:AEZ, author = "G. E. Alefeld and F. A. Potra and Yixun Shi", title = "{Algorithm 748}: Enclosing Zeros of Continuous Functions", journal = j-TOMS, volume = "21", number = "3", pages = "327--344", month = sep, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/210089.210111", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Sep 28 16:39:05 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p327-alefeld/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; asymptotic efficiency index; enclosing method; inverse cubic interpolation; quadratic interpolation; simple root; theory", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations -- convergence; iterative methods", } @Article{Rizzardi:1995:MTM, author = "Mariarosaria Rizzardi", title = "A Modification of {Talbot}'s Method for the Simultaneous Approximation of Several Values of the Inverse {Laplace} Transform", journal = j-TOMS, volume = "21", number = "4", pages = "347--371", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212068", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R10", MRnumber = "96k:65084", bibdate = "Sat Feb 10 08:48:51 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p347-rizzardi/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "complex inversion formula; inverse Laplace transform; numerical method; Talbot; trapezoidal rule", reviewer = "A. J. Rodrigues", subject = "G.1.0 [Numerical Analysis]: General -- error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- equal interval integration; error analysis; G.1.9 [Numerical Analysis]: Integral Equations -- Fredholm equations", } @Article{Sherlock:1995:AFD, author = "Barry G. Sherlock and Donald M. Monro", title = "{Algorithm 749}: Fast Discrete Cosine Transform", journal = j-TOMS, volume = "21", number = "4", pages = "372--378", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212071", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 14 09:58:14 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p372-sherlock/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "data compression; discrete cosine transform; fast transform", subject = "D.3.2 [Programming Languages]: Language Classifications -- Fortran; E.4 [Data]: Coding and Information Theory -- data compaction and compression; F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems; G.4 [Mathematics of Computing]: Mathematical Software; I.4.2 [Image Processing]: Compression", } @Article{Bailey:1995:FBM, author = "David H. Bailey", title = "A {Fortran-90} Based Multiprecision System", journal = j-TOMS, volume = "21", number = "4", pages = "379--387", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212075", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 29 15:15:44 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also extension to complex arithmetic \cite{Smith:1998:AMP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p379-bailey/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "arithmetic; Fortran 90; multiprecision", subject = "D.3.2 [Programming Languages]: Language Classifications -- Fortran 90; D.3.4 [Programming Languages]: Processors; G.1.0 [Numerical Analysis]: General; G.1.2 [Numerical Analysis]: Approximation", } @Article{Amos:1995:RAP, author = "D. E. Amos", title = "A Remark on {Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order", journal = j-TOMS, volume = "21", number = "4", pages = "388--393", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212078", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:24:54 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "complex Airy Functions; complex Bessel functions; derivatives of Airy functions; H, I, J, K, and Y Bessel functions; log gamma function", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.m [Numerical Analysis]: Miscellaneous; G.m [Mathematics of Computing]: Miscellaneous", } @Article{Carpaneto:1995:ESL, author = "G. Carpaneto and M. Dell'Amico and P. Toth", title = "Exact Solution of Large Scale Asymmetric Travelling Salesman Problems", journal = j-TOMS, volume = "21", number = "4", pages = "394--409", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212081", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C27 (90C35)", MRnumber = "96m:90062a", bibdate = "Tue Nov 14 09:58:01 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p394-carpaneto/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "assignment problem; asymmetric traveling salesman problem; branch and bound; reduction procedure; subtour elimination", reviewer = "N. I. Yanev", subject = "G.2.1 [Discrete Mathematics]: Combinatorics -- combinatorial algorithms; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms; path and circuit problems", } @Article{Carpaneto:1995:ACS, author = "G. Carpaneto and M. Dell'Amico and P. Toth", title = "{Algorithm 750}: {CDT}: a Subroutine for the Exact Solution of Large-Scale Asymmetric Travelling Salesman Problems", journal = j-TOMS, volume = "21", number = "4", pages = "410--415", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212084", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "90C27 (90C35)", MRnumber = "96m:90062b", bibdate = "Tue Nov 14 09:57:58 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p410-carpaneto/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "assignment problem; asymmetric traveling salesman problem; branch and bound; reduction procedure; subtour elimination", reviewer = "N. I. Yanev", subject = "D.3.2 [Programming Languages]: Language classifications -- Fortran; G.2.1 [Discrete Mathematics]: Combinatorics -- combinatorial algorithms; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms; path and circuit problems", } @Article{Doman:1995:SAP, author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen", title = "A Set of {Ada} Packages for High Precision Calculations", journal = j-TOMS, volume = "21", number = "4", pages = "416--431", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212087", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 14 09:57:55 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software", subject = "G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability", } @Article{Scott:1995:ACC, author = "Jennifer A. Scott", title = "An {Arnoldi} Code for Computing Selected Eigenvalues of Sparse, Real, Unsymmetric Matrices", journal = j-TOMS, volume = "21", number = "4", pages = "432--475", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212091", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F15 65F50)", MRnumber = "1 364 698", bibdate = "Tue Nov 14 09:57:52 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p432-scott/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keyword = "Arnoldi's method; Chebychev acceleration; large sparse matrices; real unsymmetric matrices", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- eigenvalues", } @Article{Kaufman:1995:CMD, author = "Linda Kaufman", title = "Computing the ${MDM}^{T}$ decomposition", journal = j-TOMS, volume = "21", number = "4", pages = "476--489", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.212092", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 14 09:57:49 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p476-kaufman/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block factorizations; LAPACK; linear systems (direct methods); symmetric indefinite", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems (direct and iterative methods); G.4 [Mathematics of Computing]: Mathematical Software -- efficiency", } @Article{Duff:1995:CCS, author = "Iain S. Duff and Jennifer A. Scott", title = "Corrigendum: Computing Selected Eigenvalues of Sparse Unsymmetric Matrices Using Subspace Iteration", journal = j-TOMS, volume = "21", number = "4", pages = "490--490", month = dec, year = "1995", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/212066.215254", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 14 09:57:46 1995", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Duff:1993:CSE}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p490-duff/", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:1996:ATC, author = "R. J. Renka", title = "{Algorithm 751}: {TRIPACK}: a constrained two-dimensional {Delaunay} triangulation package", journal = j-TOMS, volume = "22", number = "1", pages = "1--8", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225546; http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p1-renka/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 18:58:33 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Renka:1999:RAa}.", abstract = "TRIPACK is a Fortran 77 software package that employs an incremental algorithm to construct a constrained Delaunay triangulation of a set of points in the plane (nodes). The triangulation covers the convex hull of the nodes but may include polygonal constraint regions whose triangles are distinguishable from those in the remainder of the triangulation. This effectively allows for a nonconvex or multiply connected triangulation (the complement of the union of constraint regions) while retaining the efficiency of searching and updating a convex triangulation. The package provides a wide range of capabilities including an efficient means of updating the triangulation with nodal additions or deletions. For $N$ nodes, the storage requirement is $13N$ integer storage locations in addition to the $2N$ nodal coordinates.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Renka:1996:ASS, author = "R. J. Renka", title = "{Algorithm 752}: {SRFPACK}: software for scattered data fitting with a constrained surface under tension", journal = j-TOMS, volume = "22", number = "1", pages = "9--17", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225547; http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p9-renka/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Renka:1999:RAb}.", abstract = "SRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points in the plane. It employs automatically selected tension factors to preserve shape properties of the data and to avoid overshoot and undershoot associated with steep gradients. The domain of the fitting function may be nonconvex or multiply connected, and the surface may be constrained to have discontinuous value or derivative across a user-specified curve representing, for example, a geological fault line. Although triangle based, the method provides a means of avoiding the inaccuracy associated with long thin triangles on the boundary of the convex hull of the data abscissae.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Buis:1996:EVP, author = "Paul E. Buis and Wayne R. Dyksen", title = "Efficient vector and parallel manipulation of tensor products", journal = j-TOMS, volume = "22", number = "1", pages = "18--23", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225548", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68Q40", MRnumber = "1 383 183", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p18-buis/", abstract = "We present efficient vector and parallel methods for manipulating tensor products of matrices. We consider both computing the matrix-vector product $(A_{1} \otimes \cdots \otimes A_{K})x$ and solving the system of linear equations $(A_{1} \otimes \cdots \otimes A_{K})x=b$. The methods described are independent of $K$. We accompany this article with a companion algorithm which describes an implementation of a complete set of tensor product routines based on LAPACK and the Level 2 and 3 Basic Linear Algebra Subprograms (BLAS) which provide vectorization and parallelization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Buis:1996:ATL, author = "Paul E. Buis and Wayne R. Dyksen", title = "{Algorithm 753}: {TENPACK}: a {LAPACK-based} library for the computer manipulation of tensor products", journal = j-TOMS, volume = "22", number = "1", pages = "24--29", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225549", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p24-buis/", abstract = "This article presents the interface of an implementation of methods to manipulate equations of this form $A_1 \otimes \cdots \otimes A_m$ where the $A_i$ are matrices. The methods described are independent of $m$. The code is based on LAPACK and the BLAS and supports virtually all of the matrix formats supported by those packages. Timings of the implementation on several machines are also given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Duff:1996:DNF, author = "I. S. Duff and J. A. Scott", title = "The design of a new frontal code for solving sparse, unsymmetric systems", journal = j-TOMS, volume = "22", number = "1", pages = "30--45", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225550", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 383 184", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p30-duff/", abstract = "We describe the design, implementation, and performance of a frontal code for the solution of large, sparse, unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. We discuss in detail the extensive use of higher-level BLAS kernels within MA42 and illustrate the performance on a range of practical problems on a CRAY Y-MP, an IBM 3090, and an IBM RISC System/6000. We examine extending the frontal solution scheme to use multiple fronts to allow MA42 to be run in parallel. We indicate some directions for future development.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Freund:1996:QPQ, author = "Roland W. Freund and No{\"e}l M. Nachtigal", title = "{QMRPACK}: a package of {QMR} algorithms", journal = j-TOMS, volume = "22", number = "1", pages = "46--77", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225551", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F10)", MRnumber = "1 383 185", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p46-freund/", abstract = "The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative solution of large non-Hermitian linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK is a software package with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three-term and coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some of the features of the algorithms in the package, with emphasis on the issues related to using the codes. We describe in some detail two routines from the package, one for the solution of linear systems and the other for the computation of eigenvalue approximations. We present some numerical examples from applications where QMRPACK was used.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Kaagstrom:1996:LAS, author = "Bo K{\aa}gstr{\"o}m and Peter Poromaa", title = "{LAPACK-style} algorithms and software for solving the generalized {Sylvester} equation and estimating the separation between regular matrix pairs", journal = j-TOMS, volume = "22", number = "1", pages = "78--103", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225552", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65-04 (65F30)", MRnumber = "1 383 186", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p78-kagstrom/", abstract = "Robust and fast software to solve the generalized Sylvester equation ($AR - LB = C$, $DR - LE = F$) for unknowns $R$ and $L$ is presented. This special linear system of equations, and its transpose, arises in computing error bounds for computed eigenvalues and eigenspaces of the generalized eigenvalue problem $S-\lambda T$, in computing deflating subspaces of the same problem, and in computing certain decompositions of transfer matrices arising in control theory. Our contributions are twofold. First, we reorganize the standard algorithm for this problem to use Level 3 BLAS operations, like matrix multiplication, in its inner loop. This speeds up the algorithm by a factor of 9 on an IBM RS6000. Second, we develop and compare several condition estimation algorithms, which inexpensively but accurately estimate the sensitivity of the solution of this linear system.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Resende:1996:AFS, author = "Mauricio G. C. Resende and Panos M. Pardalos and Yong Li", title = "{Algorithm 754}: {Fortran} subroutines for approximate solution of dense quadratic assignment problems using {GRASP}", journal = j-TOMS, volume = "22", number = "1", pages = "104--118", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225553", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p104-resende/", abstract = "In the NP-complete quadratic assignment problem (QAP), $n$ facilities are to be assigned to $n$ sites at minimum cost. The contribution of assigning facility $i$ to site $k$ and facility $j$ to site $l$ to the total cost is $f_{ij} - d_{kl}$, where $f_{ij}$ is the flow between facilities $i$ and $j$, and $d_{kl}$ is the distance between sites $k$ and $l$. Only very small ($n\le20$) instances of the QAP have been solved exactly, and heuristics are therefore used to produce approximate solutions. This article describes a set of Fortran subroutines to find approximate solutions to dense quadratic assignment problems, having at least one symmetric flow or distance matrix. A greedy, randomized, adaptive search procedure (GRASP) is used to produce the solutions. The design and implementation of the code are described in detail, and extensive computational experiments are reported, illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms.", } @Article{Wallace:1996:FPG, author = "C. S. Wallace", title = "Fast pseudorandom generators for normal and exponential variates", journal = j-TOMS, volume = "22", number = "1", pages = "119--127", month = mar, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/225545.225554", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See comments \cite{Brent:2008:SCC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p119-wallace/", abstract = "Fast algorithms for generating pseudorandom numbers from the unit-normal and unit-exponential distributions are described. The methods are unusual in that they do not rely on a source of uniform random numbers, but generate the target distributions directly by using their maximal-entropy properties. The algorithms are fast. The normal generator is faster than the commonly used Unix library uniform generator ``random'' when the latter is used to yield real values. Their statistical properties seem satisfactory, but only a limited suite of tests has been conducted. They are written in C and as written assume 32-bit integer arithmetic. The code is publicly available as C source and can easily be adopted for longer word lengths and/or vector processing.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design; performance", remark = "Wallace's generators produce normal and exponential distributions directly, without first generation numbers from a uniform distribution.", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Griewank:1996:AAP, author = "Andreas Griewank and David Juedes and Jean Utke", title = "{Algorithm 755}: {ADOL-C}: a package for the automatic differentiation of algorithms written in {C\slash C++}", journal = j-TOMS, volume = "22", number = "2", pages = "131--167", month = jun, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/229473.229474", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p131-griewank/", abstract = "The C++ package ADOL-C described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked with C. The numerical values of derivative vectors are obtained free of truncation errors at a small multiple of the run-time and randomly accessed memory of the given function evaluation program. Derivative matrices are obtained by columns or rows. For solution curves defined by ordinary differential equations, special routines are provided that evaluate the Taylor coefficient vectors and their Jacobians with respect to the current state vector. The derivative calculations involve a possibly substantial (but always predictable) amount of data that are accessed strictly sequentially and are therefore automatically paged out to external files.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms.", } @Article{Driscoll:1996:AMT, author = "Tobin A. Driscoll", title = "{Algorithm 756}: a {MATLAB} Toolbox for {Schwarz--Christoffel} mapping", journal = j-TOMS, volume = "22", number = "2", pages = "168--186", month = jun, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/229473.229475", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p168-driscoll/", abstract = "The Schwarz--Christoffel transformation and its variations yield formulas for conformal maps from standard regions to the interiors or exteriors of possibly unbounded polygons. Computations involving these maps generally require a computer, and although the numerical aspects of these transformations have been studied, there are few software implementations that are widely available and suited for general use. The Schwarz--Christoffel Toolbox for MATLAB is a new implementation of Schwarz--Christoffel formulas for maps from the disk, half-plane, strip, and rectangle domains to polygon interiors, and from the disk to polygon exteriors. The toolbox, written entirely in the MATLAB script language, exploits the high-level functions, interactive environment, visualization tools, and graphical user interface elements supplied by current versions of MATLAB, and is suitable for use both as a standalone tool and as a library for applications written in MATLAB, Fortran, or C. Several examples and simple applications are presented to demonstrate the toolbox's capabilities.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, MATLAB. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Duff:1996:DMC, author = "I. S. Duff and J. K. Reid", title = "The design of {MA48}: a code for the direct solution of sparse unsymmetric linear systems of equations", journal = j-TOMS, volume = "22", number = "2", pages = "187--226", month = jun, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/229473.229476", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p187-duff/", abstract = "We describe the design of a new code for the direct solution of sparse unsymmetric linear systems of equations. The new code utilizes a novel restructuring of the symbolic and numerical phases, which increases speed and saves storage without sacrifice of numerical stability. Other features include switching to full-matrix processing in all phases of the computation enabling the use of all three levels of BLAS, treatment of rectangular or rank-deficient matrices, partial factorization, and integrated facilities for iterative refinement and error estimation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Duff:1996:EZD, author = "I. S. Duff and J. K. Reid", title = "Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems", journal = j-TOMS, volume = "22", number = "2", pages = "227--257", month = jun, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/229473.229480", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50", MRnumber = "1 408 491", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p227-duff/", abstract = "We describe the design of a new code for the solution of sparse indefinite symmetric linear systems of equations. The principal difference between this new code and earlier work lies in the exploitation of the additional sparsity available when the matrix has a significant number of zero diagonal entries. Other new features have been included to enhance the execution speed, particularly on vector and parallel machines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Price:1996:RA, author = "David T. Price", title = "Remark on {Algorithm 715}", journal = j-TOMS, volume = "22", number = "2", pages = "258--258", month = jun, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/229473.236186", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Cody:1993:ASE}", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/", ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hull:1996:MBP, author = "T. E. Hull and R. Mathon", title = "The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence", journal = j-TOMS, volume = "22", number = "3", pages = "261--280", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232830", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p261-hull/", abstract = "Formulas developed originally by Weierstrass have been used since the 1960s by many others for the simultaneous determination of all the roots of a polynomial. Convergence to simple roots is quadratic, but individual approximations to a multiple root converge only linearly. However, it is shown here that the mean of such individual approximations converges quadratically to that root. This result, along with some detail about the behavior of such approximations in the neighborhood of the multiple root, suggests a new approach to the design of polynomial rootfinders. It should also be noted that the technique is well suited to take advantage of a parallel environment. This article first provides the relevant mathematical results: a short derivation of the formulas, convergence proofs, an indication of the behavior near a multiple root, and some error bounds. It then provides the outline of an algorithm based on these results, along with some graphical and numerical results to illustrate the major theoretical points. Finally, a new program based on this algorithm, but with a more efficient way of choosing starting values, is described and then compared with corresponding programs from IMSL and NAG with good results. This program is available from Mathon (\path=combin@cs.utoronto.ca=).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Error analysis. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Sosonkina:1996:NEG, author = "Maria Sosonkina and Layne T. Watson and David E. Stewart", title = "Note on the end game in homotopy zero curve tracking", journal = j-TOMS, volume = "22", number = "3", pages = "281--287", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232843", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p281-sosonkina/", abstract = "Homotopy algorithms to solve a nonlinear system of equations $f(x) = 0$ involve tracking the zero curve of a homotopy map $p(a, \lambda, x)$ from $\lambda = 0$ until $\lambda = 1$. When the algorithm nears or crosses the hyperplane $\lambda = 1$, an ``end game'' phase is begun to compute the solution *** satisfying $p(a, \lambda, ***) = f(**) = 0$. This note compares several end game strategies, including the one implemented in the normal flow code FIXPNF in the homotopy software package HOMPACK.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Macleod:1996:AMS, author = "Allan J. Macleod", title = "{Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions", journal = j-TOMS, volume = "22", number = "3", pages = "288--301", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232846", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/", abstract = "MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Blom:1996:AVVa, author = "J. G. Blom and R. A. Trompert and J. G. Verwer", title = "{Algorithm 758}: {VLUGR2}: a vectorizable adaptive-grid solver for {PDEs} in {2D}", journal = j-TOMS, volume = "22", number = "3", pages = "302--328", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232850", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p302-blom/", abstract = "This article deals with an adaptive-grid finite-difference solver for time-dependent two-dimensional systems of partial differential equations. It describes the ANSI Fortran 77 code, VLUGR2, autovectorizable on the Cray Y-MP, that is based on this method. The robustness and the efficiency of the solver, both for vector and scalar processors, are illustrated by the application of the code to two example problems arising from a groundwater-flow model.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Blom:1996:AVVb, author = "J. G. Blom and J. G. Verwer", title = "{Algorithm 759}: {VLUGR3}: a vectorizable adaptive-grid solver for {PDEs} in {3D} --- {Part II}. code description", journal = j-TOMS, volume = "22", number = "3", pages = "329--347", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232853", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p329-blom/", abstract = "This article describes an ANSI Fortran 77 code, VLUGR3, autovectorizable on the Cray Y-MP, that is based on an adaptive-grid finite-difference method to solve time-dependent three-dimensional systems of partial differential equations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Andersen:1996:MSM, author = "Knud D. Andersen", title = "A modified {Schur-complement} method for handling dense columns in interior-point methods for linear programming", journal = j-TOMS, volume = "22", number = "3", pages = "348--356", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232937", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p348-andersen/", abstract = "The main computational work in interior-point methods for linear programming (LP) is to solve a least-squares problem. The normal equations are often used, but if the LP constraint matrix contains a nearly dense column the normal-equations matrix will be nearly dense. Assuming that the nondense part of the constraint matrix is of full rank, the Schur complement can be used to handle dense columns. In this article we propose a modified Schur-complement method that relaxes this assumption. Encouraging numerical results are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Akima:1996:ARS, author = "Hiroshi Akima", title = "{Algorithm 760}: rectangular-grid-data surface fitting that has the accuracy of a bicubic polynomial", journal = j-TOMS, volume = "22", number = "3", pages = "357--361", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232854", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p357-akima/", abstract = "A local algorithm for smooth surface fitting for rectangular-grid data has been presented. It has the accuracy of a bicubic polynomial.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Akima:1996:ASS, author = "Hiroshi Akima", title = "{Algorithm 761}: scattered-data surface fitting that has the accuracy of a cubic polynomial", journal = j-TOMS, volume = "22", number = "3", pages = "362--371", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232856", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:11:35 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remarks \cite{Renka:1998:RA,DeTisi:2000:RAS}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p362-akima/", abstract = "An algorithm for smooth surface fitting for scattered data has been presented. It has the accuracy of a cubic polynomial in most cases and is a local, triangle-based algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Brown:1996:ALL, author = "Barry W. Brown and Lawrence B. Levy and James Lovato and Kathy Russell and Floyd M. Spears", title = "{Algorithm 762}: {LLDRLF}, log-likelihood and some derivatives for {log-F} models", journal = j-TOMS, volume = "22", number = "3", pages = "372--382", month = sep, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/232826.232858", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:11:08 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p372-brown/", abstract = "The flexible statistical models incorporating the log-F distribution are little used because of numeric difficulties. We describe a method for calculating the log-likelihood and two derivatives with respect to the data argument. Fortran subroutines incorporating these calculations are provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Kearfott:1996:IFM, author = "R. Baker Kearfott", title = "{Algorithm 763}: {INTERVAL\_ARITHMETIC}: {A Fortran 90} Module for an Interval Data Type", journal = j-TOMS, volume = "22", number = "4", pages = "385--392", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235816", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Kearfott:1994:AIP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p385-kearfott/", abstract = "Interval arithmetic is useful in {\it automatically verified computation}, that is, in computations in which the algorithm itself rigorously proves that the answer must lie within certain bounds. In addition to rigor, interval arithmetic also provides a simple and somewhat sharp method of bounding ranges of functions for global optimization and other tasks. Convenient use of interval arithmetic requires an interval data type in the programming language. Although various packages supply such a data type, previous ones are machine specific, obsolete, and unsupported, for languages other than Fortran, or commercial. The Fortran 90 module {INTERVAL\_ARITHMETIC} provides a portable interval data type in Fortran 90. This data type is based on two double-precision real Fortran storage unit. Module {INTERVAL\_ARITHMETIC} uses the Fortran 77 library {INTLIB} (ACM TOMS {Algorithm 737}) as a supporting library. The module has been employed extensively in the author's own research.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, languages", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 90. {\bf G.1.0}: Mathematics of Computation, NUMERICAL ANALYSIS, General, Computer arithmetic, Error analysis, Numerical algorithms.", } @Article{Lehoucq:1996:CEU, author = "R. B. Lehoucq", title = "The Computation of Elementary Unitary Matrices", journal = j-TOMS, volume = "22", number = "4", pages = "393--400", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235817", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p393-lehoucq/", abstract = "The construction of elementary unitary matrices that transform a complex vector to a multiple of $e_1$, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf F.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Butcher:1996:DMS, author = "J. C. Butcher and J. R. Cash and M. T. Diamantakis", title = "{DESI} Methods for Stiff Initial Value Problems", journal = j-TOMS, volume = "22", number = "4", pages = "401--422", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235818", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p401-butcher/", abstract = "Recently, the so-called DESI (diagonally extended singly implicit) {Runge}-{Kutta} methods were introduced to overcome some of the limitations of singly implicit methods. Preliminary experiments have shown that these methods are usually more efficient than the standard singly implicit {Runge}-{Kutta} (SIRK) methods and, in many cases, are competitive with backward differentiation formulae (BDF). This article presents an algorithm for determining the full coefficient matrix from the stability function, which is already chosen to make the method {A}-stable. Because of their unconventional nature, DESI methods have to be implemented in a special way. In particular, the effectiveness of these methods depends heavily on how the starting values are chosen for the stage iterations. These and other implementation questions are discussed in detail, and the design choices we have made form the basis of an experimental code for the solution of stiff problems by DESI methods. We present here a small subset of the numerical results obtained with our code. Many of these results are quite satisfactory and suggest that DESI methods have a useful role in the solution of this type of problem.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", subject = "{\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Initial value problems, Stiff equations.", } @Article{Eastham:1996:USP, author = "Michael S. P. Eastham and Charles T. Fulton and Steven Pruess", title = "Using the {SLEDGE} Package on {Sturm--Liouville} Problems Having Nonempty Essential Spectrum", journal = j-TOMS, volume = "22", number = "4", pages = "423--446", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235819", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 24 15:44:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p423-eastham/", abstract = "We describe the performance of the Sturn-Liouville software package SLEDGE on a variety of problems having continuous spectra. The code's output is shown to be in good accord with a wide range of known theoretical results.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance", subject = "{\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Weerawarana:1996:PKB, author = "Sanjiva Weerawarana and Elias N. Houstis and John R. Rice and Anupam Joshi and Catherine E. Houstis", title = "{PYTHIA}: a Knowledge Based System for Intelligent Scientific Computing", journal = j-TOMS, volume = "22", number = "4", pages = "447--468", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235820", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p447-weerawarana/", abstract = "Problem-solving Environments (PSEs) interact with the user in a language ``natural'' to the associated discipline, and they provide a high-level abstraction of the underlying, computationally complex model. The knowledge-based system PYTHIA addresses the problem of {\tt (parameter, algorithm)} pair selection within a scientific computing domain assuming some minimum user-specified computational objectives and some characteristics of the given problem. PYTHIA's framework and methodology are general and applicable to any class of scientific problems and solvers. PYTHIA is applied in the context of Parallel ELLPACK where there are many alternatives for the numerical solution of elliptic partial differential equations (PDEs). PYTHIA matches the characteristics of the given problem with those of PDEs in an existing problem population and then uses performance profiles of the various solvers to select the appropriate method given user-specified error and solution time bounds. The profiles are automatically generated for each solver of the Parallel ELLPACK library.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGIENCE, Applications and expert systems.", } @Article{Barber:1996:QAC, author = "C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa", title = "The {Quickhull} Algorithm for Convex Hulls", journal = j-TOMS, volume = "22", number = "4", pages = "469--483", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235821", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Nov 8 14:50:36 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/", abstract = "The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, reliability", subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages and systems.", } @Article{Sarkar:1996:CAM, author = "T. K. Sarkar", title = "A Composition-Alias Method for Generating Gamma Variates with Shape Parameter Greater than 1", journal = j-TOMS, volume = "22", number = "4", pages = "484--492", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235822", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p484-sarkar/", abstract = "In this article the author describes a procedure for generating gamma variates with shape parameter $> 1$. Given a supply of ``good'' uniform $(0,1)$ variates, the procedure makes use of composition method, squeeze method, and aliasing to generate gamma variates. Comparison with existing methods shows that the author's method is faster in terms of computer time and uses a smaller number of uniform $(0,1)$ variates. The method is also statistically exact.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, theory", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Koenker:1996:RBC, author = "Roger W. Koenker and Pin T. Ng", title = "A Remark on {Bartels} and {Conn}'s Linearly Constrained, Discrete $l_1$ Problems", journal = j-TOMS, volume = "22", number = "4", pages = "493--495", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235823", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 9 10:22:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Bartels:1980:APL}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p493-koenker/", abstract = "Two modifications of Bartels and Conn's algorithm for solving linearly constrained discrete $l_1$ problems are described. The modifications are designed to improve performance of the algorithm under conditions of degeneracy.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, reliability, theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization, Gradient methods, Linear programming. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Reid:1996:RFF, author = "J. K. Reid", title = "Remark on ``{Fast Floating-Point Processing in Common Lisp}''", journal = j-TOMS, volume = "22", number = "4", pages = "496--497", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235824", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 9 10:21:08 1999", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Fateman:1995:FFP}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/", abstract = "We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.", acknowledgement = ack-nhfb # " and " # ack-rfb, affiliation = "Rutherford Appleton Lab", ajournal = "ACM Trans. Math. Softw.", classification = "721.1; 723.1.1; 902.2; 921.6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", journalabr = "ACM Trans Math Software", keywords = "Common Lisp language; Control structures; Digital arithmetic; Floating point computation; fortran (programming language); Lisp (programming language); Standards", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General, Standards. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.", } @Article{Snyder:1996:RAF, author = "W. Van Snyder", title = "Remark on {Algorithm 723}: {Fresnel} Integrals", journal = j-TOMS, volume = "22", number = "4", pages = "498--500", month = dec, year = "1996", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/235815.235825", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Snyder:1993:AFI}.", abstract = "{\it Algorithm 723: Fresnel Integrals} has been improved to provide more precise results for $x \gg 0$.", acknowledgement = ack-rfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Cools:1997:ACC, author = "Ronald Cools and Dirk Laurie and Luc Pluym", title = "{Algorithm 764}: {Cubpack++} --- {A C++} Package for Automatic Two-Dimensional Cubature", journal = j-TOMS, volume = "23", number = "1", pages = "1--15", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244770", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p1-cools/", abstract = "In this article, software for the numerical approximation of double integrals over a variety of regions is described. The software was written in C++. Classes for a large number of shapes are provided. A global adaptive integration algorithm is used based on transformations and subdivisions of regions.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, adaptive quadrature, multiple quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, reliability and robustness.", } @Article{Favati:1997:LEE, author = "Paola Favati and Guiseppe Fiorentino and Grazia Lotti and Francesco Romani", title = "Local Error Estimates and Regularity Tests for the Implementation of Double Adaptive Quadrature", journal = j-TOMS, volume = "23", number = "1", pages = "16--31", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p16-favati/", abstract = "This article presents a device which is suitable for a practical and efficient implementation of Double Adaptive Quadrature. The device includes local error estimates and attempts to detect the presence of numerical difficulties in the integrand function. If a family of rules with suitable properties is chosen, then this can be achieved without affecting the overall computational cost. Extensive numerical testing has been performed on a comprehensive set of functions showing the effectiveness of the device and its efficiency.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, reliability and robustness.", } @Article{Machiels:1997:FEO, author = "L. Machiels and M. O. Deville", title = "{Fortran 90}: An Entry to Object-Oriented Programming for Solution of Partial Differential Equations", journal = j-TOMS, volume = "23", number = "1", pages = "32--49", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p32-machiels/", abstract = "The aim of this work is to set up a programming model suitable for numerical computing while taking benefit of Fortran 90's features. The use of concepts from object-oriented programming avoids the weaknesses of the traditional global data programming model of Fortran 77. This work supports the view that object-oriented concepts are not in contradiction with good Fortran 77 programming practices but complement them. These concepts can be embodied in a module-based programming style and result in an efficient and easy-to-maintain code (maintainability means code clarity, scope for further enhancements and ease of debugging). After introducing the terminology associated with object-oriented programming, it is shown how these concepts are implemented in the framework of Fortran 90. Then, we present an object-oriented implementation of a spectral element solver for a Poisson equation.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design", subject = "{\bf D.1.5}: Software, PROGRAMMING TECHNIQUES, Object-Oriented Programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 90. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations.", } @Article{Bruaset:1997:OOD, author = "Are Magnus Bruaset and Hans Petter Langtangen", title = "Object-Oriented Design of Preconditioned Iterative Methods in {Diffpack}", journal = j-TOMS, volume = "23", number = "1", pages = "50--80", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244776", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p50-bruaset/", abstract = "As modern programming methodologies migrate from computer science to scientific computing, developers of numerical software are faced with new possibilities and challenges. Based on experiences from an ongoing project that develops C++ software for the solution of partial differential equations, this article has its focus on object-oriented design of iterative solvers for linear systems of equations. Special attention is paid to possible conflicts that have to be resolved in order to achieve a flexible, yet efficient, code.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design, performance", subject = "{\bf D.2.8}: Software, SOFTWARE ENGINEERING, Tools and Techniques, software libraries. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems, sparse and very large systems.", } @Article{Bouaricha:1997:ASS, author = "Ali Bouaricha", title = "{Algorithm 765}: {STENMIN} --- a Software Package for Large, Sparse Unconstrained Optimization Using Tensor Methods", journal = j-TOMS, volume = "23", number = "1", pages = "81--90", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244788", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p81-bouaricha/", abstract = "We describe a new package for minimizing an unconstrained nonlinear function where the Hessian is large and sparse. The software allows the user to select between a tensor method and a standard method based upon a quadratic model. The tensor method models the objective function by a fourth-order model, where the third- and fourth-order terms are chosen such that the extra cost of forming and solving the model is small. The new contribution of this package consists of the incorporation of an entirely new way of minimizing the tensor model that makes it suitable for solving large, sparse optimization problems efficiently. The test results indicate that, in general, the tensor method is often more efficient and more reliable than the standard Newton method for solving large, sparse unconstrained optimization problems.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, unconstrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cabay:1997:AEW, author = "S. Cabay and A. R. Jones and G. Labahn", title = "{Algorithm 766}: Experiments with a Weakly Stable Algorithm for Computing {Pad{\'e}} and Simultaneous {Pad{\'e}} Approximants", journal = j-TOMS, volume = "23", number = "1", pages = "91--110", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244790", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p91-cabay/", abstract = "In a recent paper, Cabay, Jones and Labahn develop a fast, iterative, lookahead algorithm for numerically computing Pad{\'e}--Hermite systems and simultaneous Pad{\'e} systems along a diagonal of the associated Pad{\'e} tables. Included in their work is a detailed error analysis showing that the algorithm is weakly stable. In this article, we describe a Fortran implementation, VECTOR\_PADE, of this algorithm together with a number of numerical experiments. These experiments show that the theoretical error bounds obtained by Cabay, Jones, and Labahn reflect the general behavior of the actual error, but that in practice these bounds are large overestimates.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, experimentation", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, rational approximation. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, error analysis, linear systems, matrix inversion.", } @Article{Geurts:1997:AFP, author = "A. J. Geurts and C. Praagman", title = "{Algorithm 767}: a {Fortran 77} Package for Column Reduction of Polynomial Matrices", journal = j-TOMS, volume = "23", number = "1", pages = "111--129", month = mar, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/244768.244791", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p111-geurts/", abstract = "A polynomial matrix is called column reduced if its column degrees are as low as possible in some sense. Two polynomial matrices $P$ and $R$ are called unimodularly equivalent if there exists a unimodular polynomial matrix $U$ such that $PU = R$. Every polynomial matrix is unimodularly equivalent to a column-reduced polynomial matrix. In this article a subroutine is described that takes a polynomial matrix $P$ as input and yields on output a unimodular matrix $U$ and a column-reduced matrix $R$ such that $PU = R$; actually, $PU - R$ is near zero. The subroutine is based on an algorithm, described in a paper by Neven and Praagman. The subroutine has been tested with a number of examples on different computers, with comparable results. The performance of the subroutine on every example tried is satisfactory in the sense that the magnitude of the elements of the residual matrix $PU-R$ is about $\parallel P \parallel \parallel U \parallel EPS$, where $EPS$ is the machine precision. To obtain these results a tolerance, used to determine the rank of some (sub)matrices, has to be set properly. The influence of this tolerance on the performance of the algorithm is discussed, from which a guideline for the usage of the subroutine is derived.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, reliability", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis.", } @Article{Blackford:1997:PEN, author = "L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling", title = "Practical Experience in the Numerical Dangers of Heterogeneous Computing", journal = j-TOMS, volume = "23", number = "2", pages = "133--147", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264030", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Nov 8 14:50:37 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/", abstract = "Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "distributed-memory systems, floating-point arithmetic, heterogeneous processor networks, message passing, numerical software, reliability", subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent Programming, Distributed programming. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", } @Article{Ho:1997:DND, author = "James K. Ho and R. P. Sundarraj", title = "Distributed Nested Decomposition of Staircase Linear Programs", journal = j-TOMS, volume = "23", number = "2", pages = "148--173", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264031", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p148-ho/", abstract = "This article considers the application of a primal nested-decomposition method to solve staircase linear programs (SLPs) on distributed-memory, multiple-instruction-multiple-data computers. Due to the coupling that exist among the stages of an SLP, a standard parallel-decomposition algorithm for these problems would allow only a subset of the subproblem processes to overlap with one another at any give time. We propose algorithms that seek to increase the amount of overlap among the processes as well as utilize idle time beneficially. Computational results testing the effectiveness of our algorithms are reported, using a standard set of test problems.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "computational linear programming, distributed computation", subject = "{\bf C.1.2} Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Multiple-instruction-stream, multiple-data-stream processors (MIMD). {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Bouaricha:1997:TSP, author = "Ali Bouaricha and Robert B. Schnabel", title = "{Algorithm 768}: {TENSOLVE}: a Software Package for Solving Systems of Nonlinear Equations and Nonlinear Least-squares Problems Using Tensor Methods", journal = j-TOMS, volume = "23", number = "2", pages = "174--195", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264032", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p174-bouaricha/", abstract = "This article describes a modular software package for solving systems of nonlinear equations and nonlinear problems, using a new class of methods called tensor methods. It is intended for small- to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or to approximate it by finite differences at each iteration. The software allows the user to choose between a tensor method and a standard method based on a linear model. The tensor method approximates F(x) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies: a line search approach and a two-dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small- and medium-sized problems in iterations and function evaluations.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nonlinear equations, nonlinear least squares, rank-deficient matrices, tensor methods", subject = "{\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Pardalos:1997:AFS, author = "Panos M. Pardalos and Leonidas S. Pitsolulis and Mauricio G. C. Resende", title = "{Algorithm 769}: {Fortran} Subroutines for Approximate Solution of Sparse Quadratic Assignment Problems Using {GRASP}", journal = j-TOMS, volume = "23", number = "2", pages = "196--208", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264038", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p196-pardalos/", abstract = "We describe Fortran subroutines for finding approximate solutions of sparse instances of the Quadratic Assignment Problem (QAP) using a Greedy Randomized Adaptive Search Procedure (GRASP). The design and implementation of the code are described in detail. Computational results comparing the new subroutines with a dense version of the code (Algorithm 754, ACM TOMS) show that the speedup increases with the sparsity of the data.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "combinatorial optimization, Fortran subroutines, GRASP, local search, quadratic assignment problem", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.m} Mathematics of Computing, MISCELLANEOUS.", } @Article{Siarry:1997:ESA, author = "Patrick Siarry and G{\'e}rard Berthiau and Fran\c{c}ois Durdin and Jacques Haussy", title = "Enhanced Simulated Annealing for Globally Minimizing Functions of Many-continuous Variables", journal = j-TOMS, volume = "23", number = "2", pages = "209--228", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264043", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p209-siarry/", abstract = "A new global optimization algorithm for functions of many continuous variables is presented, derived from the basic Simulated annealing method. Our main contribution lies in dealing with high-dimensionality minimization problems, which are often difficult to solve by all known minimization methods with or without gradient. In this article we take a special interest in the variables discretization issue. We also develop and implement several complementary stopping criteria. The original Metropolis iterative random search, which takes place in a Euclidean space $R_n$, is replaced by another similar exploration, performed within a succession of Euclidean spaces $R_p$, with $p << n$. This Enhanced Simulated Annealing (ESA) algorithm was validated first on classical highly multimodal functions of 2 to 100 variables. We obtained significant reductions in the number of function evaluations compared to six other global optimization algorithms, selected according to previously published computational results for the same set of test functions. In most cases, ESA was able to closely approximate known global optima. The reduced ESA computational cost helped us to refine further the obtained global results, through the use of some local search. We have used this new minimizing procedure to solve complex circuit design problems, for which the objective function evaluation can be exceedingly costly.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "global optimization, stochastic optimization, test functions", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Costantini:1997:BVS, author = "P. Costantini", title = "Boundary-Valued Shape-Preserving Interpolating Splines", journal = j-TOMS, volume = "23", number = "2", pages = "229--251", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264050", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p229-costantini/", abstract = "This article describes a general-purpose method for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions. Examples of applications of the related Fortran code are periodic shape-preserving spline interpolation and the construction of visually pleasing closed curves.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernstein-B\'{e}zier polynomials, dynamic programming, spline interpolation", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Costantini:1997:APC, author = "P. Costantini", title = "{Algorithm 770}: {BVSPIS} --- a Package for Computing Boundary-Valued Shape-Preserving Interpolating Splines", journal = j-TOMS, volume = "23", number = "2", pages = "252--254", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264059", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p252-costantini/", abstract = "This article describes a software package for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernstein-B\'{e}zier polynomials, dynamic programming, spline interpolation", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Wu:1997:MCR, author = "Pei-Chi Wu", title = "Multiplicative, congruential random-number generators with multiplier $\pm 2^{k_1} \pm 2^{k_2}$ and modulus $2^p - 1$", journal = j-TOMS, volume = "23", number = "2", pages = "255--265", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264056", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p255-wu/", abstract = "The demand for random numbers in scientific applications in increasing. However, the most widely used multiplicative, congruential random-number generators with modulus $2^31 - 1$ have a cycle length of about $2.1 \times 10^9$. Moreover, developing portable and efficient generators with a larger modulus such as $2^61 - 1$ is more difficult than those with modulus $2^31 - 1$. This article presents the development of multiplicative, congruential generators with modulus $m = 2p - 1$ and four forms of multipliers: $2^{k_1} - 2^{k_2}, 2^{k_1} + 2^{k_2}, m - 2^{k_1} + 2^{k_2}$, and $m - 2^{k_1} - 2^{k_2}, {k_1} > {k_2}$. The multipliers for modulus $2^{31} - 1$ and $2^{61} - 1$ are measured by spectral tests, and the best ones are presented. The generators with these multipliers are portable and vary fast. They have also passed several empirical tests, including the frequency test, the urn test, and the maximum-of-$t$ test.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cycle length, efficiency, multiplicative congruential random-number generators, portability, spectral test", subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation.", } @Article{Kocis:1997:CIL, author = "Ladislav Kocis and William J. Whiten", title = "Computational Investigations of Low-discrepancy Sequences", journal = j-TOMS, volume = "23", number = "2", pages = "266--294", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.264064", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p266-kocis/", abstract = "The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are show to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrepancy, error of numerical integration, Faure sequence, generalized Halton sequence, Halton sequence, low-discrepancy sequences, Monte Carlo and quasi Monte Carlo integration, Sobol sequence", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.6} Computing Methodologies, SIMULATION AND MODELING.", } @Article{Goano:1997:RA7, author = "Michele Goano", title = "Remark on {Algorithm 745}", journal = j-TOMS, volume = "23", number = "2", pages = "295--295", month = jun, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/264029.643581", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 9 10:19:38 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Goano:1995:ACC}.", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hull:1997:ICA, author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang", title = "Implementing the Complex Arcsine and Arccosine Functions Using Exception Handling", journal = j-TOMS, volume = "23", number = "3", pages = "299--335", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275324", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p299-hull/", abstract = "We develop efficient algorithms for reliable and accurate evaluations of the complex arcsine and arccosine functions. A tight error bound is derived for each algorithm; the results are valid for all machine-representable points in the complex plane. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. Corresponding Fortran 77 programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results of these tests are included in the article, but the Fortran 77 programs are not (these programs are available from Fairgrieve). Tests of other widely available programs fail at many points in the complex plane, and otherwise are slower and produce much less accurate results.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, design, complex elementary functions, implementation", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, error analysis, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis, reliability and robustness, verification.", } @Article{Carr:1997:CBD, author = "Steve Carr and R. B. Lehoucq", title = "Compiler Blockability of Dense Matrix Factorizations", journal = j-TOMS, volume = "23", number = "3", pages = "336--361", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275325", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p336-carr/", abstract = "The goal of the LAPACK project is to provide efficient and portable software for dense numerical linear algebra computations. By recasting many of the fundamental dense matrix computations in terms of calls to an efficient implementation of the BLAS (Basic Linear Algebra Subprograms), the LAPACK project has, in large part, achieved its goal. Unfortunately, the efficient implementation of the BLAS results often in machine-specific code that is not portable across multiple architectures without a significant loss in performance or significant effort to reoptimize them. This article examines whether most of the hand optimizations performed on matrix factorization codes are unnecessary because they can (and should) be performed by the compiler. We believe that it is better for the programmer to express algorithms in a machine-independent form and allow the compiler to handle the machine-dependent details. This gives the algorithms portability across architectures and removes the error-prone, expensive, and tedious process of hand optimization. Although there currently exist no production compilers that can perform all the loop transformations discussed in this article, a description of current research in compiler technology is provided that will prove beneficial to the numerical linear algebra community. We show that the Cholesky and optimized automatically by a compiler to be as efficient as the same hand-optimized version found in LAPACK. We also show that the QR factorization may be optimized by the compiler to perform comparably with the hand-optimized LAPACK version on modest matrix sizes. Our approach allows us to conclude that with the advent of the compiler optimizations discussed in this article, matrix factorizations may be efficiently implemented in a BLAS-less form.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "languages, performance, BLAS, cache optimization, Cholesky decomposition, LAPACK, LU decomposition, QR decomposition", subject = "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers, optimization. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, portability.", } @Article{Carrig:1997:EHQ, author = "James J. {Carrig Jr.} and Gerald G. L. Meyer", title = "Efficient {Householder} {QR} Factorization for Superscalar Processors", journal = j-TOMS, volume = "23", number = "3", pages = "362--378", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275326", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p362-carrig/", abstract = "To extract the potential promised by superscalar processors, algorithm designers must streamline memory references and allow for efficient data reuse throughout the memory hierarchy. Two parameterized Householder QR factorization algorithms are presented that take into account the caches and registers typical of such processors. Guidelines are developed for choosing parameter values that obtain near-optimal cache and register utilization. The new algorithms are implemented and performance-tuned on an Intel Pentium Pro system, a single this POWER2 node of the IBM Scalable Parallel System 2 (SP2), and a single R8000 processor of a Silicon Graphics POWER Challenge XL.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, cache model, Householder QR factorization, register model", subject = "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design Styles, Cache memories. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis, efficiency, portability.", } @Article{Duff:1997:LBL, author = "Iain S. Duff and Michele Marrone and Giuseppe Radicati and Carlo Vittoli", title = "{Level 3 Basic Linear Algebra Subprograms} for Sparse Matrices: a User Level Interface", journal = j-TOMS, volume = "23", number = "3", pages = "379--401", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275327", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Y15", MRnumber = "MR1672168", bibdate = "Mon Jan 2 09:11:24 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p379-duff/", abstract = "This article proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. A major goal is to design and develop a common framework to enable efficient, and portable, implementations of iterative algorithms for sparse matrices on high-performance computers. We have designed the routines to shield the developer of mathematical software from most of the complexities of the various data structures used for sparse matrices. We have kept the interface and suite of codes as simple as possible while at the same time including sufficient functionality to cover most sparse matrix data structures. An important aspect of our framework is that it can be easily extended to incorporate new kernels if the need arises. We discuss the design, implementation, and use of subprograms for the multiplication of a full matrix by a sparse one and for the solution of sparse triangular systems with one or more (full) right-hand sides. We include a routine for checking the input data, generating a new sparse data structure from that input, and scaling a sparse matrix. The new data structure for the transformation can be specified by the user or can be chosen automatically by vendors to be efficient on their machines. We also include a routine for permuting the columns of a sparse matrix and one for permuting the rows of a full matrix.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr # " and " # ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, reliability, high-performance computing, iterative solution, programming standards, sparse BLAS, sparse data structures, sparse matrices", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, user interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Coding, standards. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, efficiency, portability, reliability and robustness, verification.", } @Article{Brankin:1997:ARF, author = "R. W. Brankin and I. Gladwell", title = "{Algorithm 771}. {\tt rksuite\_90}: {Fortran} Software for Ordinary Differential Equation Initial Value Problems", journal = j-TOMS, volume = "23", number = "3", pages = "402--415", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275328", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p402-brankin/", abstract = "We present Fortran 90 software for the initial-value problem in ordinary differential equations, including the interfaces and how Fortran 90 language features afford the opportunity to address different types and structures of variables and to provide additional functionality. A novel feature of this software is the availability of Unix scripts which enable presentation of the software for multiple problem types.", accepted = "January 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, complex, recursion", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1997:ASD, author = "Robert J. Renka", title = "{Algorithm 772}. {STRIPACK}: {Delaunay} Triangulation and {Voronoi} Diagram on the Surface of a Sphere", journal = j-TOMS, volume = "23", number = "3", pages = "416--434", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275329", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p416-renka/", abstract = "STRIPACK is a Fortran 77 software package that employs an incremental algorithm to construct a Delaunay triangulation and, optionally, a Voronoi diagram of a set of points (nodes) on the surface of the unit sphere. The triangulation covers the convex hull of the nodes, which need not be the entire surface, while the Voronoi diagram covers the entire surface. The package provides a wide range of capabilities including an efficient means of updating the triangulation with nodal additions or deletions. For N nodes, the storage requirement for the triangulation is 13N integer storage locations in addition to 3N nodal coordinates. Using an off-line algorithm and work space of size 3N, the triangulation can be constructed with time complexity O(NlogN).", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, Delaunay triangulation, Dirichlet tessellation, sphere, Thiessen regions, Voronoi diagram", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1997:ASI, author = "Robert J. Renka", title = "{Algorithm 773}. {SSRFPACK}: Interpolation of Scattered Data on the Surface of a Sphere with a Surface under Tension", journal = j-TOMS, volume = "23", number = "3", pages = "435--442", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275330", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p435-renka/", abstract = "SSRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points on the surface of a sphere. It employs automatically selected tension factors to preserve shape properties of the data and avoid overshoot and undershoot associated with steep gradients.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, scattered data fitting, smoothing, surface under tension, triangle-based interpolation", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Facchinei:1997:GBC, author = "Francisco Facchinei and Joaquim J{\'u}dice and Jo{\~a}o Soares", title = "Generating Box Constrained Optimization Problems", journal = j-TOMS, volume = "23", number = "3", pages = "443--447", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275331", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p443-facchinei/", abstract = "We present a method for generating box-constrained nonlinear programming test problems. The technique allows the user to control some properties of the generated test problems that are known to influence the behavior of algorithms for their solution. A corresponding set of Fortran 77 routines is described in a companion algorithm (774).", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, verification, nonlinear programming test problems, optimization, test problems generation", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, verification.", } @Article{Facchinei:1997:AFS, author = "Francisco Facchinei and Joaquim J{\'u}dice and Jo{\~a}o Soares", title = "{Algorithm 774}. {FORTRAN} Subroutine for Generating Box Constrained Optimization Problems", journal = j-TOMS, volume = "23", number = "3", pages = "448--450", month = sep, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/275323.275332", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 6 11:23:41 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p448-facchinei/", abstract = "We describe a set of Fortran routines for generating box-constrained nonlinear programming test problems. The technique, as described by Facchinei et al. (this issue), allows the user to control relevant properties of the generated problems.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, verification, nonlinear programming test problems, optimization, test problems generation", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, verification.", } @Article{Greenberg:1997:ACS, author = "Leon Greenberg and Marco Marletta", title = "{Algorithm 775}. The Code {SLEUTH} for Solving Fourth-Order {Sturm--Liouville} Problems", journal = j-TOMS, volume = "23", number = "4", pages = "453--493", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279231", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Sep 17 15:28:33 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p453-greenberg/", abstract = "We describe a new code (SLEUTH) for numerical solution of regular two-point fourth-order Sturm--Liouville eigenvalue problems. Eigenvalues are computed according to index: the user specifies an integer $k \geq 0$, and the code computes an approximation to the $k$th eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. The code will be made available through netlib.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, SLEUTH", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 77. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Bai:1997:ASF, author = "Z. Bai and G. W. Stewart", title = "{Algorithm 776}. {SRRIT} --- a {FORTRAN} Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix", journal = j-TOMS, volume = "23", number = "4", pages = "494--513", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279234; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p494-bai/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SRRIT is a Fortran program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix $A$ by the method of simultaneous iteration. Specifically, given an integer $m$, SRRIT computes a matrix $Q$ with $m$ orthonormal columns and real quasi-triangular matrix $T$ of order $m$ such that the equation $AQ = QT$ is satisfied up to a tolerance specified by the user. The eigenvalues of $T$ are approximations to the $m$ eigenvalues of largest absolute magnitude of $A$, and the columns of $Q$ span the invariant subspace corresponding to those eigenvalues. SRRIT references $A$ only through a user-provided subroutine to form the product $AQ$; hence it is suitable for large sparse problems.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, invariant subspace, nonsymmetric eigenvalue problem, project method", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing.", } @Article{Watson:1997:ASF, author = "Layne T. Watson and Robert C. Melville and Alexander P. Morgan and Homer F. Walker", title = "{Algorithm 777}. {HOMPACK90}: a Suite of {Fortran} 90 Codes for Globally Convergent Homotopy Algorithms", journal = j-TOMS, volume = "23", number = "4", pages = "514--549", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279235; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p514-watson/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "HOMPACK90 is a Fortran 90 version of the Fortran 77 package HOMPACK (Algorithm 652), a collection of codes for finding zeros of fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms. Three qualitatively different algorithms --- ordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix --- are provided for tracking homotopy zero curves, as well as separate routine for dense and sparse Jacobian matrices. A high level driver for the special case of polynomial systems is also provided. Changes to HOMPACK include numerous minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices.", accepted = "April 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, Chow-Yorke algorithm, curve tracking, fixed point, globally convergent, homotopy methods, polynomial systems, probability-one, zero.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Zhu:1997:ALF, author = "Ciyou Zhu and Richard H. Byrd and Peihuang Lu and Jorge Nocedal", title = "{Algorithm 778}. {L-BFGS-B}: {Fortran} Subroutines for {Large-Scale} Bound Constrained Optimization", journal = j-TOMS, volume = "23", number = "4", pages = "550--560", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279236; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p550-zhu/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Morales:2011:RAB}.", abstract = "L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be user for unconstrained problems and in this case performs similarly to its predecessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.", accepted = "April 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, large-scale optimization, limited-memory method, nonlinear optimization, variable metric method.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; gradient methods; nonlinear programming; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Karp:1997:HPD, author = "Alan H. Karp and Peter Markstein", title = "High-Precision Division and Square Root", journal = j-TOMS, volume = "23", number = "4", pages = "561--589", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279237", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Nov 8 14:50:37 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/", abstract = "We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, performance, division, quad precision, square root.", subject = "G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.", } @Article{MacLeod:1998:AFD, author = "Allan J. MacLeod", title = "{Algorithm 779}: {Fermi--Dirac} Functions of Order $-1/2, 1/2, 3/2, 5/2$", journal = j-TOMS, volume = "24", number = "1", pages = "1--12", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285862; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p1-macleod/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The computations of Fermi--Dirac ${\cal F}_k$ integrals is discussed for the values $k = -1, 1/2, 3/2, 5/2$. We derive Chebyshev polynomial expansions which allow the computation of these functions to double precision IEEE accuracy.", accepted = "May 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, Chebyshev polynomials, collocation, Fermi--Dirac, floating-point arithmetic.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Sharp:1998:GHO, author = "P. W. Sharp and J. H. Verner", title = "Generation of High-order Interpolants for Explicit {Runge--Kutta} Pairs", journal = j-TOMS, volume = "24", number = "1", pages = "13--29", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285863; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p13-sharp/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Explicit Runge--Kutta pairs can be enhanced by providing them with interpolants. Enhancements include the ability to estimate and control the defect, to produce dense output, and to calculate past values in delay differential equations. The coefficients of an interpolant are easily generated by bootstrapping on the order conditions. However, the generation of high-order interpolants requires a large number of arithmetic operations. We describe an efficient algorithm for the generation of high-order interpolants and illustrate the use of the algorithm with three applications.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, explicit, generation, high order, interpolants, pairs, Runge--Kutta.", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Houstis:1998:PPS, author = "E. N. Houstis and J. R. Rice and S. Weerawarana and A. C. Catlin and P. Papachiou and K.-Y. Wang and M. Gaitatzes", title = "{PELLPACK}: a Problem Solving Environment for {PDE} Based Applications on Multicomputer Platforms", journal = j-TOMS, volume = "24", number = "1", pages = "30--73", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285864; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p30-houstis/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents the software architecture and implementation of the problem-solving environment (PSE) PELLPACK for modeling physical objects described by partial differential equations (PDEs). The scope of this PDE is broad, as PELLPACK incorporates many PDE solving systems, and some of these, in turn, include several specific PDE solving methods. Its coverage for 1D, 2D, and 3D elliptic or parabolic problems is quite broad, and it handles some hyperbolic problems. Since a PSE should provide complete support for the problem-solving process, PELLPACK also contains a large amount of code to support graphical user interfaces, analytic tools, user help, domain or mesh partitioning, machine and data selection, visualization, and various other tasks. Its total size is well over 1 million lines of code. Its open-ended software architecture consists of several software layers. The top layer is an interactive graphical interface for specifying the PDE model and its solution framework. This interface saves the results of the user specification in the form of a very high level PDE language which is an alternate interface to the PELLPACK system. This language also allows a user to specify the PDE problem and its solution framework textually in a natural form. The PELLPACK language preprocessor generates a Fortran control program with the interfaces, calls to specified components and libraries of the PDE solution framework, and functions defining the PDE problem. The PELLPACK program execution is supported by a high-level tool where the virtual parallel system is defined, where the execution mode, file system, and hardware resources are selected, and where the compilation, loading, and execution are controlled. Finally, the PELLPACK PSE integrates several PDE libraries and PDE systems available in the public domain. The system employs several parallel reuse methodologies based on the decomposition of discrete geometric data to map sparse PDE computations to parallel machines. An instance of the system is available as a Web server (WebPELLPACK) for public use at http://pellpack.cs.purdue.edu.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, design, languages, management, performance, execution models, knowledge bases, libraries, parallel reuse methodologies, PDE language, problem-solving environments, programming-in-the-large, software bus.", subject = "{\bf C.3}: Computer Systems Organization, SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS. {\bf D.2.6}: Software, SOFTWARE ENGINEERING, Programming Environments, Graphical environments, interactive environments and integrated environments. {\bf D.2.11}: Software, SOFTWARE ENGINEERING, Software Architectures, Domain-specific architectures. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Very high-level languages. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Domain decomposition methods, elliptic equations, hyperbolic equations, iterative solution techniques, multigrid and multilevel methods, and parabolic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Parallel and vector implementations. {\bf I.2.5}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Programming Languages and Software, Expert system tools and techniques. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering, and mathematics and statistics.", } @Article{Gupta:1998:DIE, author = "Anshul Gupta and Fred G. Gustavson and Mahesh Joshi and Sivan Toledo", title = "The Design, Implementation and Evaluation of a Symmetric Banded Linear Solver for Distributed-Memory Parallel Computers", journal = j-TOMS, volume = "24", number = "1", pages = "74--101", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285865; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p74-gupta/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes the design, implementation, and evaluation of a parallel algorithm for the Cholesky factorization of symmetric banded matrices. The algorithm is part of IBM's parallel engineering and scientific subroutine library version 1.2 and is compatible with ScaLAPACK's banded solver. Analysis, as well as experiments on an IBM SP2 distributed-memory parallel computer, shows that the algorithm efficiently factors banded matrices with wide bandwidth. For example, a 31-mode SP2 factors a large matrix more than 16 times faster than a single node would factor it using the best sequential algorithm, and more than 20 times faster than a single node would using LAPACK's DPBTRF. The algorithm uses novel ideas in the area of distributed dense-matrix computations that include the use of a dynamic schedule for a blocked systolic-like algorithm and the separation of the input and output layouts from the layout the algorithm uses internally. The algorithm alson uses known techniques such as blocking to improve its communication-to-computation ratio and its data-cache behavior.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms, performance, banded matrices, Cholesky factorization, distributed memory, parallel algorithms.", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis, and efficiency.", } @Article{Hamilton:1998:AEP, author = "K. G. Hamilton", title = "{Algorithm 780}: Exponential Pseudorandom Distribution", journal = j-TOMS, volume = "24", number = "1", pages = "102--106", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285866; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p102-hamilton/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An algorithm is presented for the calculation of exponentially distributed random numbers. It is based on mathematics that was published by Ahrend and Dieter, but some errors have been corrected.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms, exponential distribution, random numbers, pseudorandom numbers.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf I.6.0}: Computing Methodologies, SIMULATION AND MODELING, General.", } @Article{Fulton:1998:CSD, author = "Charles T. Fulton and Steven Pruess", title = "The Computation of Spectral Density Functions for Singular {Sturm--Liouville} Problems Involving Simple Continuous Spectra", journal = j-TOMS, volume = "24", number = "1", pages = "107--129", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285867; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p107-fulton/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The software package SLEDGE has as one of its options the estimation of spectral density functions $p(t)$ for a wide class of singular Sturm--Liouville problems. In this article the underlying theory and implementation issues are discussed. Several examples exhibiting quite varied asymptotic behavior in $p$ are presented.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms, performance, continuous spectrum, eigenfunction norm, eigenvalue, limit circle, limit point, oscillatory, singular endpoints, spectral density functions, Sturm--Liouville problems.", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis.", } @Article{Sidje:1998:ESP, author = "Roger B. Sidje", title = "{EXPOKIT}: Software Package for Computing Matrix Exponentials", journal = j-TOMS, volume = "24", number = "1", pages = "130--156", month = mar, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/285861.285868; http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p130-sidje/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms, Krylov methods, Markov chains, matrix exponential.", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Chow:1998:OFB, author = "Edmond Chow and Michael A. Heroux", title = "An object-oriented framework for block preconditioning", journal = j-TOMS, volume = "24", number = "2", pages = "159--183", month = jun, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/290200.287639", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p159-chow/", abstract = "General software for preconditioning the iterative solution of linear systems is greatly lagging behind the literature. This is partly because specific problems and specific matrix and preconditioner data structures in order to be solved efficiently, i.e., multiple implementations of a preconditioner with specialized data structures are required. This article presents a framework to support preconditioning with various, possibly user-defined, data structures for matrices that are partitioned into blocks. The main idea is to define data structures for the blocks, and an upper layer of software which uses these blocks transparently of their data structure. This transparency can be accomplished by using an object-oriented language. Thus, various preconditioners, such as block relaxations and block-incomplete factorizations, only need to be defined once and will work with any block type. In addition, it is possible to transparently interchange various approximate or exact techniques for inverting pivot blocks, or solving systems whose coefficient matrices are diagonal blocks. This leads to a rich variety of preconditioners that can be selected. Operations with the blocks are performed with optimized libraries or fundamental data types. Comparisons with an optimized Fortran 77 code on both workstations and Cray supercomputers show that this framework can approach the efficiency of Fortran 77, as long as suitable block sized and block types are chosen.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Breinholt:1998:AGH, author = "Greg Breinholt and Christoph Schierz", title = "{Algorithm 781}: generating {Hilbert}'s space-filling curve by recursion", journal = j-TOMS, volume = "24", number = "2", pages = "184--189", month = jun, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/290200.290219", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p184-breinholt/", abstract = "An efficient algorithm for the generation of Hilbert's space-filling curve is given. The algorithm implements a recursive procedure that involves simple integer operations and quickly converges to the set of points that make the Hilbert curve. The algorithm is elegant, short, and considerably easier to implement than previous recursive and nonrecursive algorithms and can be efficiently implemented in all programming languages that have integer operations and allow recursion. The fundamental Hilbert shape (a line joining the four corners of a square) is represented by two variables with values of either 0 or 1. This coding technique could be successfully applied to the generation of other regular space-filling curves, such as the Peano curve.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf I.3.3} Computing Methodologies, COMPUTER GRAPHICS, Picture/Image Generation, Line and curve generation. {\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Bik:1998:AGS, author = "Aart J. C. Bik and Peter J. H. Brinkhaus and Peter M. W. Knijnenburg and Harry A. G. Wijshoff", title = "The automatic generation of sparse primitives", journal = j-TOMS, volume = "24", number = "2", pages = "190--225", month = jun, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/290200.287636", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p190-bik/", abstract = "Primitives in mathematical software are usually written and optimized by hand. With the implementation of a ``sparse compiler'' that is capable of automatically converting a dense program into sparse code, however, a completely different approach to the generation of sparse primitives can be taken. A {\em dense\/} implementation of a particular primitive is supplied to the sparse compiler, after which it can be converted into many different {\em sparse\/} versions of this primitive. Each version is specifically tailored to a class of sparse matrices having a specific nonzero structure. In this article, we discuss some of our experiences with this new approach.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf D.1.2} Software, PROGRAMMING TECHNIQUES, Automatic Programming. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf E.2} Data, DATA STORAGE REPRESENTATIONS. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Bischof:1998:CRQ, author = "Christian H. Bischof and G. Quintana--Ort{\'\i}", title = "Computing rank-revealing {$QR$} factorizations of dense matrices", journal = j-TOMS, volume = "24", number = "2", pages = "226--253", month = jun, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/290200.287637", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p226-bischof/", abstract = "We develop algorithms and implementations for computing rank-revealing QR (RRQR) factorizations of dense matrices. First, we develop an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy, aided by incremental condition estimation. Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang. We suggest algorithmic improvements with respect to condition estimation, termination criteria, and Givens updating. By combining the block algorithm with one of the triangular postprocessing steps, we arrive at an efficient and reliable algorithm for computing an RRQR factorization of a dense matrix. Experimental results on IBM RS/6000 SGI R8000 platforms show that this approach performs up to three times faster that the less reliable QR factorization with column pivoting as it is currently implemented in LAPACK, and comes within 15\% of the performance of the LAPACK block algorithm for computing a QR factorization without any column exchanges. Thus, we expect this routine to be useful in may circumstances where numerical rank deficiency cannot be ruled out, but currently has been ignored because of the computational cost of dealing with it.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Bischof:1998:ACR, author = "C. H. Bischof and G. Quintana-Ort{\'\i}", title = "{Algorithm 782}: {Codes} for rank-revealing {$QR$} factorizations of dense matrices", journal = j-TOMS, volume = "24", number = "2", pages = "254--257", month = jun, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/290200.287638", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p254-bischof/", abstract = "This article describes a suite of codes as well as associated testing and timing drivers for computing rank-revealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy and improved versions of the RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang, respectively, We highlight usage and features of these codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Mathematica.", } @Article{Peters:1998:APF, author = "J{\"o}rg Peters", title = "{Algorithm 783}: {Pcp2Nurb} --- smooth free-form surfacing with linearly trimmed bicubic {B}-splines", journal = j-TOMS, volume = "24", number = "3", pages = "261--267", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292399", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p261-peters/", abstract = "Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary topology and local patch-layout by allowing {\em n\/}-sided, possibly nonplanar, facets and {\em m\/}-valent vertices. By cutting off edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a {\em planar-cut polyhedron\/}. A planar-cut polyhedron is a generalization of the well-known tensor-product control structure. The routine Pcp2Nurb in turn translates planar-cut polyhedra to a collection of four-sided linearly trimmed bicubic B-splines and untrimmed biquadratic B-splines. The routine can thus serve as central building block for overcoming topological constraints in the mathematical modeling of smooth surfaces that are stored, transmitted, and rendered using only the standard representation in industry. Specifically, on input of a nine-point subnet of a planar-cut polyhedron, the routine outputs a trimmed bicubic NURBS patch. If the subnet does not have geometrically redundant edges, this patch joins smoothly with patches from adjacent subnets as a four-sided piece of a regular {\em C1\/} surface. The patch integrates smoothly with untrimmed biquadratic tensor-product surfaces derived from subnets with tensor-product structure. Sharp features can be retained in this representation by using geometrically redundant edges in the planar-cut polyhedron. The resulting surface follows the outlines of the planar-cut polyhedron in the manner traditional tensor-product splines follow the outline of their rectilinear control polyhedron. In particular, it stays in the local convex hull of the planar-cut polyhedron.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Splines. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Boundary representations.", } @Article{Kaagstrom:1998:GLB, author = "Bo K{\aa}gstr{\"o}m and Per Ling and Charles {Van Loan}", title = "{GEMM-based} level 3 {BLAS}: high-performance model implementations and performance evaluation benchmark", journal = j-TOMS, volume = "24", number = "3", pages = "268--302", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p268-kagstrom/", abstract = "The level 3 Basic Linear Algebra Subprograms (BLAS) are designed to perform various matrix multiply and triangular system solving computations. Due to the complex hardware organization of advanced computer architectures the development of optimal level 3 BLAS code is costly and time consuming. However, it is possible to develop a portable and high-performance level 3 BLAS library mainly relying on a highly optimized GEMM, the routine for the general matrix multiply and add operation. With suitable partitioning, all the other level 3 BLAS can be defined in terms of GEMM and a small amount of level 1 and level 2 computations. Our contribution is twofold. First, the model implementations in Fortran 77 of the GEMM-based level 3 BLAS are structured to reduced effectively data traffic in a memory hierarchy. Second, the GEMM-based level 3 BLAS performance evaluation benchmark is a tool for evaluating and comparing different implementations of the level 3 BLAS with the GEMM-based model implementations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification**.", } @Article{Kaagstrom:1998:AGL, author = "Bo K{\aa}gstr{\"o}m and Per Ling and Charles {Van Loan}", title = "{Algorithm 784}: {GEMM-based} level 3 {BLAS}: portability and optimization issues", journal = j-TOMS, volume = "24", number = "3", pages = "303--316", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292426", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p303-kagstrom/", abstract = "This companion article discusses portability and optimization issues of the GEMM-based level 3 BLAS model implementations and the performance evaluation benchmark. All software comes in all four data types (single- and double-precision, real and complex) and are designed to be easy to implement and use on different platforms. Each of the GEMM-based routines has a few machine-dependent parameters that specify internal block sizes, cache characteristics, and branch points for alternative code sections. These parameters provide means for adjustment to the characteristics of a memory hierarchy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; measurement; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification**.", } @Article{Hu:1998:ASP, author = "Chenglie Hu", title = "{Algorithm 785}: a software package for computing {Schwarz--Christoffel} conformal transformation for doubly connected polygonal regions", journal = j-TOMS, volume = "24", number = "3", pages = "317--333", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.291204", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p317-hu/", abstract = "A software package implementing Schwarz--Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping ``difficult'' regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Espelid:1998:RAD, author = "Terje O. Espelid", title = "Remark on {Algorithm 706}: {DCUTRI} --- an algorithm for adaptive cubature over a collection of triangles", journal = j-TOMS, volume = "24", number = "3", pages = "334--335", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.291205", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:18:39 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Berntsen:1992:ADA}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p334-espelid/", abstract = "We present corrections to {Algorithm 706} ({\em ACM Trans. Math. Softw.\/} 18, 3, Sept. 1992, pages 329-342; CALGO supplement 123).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive and iterative quadrature. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multidimensional (multiple) quadrature. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Levin:1998:RAS, author = "Stewart A. Levin", title = "Remark on {Algorithm 622}: a simple macroprocessor", journal = j-TOMS, volume = "24", number = "3", pages = "336--340", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292448", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:17:52 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Rice:1984:ASM}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p336-levin/", abstract = "A number of updates to the macroprocessor are described that bring the code into line with the Fortran 77 standard. This is followed by an outline of how the macroprocessor was used for the rapid porting of geophysical software from a 64-bit supercomputer environment to a number of different Unix workstations. Finally a number of deficiencies remaining in the macroprocessor are noted and workarounds suggested where possible.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Macro and assembly languages. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Preprocessors.", } @Article{Marsaglia:1998:MPM, author = "George Marsaglia and Wai Wan Tsang", title = "The {Monty Python} method for generating random variables", journal = j-TOMS, volume = "24", number = "3", pages = "341--350", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292453; http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", ZMnumber = "0930.65002", abstract = "We suggest an interesting and fast method for generating normal, exponential, $t$, von Mises, and certain other important random variables used in Monte Carlo studies. The right half of a symmetric density is cut into pieces, then, using simple area-preserving transformations, reassembled into a rectangle from which the $x$-coordinate---or a linear function of the $x$-coordinate---of a random point provides the required variate. To illustrate the speed and simplicity of the Monty Python method, we provide a small C program, self-contained, for rapid generation of normal (Gaussian) variables. It is self-contained in the sense that required uniform variates are generated in-line, as pairs of 16-bit integers by means of the remarkable new multiply-with-carry method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "$t$ variates; algorithms; Monte Carlo studies; Monty Python method; normal variates; random variable generation; theory; von Mises variates", subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1} Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", ZMclass = "*65C10 Random number generation 65C05 Monte Carlo methods", } @Article{Hopkins:1998:CAF, author = "Tim Hopkins", title = "Certification of {Algorithm 734}: a {Fortran 90} code for unconstrained nonlinear minimization", journal = j-TOMS, volume = "24", number = "3", pages = "351--354", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292460", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p351-hopkins/", abstract = "A Fortran 90 Code for Unconstrained Nonlinear Minimization ({\em ACM Trans. Math. Softw. 20\/}, 3 (Sept. 1994), pages 354-372; CALGO Supplement 131) was ported to a number of compiler-platform combinations. The necessary changes to the code are given along with some comparative timings.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Gautschi:1998:RAO, author = "Walter Gautschi", title = "Remark on {Algorithm 726}: {ORTHPOL} --- a package of routines for generating orthogonal polynomials and {Gauss}-type quadrature rules", journal = j-TOMS, volume = "24", number = "3", pages = "355--355", month = sep, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/292395.292467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:16:21 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Gautschi:1994:ACP}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p355-gautschi/", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Smith:1998:AMP, author = "David M. Smith", title = "{Algorithm 786}: Multiple-Precision Complex Arithmetic and Functions", journal = j-TOMS, volume = "24", number = "4", pages = "359--367", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293687", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:09:51 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/", abstract = "The article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always correctly rounded. For best efficiency on different machines, the user can change the arithmetic type used to represent the multiple-precision numbers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance; reliability", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**.", } @Article{Ekeland:1998:SDE, author = "Kersti Ekeland and Brynjulf Owren and Eivor {\O}ines", title = "Stiffness Detection and Estimation of Dominant Spectra with Explicit {Runge--Kutta} Methods", journal = j-TOMS, volume = "24", number = "4", pages = "368--382", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.287641", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p368-ekeland/", abstract = "A new stiffness detection scheme based on explicit Runge--Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worthwhile alternative to other known stiffness detection schemes, especially when the systems are large and when it is desirable to know more about the spectrum of the Jacobian than just the spectral radius.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, One-step (single step) methods. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations.", } @Article{Renka:1998:RA, author = "Robert J. Renka and Ron Brown", title = "Remark on {Algorithm 761}", journal = j-TOMS, volume = "24", number = "4", pages = "383--385", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293689; http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p383-renka/", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:12:24 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1996:ASS,DeTisi:2000:RAS}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Resende:1998:AFS, author = "Mauricio G. C. Resende and Thomas A. Feo and Stuart H. Smith", title = "{Algorithm 787}: {Fortran} Subroutines for Approximate Solution of Maximum Independent Set Problems Using {GRASP}", journal = j-TOMS, volume = "24", number = "4", pages = "386--394", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293690", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 10:13:13 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p386-resende/", abstract = "Let $G=(V, E)$ be an undirected graph where $V$ and $E$ are the sets of vertices and edges of $G$, respectively. A subset of the vertices $S \subseteq V$ is independent if all of its members are pairwise nonadjacent, i.e., have no edge between them. A solution to the NP-hard maximum independent set problem is an independent set of maximum cardinality. This article describes gmis, a set of Fortran subroutines to find an approximate solution of a maximum independent set problem. A greedy randomized adaptive search procedure (GRASP) is used to produce the solutions. The algorithm is described in detail. Implementation and usage of the package is outlined, and computational experiments are reported, illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.m} Mathematics of Computing, MISCELLANEOUS.", } @Article{Atkinson:1998:AAB, author = "Kendall Atkinson and Youngmok Jeon", title = "{Algorithm 787}: {Automatic} Boundary Integral Equation Programs for the Planar {Laplace} Equation", journal = j-TOMS, volume = "24", number = "4", pages = "395--417", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293692", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p395-atkinson/", abstract = "Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each boundary value problem as a boundary integral equation of the second kind. The Nystr{\"o}m method is used to solve the integral equations, and convergence of arbitrary high order is observed when the boundary data are analytic. The Kelvin transformation is introduced to allow a simple conversion between internal and external problems. Two Fortran program implementations, DRCHLT and NEUMAN, are defined, analyzed, and illustrated.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", } @Article{Govaerts:1998:IHD, author = "W. Govaerts and F. W. O. Kuznetsov and B. Sijnave", title = "Implementation of {Hopf} and Double-{Hopf} Continuation Using Bordering Methods", journal = j-TOMS, volume = "24", number = "4", pages = "418--436", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293693", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p418-govaerts/", abstract = "We discuss the computational study of curves of Hopf and double-Hopf points in the software package CONTENT developed at CWI, Amsterdam. These are important points in the numerical study of dynamical systems characterized by the occurrence of one or two conjugate pairs of pure imaginary eigenvalues in the spectrum of the Jacobian matrix. The bialternate product of matrices is extensively used in three codes for the numerical continuation of curves of Hopf points and in one for the continuation of curves of double-Hopf points. In the double-Hopf and two of the single-Hopf cases this is combined with a bordered matrix method. We use this software to find special points on a Hopf curve in a model of chemical oscillations and by computing a Hopf and a double-Hopf curve in a realistic model of a neuron.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; design", subject = "{\bf D.2.6} Software, SOFTWARE ENGINEERING, Programming Environments. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Giering:1998:RAC, author = "Ralf Giering and Thomas Kaminski", title = "Recipes for Adjoint Code Construction", journal = j-TOMS, volume = "24", number = "4", pages = "437--474", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293695", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p437-giering/", abstract = "Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sensitivity analysis, and determination of singular vectors. The adjoint model computes the gradient of a cost function with respect to control variables. Generation of adjoint code may be seen as the special case of differentiation of algorithms in reverse mode, where the dependent function is a scalar. The described method for adjoint code generation is based on a few basic principles, which permits the establishment of simple construction rules for adjoint statements and complete adjoint subprograms. These rules are presented and illustrated with some examples. Conflicts that occur due to loops and redefinition of variables are also discussed. Direct coding of the adjoint of a more sophisticated model is extremely time consuming and subject to errors. Hence, automatic generation of adjoint code represents a distinct advantage. An implementation of the method, described in this article, is the tangent linear and adjoint model compiler (TAMC).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; theory", subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Automatic differentiation. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf I.2.2} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming, Program transformation.", } @Article{Berzins:1998:SAS, author = "M. Berzins and R. Fairlie and S. V. Pennington and J. M. Ware and L. E. Scales", title = "{SPRINT2D}: adaptive software for {PDEs}", journal = j-TOMS, volume = "24", number = "4", pages = "475--499", month = dec, year = "1998", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/293686.293696", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p475-berzins/", abstract = "SPRINT2D is a set of software tools for solving both steady and unstea dy partial differential equations in two-space variables. The software consists of a set of coupled modules for mesh generation, spatial discretization, time integration, nonlinear equations, linear algebra, spatial adaptivity, and visualization. The software uses unstructured triangular meshes and adaptive local error control in both space and time. the class of problems solved includes systems of parabolic, elliptic, and hyperbolic equations; for the latter by use of Riemann-solve-based methods. This article describes the software and show how the adaptive techniques may be used to increase the reliability of the solution for a Burgers' equations problem, an electrostatics problem from elastohydrodynamic lubrication, and a challenging gas jet problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Method of lines. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Hyperbolic equations. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Anonymous:1998:AI, author = "Anonymous", title = "1998 Author Index", journal = j-TOMS, volume = "24", number = "4", pages = "500--502", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 09 17:22:53 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", xxURL = "Missing from ACM Digital Library", } @Article{Davis:1999:CUM, author = "Timothy A. Davis and Iain S. Duff", title = "Combined Unifrontal\slash Multifrontal Method for Unsymmetric Sparse Matrices", journal = j-TOMS, volume = "25", number = "1", pages = "1--20", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.287640", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1999-25/; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p1-davis/", abstract = "We discuss the organization of frontal matrices in multifrontal methods for the solution of large sparse sets of unsymmetric linear equations. In the multifrontal method, work on a frontal matrix can be suspended, the frontal matrix can be stored for later reuse, and a new frontal matrix can be generated. There are thus several frontal matrices stored during the factorization, and one or more of these are assembled (summed) when creating a new frontal matrix. Although this means that arbitrary sparsity patterns can be handled efficiently, extra work is required to sum the frontal matrices together and can be costly because indirect addressing is required. The (uni)frontal method avoids this extra work by factorizing the matrix with a single frontal matrix. Rows and columns are added to the frontal matrix, and pivot rows and columns are removed. Data movement is simpler, but higher fill-in can result if the matrix cannot be permuted into a variable-band form with small profile. We consider a combined unifrontal/multifrontal algorithm to enable general fill-in reduction orderings to be applied without the data movement of previous multifrontal approaches. We discuss this technique in the context of a code designed for the solution of sparse systems with unsymmetric pattern.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; experimentation; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis.", } @Article{Pryce:1999:TPS, author = "J. D. Pryce", title = "A Test Package for {Sturm--Liouville} Solvers", journal = j-TOMS, volume = "25", number = "1", pages = "21--57", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.287651", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p21-pryce/p21-pryce/", abstract = "The author and colleagues have produced a collection of 60 test problems which offer a realistic performance test of the currently available automatic codes for eigenvalues of the classical Sturm--Liouville problem. We describe a Fortran implementation and the considerations that went into its design. A novel feature is that (almost) all the code defining one problem is textually contiguous in the Fortran text, unlike for example the DETEST package for ODE initial-value solvers where the definition of a problem is spread over several routines. The described implementation forms the infrastructure of the SLDRVER interactive package which supports exploration of a set of Sturm--Liouville problems with the four SL-solvers SLEIGN, SLEDGE, SL02F, and SLEIGN2. A ``standard'' set of 60 problems is provided, but it is simple to replace this by another one.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf D.2.5} Software, SOFTWARE ENGINEERING, Testing and Debugging. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {/bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {/bf I.2.4} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods.", } @Article{Pryce:1999:AST, author = "J. D. Pryce", title = "{Algorithm 789}: {SLTSTPAK}: a Test Package for {Sturm--Liouville} Solvers", journal = j-TOMS, volume = "25", number = "1", pages = "58--69", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.287652", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/789.gz; http://phase.etl.go.jp/netlib/toms/789; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p58-pryce/; http://www.hensa.ac.uk/netlib/toms/789.gz; http://www.netlib.no/netlib/toms/789; http://www.netlib.org/toms/789", abstract = "We give technical details of the Sturm--Liouville test package SLTSTPAK, complementing the companion article (this issue) on its design. SLTSTPAK comprises the following: a specification of how to write a routine TSTSET containing a set of Sturm--Liouville problems; a number of routines that act as a harness between a TSTSET, written to this specification, and a driver program. A set of 60 standard problems is provided, but it is simple to replace this by another one.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{/bf D.2.5} Software, SOFTWARE ENGINEERING, Testing and Debugging. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Renka:1999:ACC, author = "R. J. Renka", title = "{Algorithm 790}: {CSHEP2D}: Cubic {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "25", number = "1", pages = "70--73", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305737", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/790.gz; http://phase.etl.go.jp/netlib/toms/790; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p70-renka/; http://www.hensa.ac.uk/netlib/toms/790.gz; http://www.netlib.no/netlib/toms/790; http://www.netlib.org/toms/790", abstract = "We describe a new algorithm for scattered data interpolation. The method is similar to that of Algorithm 660 but achieves cubic precision and C2 continuity at very little additional cost. An accompanying article presents test results that show the method to be among the most accurate available.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:ATC, author = "R. J. Renka and Ron Brown", title = "{Algorithm 791}: {TSHEP2D}: Cosine series {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "25", number = "1", pages = "74--77", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305754", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/791.gz; http://phase.etl.go.jp/netlib/toms/791; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p74-renka/; http://www.hensa.ac.uk/netlib/toms/791.gz; http://www.netlib.no/netlib/toms/791; http://www.netlib.org/toms/791", abstract = "We describe a new algorithm for scattered data interpolation. It is based on a modified Shepard method similar to that of Algorithm 660 but uses 10-parameter cosine series nodal functions in place of quadratic polynomials. Also, the interpolant has continuous second partial derivatives. An accompanying survey article presents test results that show the method to be more accurate that polynomial-based methods in terms of reproducing test functions with large variations and steep gradients.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:AAT, author = "R. J. Renka and Ron Brown", title = "{Algorithm 792}: Accuracy Tests of {ACM} Algorithms for Interpolation of Scattered Data in the Plane", journal = j-TOMS, volume = "25", number = "1", pages = "78--94", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305745", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/792.gz; http://phase.etl.go.jp/netlib/toms/792; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p78-renka/; http://www.hensa.ac.uk/netlib/toms/792.gz; http://www.netlib.no/netlib/toms/792; http://www.netlib.org/toms/792", abstract = "We present results of accuracy tests on scattered-data fitting methods that have been published as ACM algorithms. The algorithms include seven triangulation-based methods and three modified Shepard methods, two of which are new algorithms. Our purpose is twofold: to guide potential users in the selection of an appropriate algorithm and to provide a test suite for assessing the accuracy of new methods (or existing methods that are not included in this survey). Our test suite consists of five sets of nodes, with nodes counts ranging from 25 to 100, and 10 test functions. These are made available in the form of three Fortran subroutines: TESTDT returns one of the node sets; TSTFN1 returns a value and, optionally, a gradient value, of one of the test function; and TSTFN2 returns a value, first partials, and second partial derivatives of one of the test functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Testa:1999:RA, author = "F. J. Testa and R. J. Renka", title = "Remark on {Algorithm 716}", journal = j-TOMS, volume = "25", number = "1", pages = "95--96", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.287656", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Renka:1993:ATT}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p95-testa/", abstract = "The curve-fitting package TSPACK has been converted to double precision. Also, portability has been improved by eliminating some potential errors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:RAa, author = "R. J. Renka", title = "Remark on {Algorithm 751}", journal = j-TOMS, volume = "25", number = "1", pages = "97--98", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305726", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Renka:1996:ATC}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p97-renka/", abstract = "The triangulation package TRIPACK has been revised to run more efficiently and to eliminate some potential errors. Also, a portable triangulation plotting routine was added.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:RAb, author = "R. J. Renka", title = "Remark on {Algorithm 752}", journal = j-TOMS, volume = "25", number = "1", pages = "99--100", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305731", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Renka:1996:ASS}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p99-renka/", abstract = "The triangulation-based scattered-data fitting package SRFPACK was updated for (a) compatibility with a revised interface to the triangulation package TRIPACK, (b) the elimination of potential errors in the treatment of tension factors and in the extrapolation procedure, and (c) the addition of a more accurate local gradient-estimation procedure and a simple but portable contour-plotting capability.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Gautschi:1999:NRC, author = "Walter Gautschi", title = "A Note on the Recursive Calculation of Incomplete Gamma Functions", journal = j-TOMS, volume = "25", number = "1", pages = "101--107", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305717", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/", abstract = "It is known that the recurrence relation for incomplete gamma functions $\Gamma(a + n, x), 0 \le a < 1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is unstable---more so the larger $x$. Nevertheless, the recursion can be used in the range $0 \le n \le x$ practically without error growth, and in larger ranges $0 \le n \le N$ with a loss of accuracy that can be controlled by suitably limiting $N$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; reliability", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability). {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Xie:1999:RAU, author = "Dexuan Xie and Tamar Schlick", title = "Remark on {Algorithm 702}: The Updated Truncated {Newton} Minimization Package", journal = j-TOMS, volume = "25", number = "1", pages = "108--122", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305698", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Schlick:1992:ATE}.", URL = "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p108-xie/", abstract = "A truncated Newton minimization package, TNPACK, was described in ACM Transactions on Mathematical Software 14, 1 (Mar. 1992), pp.46-111. Modifications to enhance performance, especially for large-scale minimization of molecular potential functions, are described here. They involve three program segments of TNPACK: negative curvature test, modified Cholesky factorization, and line-search stopping rule.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; performance", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf J.3} Computer Applications, LIFE AND MEDICAL SCIENCES.", } @Article{Gay:1999:SAF, author = "David M. Gay and Eric Grosse", title = "Self-adapting {Fortran 77} Machine Constants: Comment on {Algorithm 528}", journal = j-TOMS, volume = "25", number = "1", pages = "123--126", month = mar, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/305658.305711", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 12:38:08 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", note = "See \cite{Fox:1978:AFP}.", URL = "http://cm.bell-labs.com/who/ehg/mach/d1mach.ps; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gay:1999:SAF; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMScitation?Fox:1978:AFP; http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p123-gay/", abstract = "This note discusses user dissatisfaction with the need to uncomment data statements in Algorithm 528, comments on alternative approaches tried by the community, and proposes a solution that is both automatic and safe.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; d1mach; languages; machine environment parameters", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @Article{Flores:1999:CFR, author = "Juan Flores", title = "Complex Fans: a Representation for Vectors in Polar Form with Interval Attributes", journal = j-TOMS, volume = "25", number = "2", pages = "129--156", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317277", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p129-flores/", abstract = "If we allow the magnitude and angle of a complex number (expressed in polar form) to range over an interval, it describes a semicircular region, similar to a fan; these regions are what we call complex fans. Complex numbers are a special case of complex fans, where the magnitude and angle are point intervals. Operations (especially addition) with complex numbers in polar form are complicated. What most applications do is to convert them to rectangular form, perform operations, and return the result to polar form. However, if the complex number is a Complex Fan, that transformation increases ambiguity in the result. That is, the resulting Fan is not the smallest Fan that contains all possible results. The need for minimal results took us to develop algorithms to perform the basic arithmetic operations with complex fans, ensuring the result will always be the smallest possible complex fan. We have developed the arithmetic operations of addition, negation, subtraction, product, and division of complex fans. The algorithms presented in this article are written in pseudocode, and the programs in Common Lisp, making use of CLOS (Common Lisp Object System). Translation to any other high-level programming language should be straightforward.", accepted = "March 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "abstract data type; complex fans; complex numbers; interval computation; qualitative reasoning", subject = "Mathematics of Computing - Mathematical Software ({\bf G.4}): Algorithm design and analysis; Computing Methodologies -Artificial Intelligence - Knowledge Representation Formalisms and Methods ({\bf I.2}); Computer Applications - Physical Sciences and Engineering ({\bf J.2}): Engineering", } @Article{Heinkenschloss:1999:IBO, author = "Matthias Heinkenschloss and Luis N. Vicente", title = "An Interface Between Optimization and Application for the Numerical Solution of Optimal Control Problems", journal = j-TOMS, volume = "25", number = "2", pages = "157--190", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317278", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p157-heinkenschloss/", abstract = "An interface between the application problem and the nonlinear optimization algorithm is proposed for the numerical solution of distributed optimal control problems. By using this interface, numerical optimization algorithms can be designed to take advantage of inherent problem features like the splitting of the variables into states and controls and the scaling inherited from the functional scalar products. Further, the interface allows the optimization algorithm to make efficient use of user-provided function evaluations and derivative calculations.", accepted = "February 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "optimal control; optimization; simulation", subject = "Mathematics of Computing --- Mathematical Software (G.4); Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): Constrained optimization; General Terms: Algorithms, Design", } @Article{Gockenbach:1999:CCL, author = "Mark S. Gockenbach and Matthew J. Petro and William W. Symes", title = "{C++} Classes for Linking Optimization with Complex Simulations", journal = j-TOMS, volume = "25", number = "2", pages = "191--212", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317280", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p191-gockenbach/", abstract = "The object-oriented programming paradigm can be used to overcome the incompatibilities between off-the-shelf optimization software and application software. The Hilbert Class Library (HCL) defines the fundamental mathematical objects arising in optimization problems, such as vectors, linear operators, and so forth, as C++ classes, making it possible to write optimization code in a natural fashion, while allowing application software such as simulators to use the most convenient data structures and programming style. In spite of the poor reputation C++ has for runtime performance, the use of mixed-language programming allows performance equal to that achieved by standard Fortran packages, as comparisons with the popular code LBFGS and ARPACK demonstrate.", accepted = "April 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "object-oriented design; optimization; simulation", subject = "Software --- Programming Techniques --- Object-oriented Programming (D.1.5); General Terms: Algorithms, Languages, Performance", } @Article{Gautschi:1999:AGG, author = "Walter Gautschi", title = "{Algorithm 793}: {GQRAT} --- {Gauss} Quadrature for Rational Functions", journal = j-TOMS, volume = "25", number = "2", pages = "213--239", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317282", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/793.gz; http://phase.etl.go.jp/netlib/toms/793; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p213-gautschi/; http://www.hensa.ac.uk/netlib/toms/793.gz; http://www.netlib.no/netlib/toms/793; http://www.netlib.org/toms/793", abstract = "The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented as well as methods for constructing such rational Gauss formulae. Relevant computer routines are provided and applied to a number examples, including Fermi--Dirac and Bose--Einstein integrals of interest in solid state physics.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "construction of quadrature rules; Gaussian quadrature exact for rational functions; generalized Fermi--Dirac and Bose Einstein integrals", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- Quadrature and Numerical Differentiation (G.1.4); General Terms: Algorithms", } @Article{Wieder:1999:ANH, author = "Thomas Wieder", title = "{Algorithm 794}: Numerical {Hankel} transform by the {Fortran} program {HANKEL}", journal = j-TOMS, volume = "25", number = "2", pages = "240--250", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317284; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/; http://www.netlib.org/toms/794; ftp://netlib.bell-labs.com/netlib/toms/794.gz; http://www.netlib.no/netlib/toms/794; http://www.hensa.ac.uk/netlib/toms/794.gz; http://phase.etl.go.jp/netlib/toms/794", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.", accepted = "February 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Hankel transform; numerical analysis", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computation of transforms", } @Article{Verschelde:1999:APG, author = "Jan Verschelde", title = "{Algorithm 795}: {PHCPACK}: a general-purpose solver for polynomial systems by homotopy continuation", journal = j-TOMS, volume = "25", number = "2", pages = "251--276", month = jun, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/317275.317286; http://phase.etl.go.jp/netlib/toms/795; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p251-verschelde/; http://www.hensa.ac.uk/netlib/toms/795.gz; http://www.netlib.no/netlib/toms/795; http://www.netlib.org/toms/795", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "ftp://netlib.bell-labs.com/netlib/toms/795.gz", abstract = "Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this article the structure and design of the software package PHC is described. The main program operates in several modes, is menu driven, and is file oriented. This package features great variety of root-counting methods among its tools. The outline of one black-box solver is sketched, and a report is given on its performance on a large database of test problems. The software has been developed on four different machine architectures. Its portability is ensured by the gnu-ada compiler.", accepted = "15 feb 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bernshtein's theorem; B{\'e}zout number; B{\'e}zout's theorem; enumerative geometry; homotopy continuation; mixed volume; polyhedral homotopy; polynomial systems; root count; Schubert calculus; start system", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): Ada; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): Systems of equations; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): Polynomials, methods for; Mathematics of Computing --- Discrete Mathematics --- Combinatorics (G.2.1): Counting problems; Mathematics of Computing --- Mathematical Software (G)", } @Article{DAmore:1999:IFS, author = "Luisa D'Amore and Giuliano Laccetti and Almerico Murli", title = "An Implementation of a {Fourier} Series Method for the Numerical Inversion of the {Laplace} Transform", journal = j-TOMS, volume = "25", number = "3", pages = "279--305", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326148; http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p279-d_amore/p279-d_amore.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/#abstract; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/#indterms", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demonstrate how this expression can be used in the development of an {\em automatic routine}, one in which the user needs to specify only the required accuracy", accepted = "10 feb 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic stopping criterion; Fourier series methods; Laplace transform inversion", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- General (G.1.0): Numerical algorithms; Mathematics of Computing --- Numerical Analysis --- Integral Equations (G.1.9); Mathematics of Computing --- Numerical Analysis --- Approximation (G.1.2): Nonlinear approximation; General Terms: Algorithms", } @Article{DAmore:1999:AFS, author = "Luisa D'Amore and Guiliano Laccetti and Almerico Murli", title = "{Algorithm 796}: a {Fortran} Software Package for the Numerical Inversion of the {Laplace} Transform Based on a {Fourier} Series Method", journal = j-TOMS, volume = "25", number = "3", pages = "306--315", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326149; http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p306-d_amore/p306-d_amore.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/#abstract; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/#indterms", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A software package for the numerical inversion of a Laplace Transform function is described. Besides function values of $F(z)$ for complex and real $z$, the user has only to provide the numerical value of the Laplace convergence abscissa or, failing this, an upper bound to this quantity, and the accuracy he or she requires in the computed value of the inverse Transform. The method implemented is based on a Fourier series expansion of the inverse transform, and it is especially suitable when such inverse Laplace Transform is sectionally continuous.", accepted = "10 feb 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic stopping criterion; Fourier series methods; Laplace transform inversion", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- Integral Equations (G.1.9); Mathematics of Computing --- Numerical Analysis --- Approximation (G.1.2): Nonlinear approximation; General Terms: Algorithms", } @Article{Dayde:1999:RBB, author = "Michel J. Dayd{\'e} and Iain S. Duff", title = "The {RISC BLAS}: a Blocked Implementation of {Level 3 BLAS} for {RISC} Processors", journal = j-TOMS, volume = "25", number = "3", pages = "316--340", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326150; http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p316-dayde/p316-dayde.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/#abstract; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/#indterms", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a version of the Level 3 BLAS which is designed to be efficient on RISC processors. This is an extension of previous studies by the authors and colleagues on a similar approach for efficient serial and parallel implementations on virtual-memory and shared-memory multiprocessors. All our codes are written in Fortran and use loop-unrolling, blocking, and copying to improve the performance. A blocking technique is used to express the BLAS in terms of operations involving triangular blocks and calls to the matrix-matrix multiplication kernel (GEMM). No manufacturer-supplied or assembler code is used. This blocked implementation uses the same blocking ideas as in our implementation for vector machines except that the ordering of loops is designed for efficient reuse of date held in cache and not necessarily for parallelization. All the codes are specifically tuned for RISC processors. The software also includes a tuned version of GEMM. A parameter which controls the blocking allows efficient exploitation of the memory hierarchy on the various target computers. We present results on a range of RISC-based workstations and multiprocessors: CRAY T3D, DEC 8400 5/300, HP 715/64, IBM SP2, MEIKO CS2-HA, SGI Power Challenge 10000, and SUN UltraSPARC-1 model 140. This implementation of the Level 3 BLAS is available on anonymous FTP, and we welcome input from users to improve and extend our BLAS implementation.", accepted = "April 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "blocking; level 3 BLAS; loop-unrolling; matrix-matrix kernels; RISC processors", subject = "Mathematics of Computing --- Mathematical Software (G.4); Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computations on matrices; Mathematics of Computing --- Numerical Analysis --- General (G.1.0): Numerical algorithms; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): Linear systems (direct and iterative methods); General Terms: Algorithms, Measurement, Performance", } @Article{Ribeiro:1999:AFS, author = "Celso C. Ribeiro and Mauricio G. C. Resende", title = "{Algorithm 797}: {Fortran} subroutines for approximate solution of graph planarization problems using {GRASP}", journal = j-TOMS, volume = "25", number = "3", pages = "341--352", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326153", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p341-ribeiro/p341-ribeiro.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/#abstract; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/#indterms", abstract = "We describe Fortran subroutines for finding approximate solutions of the maximum planar subgraph problem (graph planarization) using a Greedy Randomized Adaptive Search Procedure (GRASP). The design and implementation of the code are described in detail. Computational results with the subroutines illustrate the quality of solutions found as a function of number of GRASP iterations.", accepted = "5 may 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic graph drawing; combinatorial optimization; graph planarization; GRASP; local search", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Discrete Mathematics --- Combinatorics (G.2.1): Combinatorial algorithms; Mathematics of Computing --- Miscellaneous (G.m); General Terms: Algorithms, Performance", } @Article{Berry:1999:AHD, author = "Michael W. Berry and Karen S. Minser", title = "{Algorithm 798}: High-Dimensional Interpolation Using the Modified {Shepard} Method", journal = j-TOMS, volume = "25", number = "3", pages = "353--366", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326154; http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p353-berry/p353-berry.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/#abstract; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/#indterms", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new implementation of the Modified Quadratic Shepard Method for the interpolation of scattered data is presented. QSHEP5D is a C++ translation of the original Fortran-77 program QSHEP3D developed by Renka (for 2-D and 3-D interpolation) which has been upgraded for 5-D interpolation. This software development was motivated by the need for interpolated 5-D hypervolumes of environmental response variables produced by forest growth and production models.", accepted = "3 jun 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "C++ implementation, modified Shepard method, multivariate interpolation, netCDF file format", subject = "Mathematics of Computing --- Mathematical Software (G.4): Algorithm design and analysis; Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1); General Terms: Algorithms, Measurement, Performance", } @Article{LEcuyer:1999:BLC, author = "Pierre L'Ecuyer and Richard Simard", title = "Beware of Linear Congruential Generators with Multipliers of the Form $a = \pm 2^q \pm 2^r$", journal = j-TOMS, volume = "25", number = "3", pages = "367--374", month = sep, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/326147.326156", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p367-l_ecuyer/; http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p367-l_ecuyer/p367-l_ecuyer.pdf", abstract = "Linear congruential random-number generators with Mersenne prime modulus and multipliers of the form $a = \pm 2^q \pm 2^r$ have been proposed recently. Their main advantage is the availability of a simple and fast implementation algorithm for such multipliers. This note generalizes this algorithm, points out statistical weaknesses of these multipliers when used in a straightforward manner, and suggests in what context they could be used safely.", accepted = "24 Aug 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "correlation test; linear congruential generators; random number generation", subject = "Mathematics of Computing --- Mathematical Software (G.4): {\bf Algorithm design and analysis}; Computing Methodologies --- Simulation and Modeling (I.6); Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}; General Terms: Algorithms, Experimentation, Measurement, Performance", } @Article{Kees:1999:CIN, author = "Christopher E. Kees and Cass T. Miller", title = "{C++} implementations of numerical methods for solving differential-algebraic equations: design and optimization considerations", journal = j-TOMS, volume = "25", number = "4", pages = "377--403", month = dec, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/332242.334001", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/articles/journals/toms/1999-25-4/p377-kees/p377-kees.pdf; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p377-kees/", abstract = "Object-oriented programming can produce improved implementations of complex numerical methods, but it can also introduce a performance penalty. Since computational simulation often requires intricate and highly efficient codes, the performance penalty of high-level techniques must always be weighed against the improvements they enable. These issues are addressed in a general object-oriented (OO) toolkit for the numerical solution of differential-algebraic equations (DAEs). The toolkit can be configured in several different ways to solve DAE initial-value problems with an adaptive multistep method. It contains a wrapped version of the Fortran 77 code DASPK and a translation of this to C++. Two C++ constructs for assembling the tools are provided, as are two implementations an important DAE test problem. Multiple configurations of the toolkit for DAE test problems are compared in order to assess the performance penalties of C++. The mathematical methods and implementation techniques are discussed in detail in order to provide heuristics for efficient OO scientific programming and to demonstrate the effectiveness of OO techniques in managing complexity and producing better code. The codes were tested on a variety of problems using publicly available Fortran 77 and C++ compilers. Extensive efficiency comparisons are presented in order to isolate computationally inefficient OO techniques. Techniques that caused difficulty in implementation and maintenance are also highlighted. The comparisons demonstrate that the majority of C++'s built-in support for OO programming has a negligible effect on performance, when used at sufficiently high levels, and provides flexible and extensible software for numerical methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms, design, experimentation, languages, performance, differential-algebraic equations", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf C++}; Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Mathematics of Computing --- Numerical Analysis --- Ordinary Differential Equations (G.1.7): {\bf Differential-algebraic equations}; Software --- Programming Techniques --- Object-oriented Programming (D.1.5); Software --- Software Engineering --- Coding Tools and Techniques (D.2.3): {\bf Object-oriented programming}", } @Article{Duff:1999:FCS, author = "Iain S. Duff and Jennifer A. Scott", title = "A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications", journal = j-TOMS, volume = "25", number = "4", pages = "404--424", month = dec, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/332242.332243; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p404-duff/; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p404-duff/p404-duff.pdf", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe the design, implementation, and performance of a frontal code for the solution of large sparse symmetric systems of linear finite-element equations. The code is intended primarily for positive-definite systems, since numerical pivoting is not performed. The resulting software package, MA62, will be included in the Harwell Subroutine Library. We illustrate the performance of our new code on a range of problems arising from real engineering and industrial applications. The performance of the code is compared with that of the Harwell Subroutine Library general frontal solver MA42 and with other positive-definite codes from the Harwell Subroutine Library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; finite-element equations; Gaussian elimination; Level 3 BLAS; performance; sparse symmetric linear equations; symmetric frontal method", subject = "Mathematics of Computing --- Numerical Analysis --- General (G.1.0): {\bf Numerical algorithms}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3); Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Sparse, structured, and very large systems (direct and iterative methods)}", } @Article{Dackland:1999:BAS, author = "Krister Dackland and Bo K{\aa}gstr{\"{o}}m", title = "Blocked algorithms and software for reduction of a regular matrix pair to generalized {Schur} form", journal = j-TOMS, volume = "25", number = "4", pages = "425--454", month = dec, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/332242.332244; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p425-dackland/; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p425-dackland/p425-dackland.pdf", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A two-stage blocked algorithm for reduction of a regular matrix pair $(A,B)$ to upper Hessenberg-triangular form is presented. In stage 1 $(A,B)$ is reduced to block upper Hessenberg-triangular form using mainly level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. In the second stage all but one of the $r$ subdiagonals of the block Hessenberg $A$-part are set to zero using Givens rotations. The algorithm proceeds in a sequence of supersweeps, each reducing $m$ columns. The updates with respect to row and column rotations are organized to reference consecutive columns of $A$ and $B$. To further improve the data locality, all rotations produced in a supersweep are stored to enable a left-looking reference pattern, i.e., all updates are delayed until they are required for the continuation of the supersweep. Moreover, we present a blocked variant of the single-diagonal double-shift QZ method for computing the generalized Schur form of $(A,B)$ in upper Hessenberg-triangular form. The blocking for improved data locality is done similarly, now by restructuring the reference pattern of the updates associated with the bulge chasing in the QZ iteration. Timing results show that our new blocked variants outperform the current LAPACK routines, including drivers for the generalized eigenvalue problem, by a factor 2--5 for sufficiently large problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; blocked algorithms; generalized Schur form; Hessenberg-triangular reduction; LAPACK; memory hierarchy; parallelization; performance; QZ-algorithm", subject = "Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1); Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3); Mathematics of Computing --- Mathematical Software (G.4): {\bf Certification and testing}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Portability**}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Reliability and robustness}", } @Article{Edwards:1999:CSC, author = "John A. Edwards", title = "Characteristic Spectra of the Curvature Functional: a Numerical Study in Bifurcation", journal = j-TOMS, volume = "25", number = "4", pages = "455--475", month = dec, year = "1999", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/332242.332245; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p455-edwards/; http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p455-edwards/p455-edwards.pdf", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A method is described for the eigenvalues of piecewise smooth $C^2$ extremum-energy curves. Typical interpolants are investigated within the framework of their eigensystems, and conclusions are presented concerning their natural modes of vibration, stability state, and limits of existence. In the present discussion the word ``spline'' means exclusively an interpolating elastica.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "acoustics; algorithms; buckling; catastrophes; degenerate critical points; deterministic chaos; dynamical systems; eigenanalysis; elastica; elasticity; energy extrema; generalized coordinates; modal analysis; Morse theory; structural stability; theory; variational methods; vibrations", subject = "Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1): {\bf Spline and piecewise polynomial interpolation}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Determinants**}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Eigenvalues and eigenvectors (direct and iterative methods)}; Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): {\bf Constrained optimization}; Mathematics of Computing --- Numerical Analysis --- Ordinary Differential Equations (G.1.7): {\bf Boundary value problems}; Computing Methodologies --- Symbolic and Algebraic Manipulation --- Algorithms (I.1.2): {\bf Algebraic algorithms}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Engineering}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Physics}; Computer Applications --- Computer-Aided Engineering (J.6): {\bf Computer-aided design (CAD)}; Computer Applications --- Computer-Aided Engineering (J.6): {\bf Computer-aided manufacturing (CAM)}", } @Article{Ferris:2000:NCS, author = "Michael C. Ferris and Michael P. Mesnier and Jorge J. Mor{\'e}", title = "{NEOS} and {Condor}: solving optimization problems over the {Internet}", journal = j-TOMS, volume = "26", number = "1", pages = "1--18", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347842; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p1-ferris/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p1-ferris/p1-ferris.pdf", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; complementarity problems; computational servers; network computing; resource management", subject = "Mathematics of Computing --- Mathematical Software (G.4); Computer Systems Organization --- Computer-Communication Networks --- General (C.2.0); Software --- Software Engineering --- General (D.2.0)", } @Article{Griewank:2000:ARI, author = "Andreas Griewank and Andrea Walther", title = "{Algorithm 799}: {Revolve}: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation", journal = j-TOMS, volume = "26", number = "1", pages = "19--45", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347846", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p19-griewank/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p19-griewank/p19-griewank.pdf", abstract = "In its basic form, the reverse mode of computational differentiation yields the gradient of a scalar-valued function at a cost that is a small multiple of the computational work needed to evaluate the function itself. However, the corresponding memory requirement is proportional to the run-time of the evaluation program. Therefore, the practical applicability of the reverse mode in its original formulation is limited despite the availability of ever larger memory systems. This observation leads to the development of checkpointing schedules to reduce the storage requirements. This article presents the function {\tt revolve}, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion. This routine is intended to be used as an explicit ``controller'' for running a time-dependent applications program.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DeTisi:2000:RAS, author = "Flavia {De Tisi} and Alba Valtulina", title = "Remark on {Algorithm 761}: scattered-data surface fitting that has the accuracy of a cubic polynomial", journal = j-TOMS, volume = "26", number = "1", pages = "46--48", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.349795", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Akima:1996:ASS,Renka:1998:RA}.", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p46-de_tisi/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p46-de_tisi/p46-de_tisi.pdf", abstract = "Several improvements to the estimation of partial derivatives in Algorithm 761 are presented. The problems corrected are (1) in the calculation of the probability weight in subroutine {\tt SDPD3P} which may result in overflow, (2) in the calculation of final weight in subroutine {\tt SDPD3P} which may result in overflow, (3) in the computation of a determinant in subroutine {\tt SDLEQN} which is not necessary, and (4) in the computation of the condition number of a matrix in subroutine {\tt SDLEQN} which generates very different results for matrices that differ only in row order.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bivariate interpolation; interpolation; local interpolation", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1): {\bf Interpolation formulas}; Mathematics of Computing --- Mathematical Software (G.4)", } @Article{Benner:2000:AFS, author = "Peter Benner and Ralph Byers and Eric Barth", title = "{Algorithm 800}: {Fortran 77} subroutines for computing the eigenvalues of {Hamiltonian} matrices {I}: the square-reduced method", journal = j-TOMS, volume = "26", number = "1", pages = "49--77", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347852", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p49-benner/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p49-benner/p49-benner.pdf", abstract = "This article describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamiltonian matrix to a square-reduced form transforms a Hamiltonian eigenvalue problem of order $ 2 n $ to a Hessenberg eigenvalue problem of order $n$. The eigenvalues of the Hamiltonian matrix are the square roots of those of the Hessenberg matrix. Symplectic scaling and norm scaling are provided, which, in some cases, improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "(square-reduced) algebraic Riccati equation; eigenvalues; Hamiltonian matrix; skew-Hamiltonian matrix", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): {\bf Computations on matrices}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Eigenvalues and eigenvectors (direct and iterative methods)}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Algorithm design and analysis}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Certification and testing}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Documentation}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Reliability and robustness}", } @Article{Leydold:2000:ASR, author = "Josef Leydold", title = "Automatic Sampling with the Ratio-of-Uniforms Method", journal = j-TOMS, volume = "26", number = "1", pages = "78--98", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347863", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p78-leydold/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p78-leydold/p78-leydold.pdf", abstract = "Applying the ratio-of-uniforms method for generating random variates results in very efficient, fast, and easy-to-implement algorithms. However parameters for every particular type of density must be precalculated analytically. In this article we show, that the ratio-of-uniforms method is also useful for the design of a black-box algorithm suitable for a large class of distributions, including all with log-concave densities. Using polygonal envelopes and squeezes results in an algorithm that is extremely fast. In opposition to any other ratio-of-uniforms algorithm the expected number of uniform random numbers is less than two. Furthermore, we show that this method is in some sense equivalent to transformed density rejection.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "adaptive method; log-concave; nonuniform; random-number generation; ratio of uniforms; rejection method; T-concave; universal method", subject = "Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}", } @Article{Hu:2000:HHP, author = "Y. Charlie Hu and Guohua Jin and S. Lennart Johnsson and Dimitris Kehagias and Nadia Shalaby", title = "{HPFBench}: a {High Performance Fortran} benchmark suite", journal = j-TOMS, volume = "26", number = "1", pages = "99--149", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347872", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p99-hu/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p99-hu/p99-hu.pdf", abstract = "The High Performance Fortran (HPF) benchmark suite HPFBench is designed for evaluating the HPF language and compilers on scalable architectures. The functionality of the benchmarks covers scientific software library functions and application kernels that reflect the computational structure and communication patterns in fluid dynamic simulations, fundamental physics, and molecular studies in chemistry and biology. The benchmarks are characterized in terms of FLOP count, memory usage, communication pattern, local memory accesses, array allocation mechanism, as well as operation and communication counts per iteration. The benchmarks output performance evaluation metrics in the form of elapsed times, FLOP rates, and communication time breakdowns. We also provide a benchmark guide to aid the choice of subsets of the benchmarks for evaluating particular aspects of an HPF compiler. Furthermore, we report an evaluation of an industry-leading HPF compiler from the Portland Group Inc. using the HPFBench benchmarks on the distributed-memory IBM SP2", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "benchmarks; compilers; high performance Fortran", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf Concurrent, distributed, and parallel languages}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Linear systems (direct and iterative methods)}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Parallel and vector implementations}; Computing Methodologies --- Simulation and Modeling --- Applications (I.6.3); Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Astronomy}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Chemistry}; Computer Applications --- Life and Medical Sciences (J.3): {\bf Biology and genetics}", } @Article{Coleman:2000:AAD, author = "Thomas F. Coleman and Arun Verma", title = "{ADMIT-1}: Automatic Differentiation and {MATLAB} Interface Toolbox", journal = j-TOMS, volume = "26", number = "1", pages = "150--175", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347879; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p150-coleman/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p150-coleman/p150-coleman.pdf", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "ADMIT-1 enables the computation of {\em sparse} Jacobian and Hessian matrices, using automatic differentiation technology, from a MATLAB environment. Given a function to be differentiated, ADMIT-1 will exploit sparsity if present to yield sparse derivative matrices (in sparse MATLAB form). A generic automatic differentiation tool, subject to some functionality requirements, can be plugged into ADMIT-1; examples include ADOL-C (C/C++ target functions) and ADMAT (MATLAB target functions). ADMIT-1 also allows for the calculation of gradients and has several other related functions. This article provides an introduction to the design and usage of ADMIT-1.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; computational differentiation; efficient computation of gradient; graph coloring; Jacobians and Hessians; user interface", subject = "Mathematics of Computing --- Numerical Analysis --- General (G.1.0): {\bf Numerical algorithms}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Systems of equations}; Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): {\bf Unconstrained optimization}; Mathematics of Computing --- Mathematical Software (G.4): {\bf MATLAB}", } @Article{Wise:2000:APP, author = "Steven M. Wise and Andrew J. Sommese and Layne T. Watson", title = "{Algorithm 801}: {POLSYS\_PLP}: a partitioned linear product homotopy code for solving polynomial systems of equations", journal = j-TOMS, volume = "26", number = "1", pages = "176--200", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347885", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p176-wise/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p176-wise/p176-wise.pdf", abstract = "Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS\_PLP consists of Fortran 90 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP) polynomial system structure. PLP structure is a generalization of $m$-homogeneous structure, whereby each component of the system can have a different $m$-homogeneous structure. The code requires a PLP structure as input, and although finding the optimal PLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good structure. POLSYS\_PLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different PLP structures and their corresponding B{\'e}zout numbers can be systematically explored before committing to root finding.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "$m$-homogeneous; Chow-Yorke algorithm; curve tracking; fixed point; globally convergent; homotopy methods; partitioned linear product; probability-one; zero", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf Fortran 90}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Continuation (homotopy) methods}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Polynomials, methods for}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Systems of equations}; Mathematics of Computing --- Mathematical Software (G.4)", } @Article{Hormann:2000:AAG, author = "Wolfgang H{\"o}rmann", title = "{Algorithm 802}: an automatic generator for bivariate log-concave distributions", journal = j-TOMS, volume = "26", number = "1", pages = "201--219", month = mar, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/347837.347908", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p201-hormann/; http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p201-hormann/p201-hormann.pdf", abstract = "Different automatic (also called universal or black-box) methods have been suggested to sample from univariate log-concave distributions. Our new automatic algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes, which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that points that are rejected by the rejection algorithm can be used as additional points of contact. The article describes the details how this main idea can be used to construct Algorithm ALC2D that can generate random pairs from all bivariate log-concave distributions with known domain, computable density, and computable partial derivatives.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic generator; bivariate log-concave distributions; rejection method; universal generator", subject = "Software --- Programming Languages --- Language Classifications (D.3.2); Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}", } @Article{Boisvert:2000:ESI, author = "Ronald F. Boisvert and Wayne R. Dyksen and Elias N. Houstis", title = "Editorial: special issue in honor of {John Rice}'s 65th birthday", journal = j-TOMS, volume = "26", number = "2", pages = "223--223", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.354094", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anonymous:2000:JRR, author = "Anonymous", title = "{John R. Rice}: biographical and professional notes", journal = j-TOMS, volume = "26", number = "2", pages = "225--226", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.354105", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Houstis:2000:PIK, author = "Elias N. Houstis and Ann C. Catlin and John R. Rice and Vassilios S. Verykios and Naren Ramakrishnan and Catherine E. Houstis", title = "{PYTHIA-II}: a knowledge\slash database system for managing performance data and recommending scientific software", journal = j-TOMS, volume = "26", number = "2", pages = "227--253", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.353475", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Often scientists need to locate appropriate software for their problems and then select from among many alternatives. We have previously proposed an approach for dealing with this task by processing performance data of the targeted software. This approach has been tested using a customized implementation referred to as PYTHIA. This experience made us realize the complexity of the algorithmic discovery of knowledge from performance data and of the management of these data together with the discovered knowledge. To address this issue, we created PYTHIA-II--a modular framework and system which combines a general knowledge discovery in databases (KDD) methodology and recommender system technologies to provide advice about scientific software/hardware artifacts. The functionality and effectiveness of the system is demonstrated for two existing performance studies using sets of software for solving partial differential equations. From the end-user perspective, PYTHIA-II allows users to specify the problem to be solved and their computational objectives. In turn, PYTHIA-II (i) selects the software available for the user's problem (ii) suggests parameter values, and (iii) assesses the recommendation provided. PYTHIA-II provides all the necessary facilities to set up database schemas for testing suites and associated performance data in order to test sets of software. Moreover, it allows easy interfacing of alternative data mining and recommendation facilities. PYTHIA-II is an open-ended system implemented on public domain software and has been used for performance evaluation in several different problem domains.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ramakrishnan:2000:MVR, author = "Naren Ramakrishnan and Calvin J. Ribbens", title = "Mining and visualizing recommendation spaces for elliptic {PDEs} with continuous attributes", journal = j-TOMS, volume = "26", number = "2", pages = "254--273", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.353481", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this paper we extend previous work in mining recommendation spaces based on symbolic problem features to PDE problems with continuous-valued attributes. We identify the research issues in mining such spaces, present a dynamic programming algorithm form the data-mining literature, and describe how a priori domain metaknowledge can be used to control the complexity of induction. A visualization aid for continuous-valued recommendation spaces is also outlined. Two case studies are presented to illustrate our approach and tools: (i) a comparison of an iterative and a direct linear system solver on nearly singular problems, and (ii) a comparison of two iterative solvers on problems posed on nonrectangular domains. Both case studies involve continuously varying problem and method parameters which strongly influence the choice of best algorithm in particular cases. By mining the results from thousands of PDE solves, we can gain valuable insight into the relative performance of these methods on similar problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Enright:2000:AAS, author = "W. H. Enright", title = "Accurate Approximate Solution of Partial Differential Equations at Off-mesh Points", journal = j-TOMS, volume = "26", number = "2", pages = "274--292", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.353482", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Numerical methods for partial differential equations often determine approximations that are more accurate at the set of discrete meshpoints than they are at the ``off-mesh'' points in the domain of interest. These methods are generally most effective if they are allowed to adjust the location of the mesh points to match the local behavior of the solution. Different methods will typically generate their respective approximations on incompatible, unstructured meshes, and it can be difficult to evaluate the quality of a particular solution, or to visualize important properties of a solution. In this paper we will introduce a generic approach which can be used to generate approximate solution values at arbitrary points in the domain of interest for any method that determines approximations to the solution and low-order derivatives at meshpoints. This approach is based on associating a set of ``collocation'' points with each mesh element and requiring that the local approximation interpolate the meshpoint data and almost satisfy the partial differential equation at the collocation points. The accuracy associated with this interpolation/collocation approach is consistent with the ``meshpoint accuracy'' of the underlying method. The approach that we develop applies to a large class of methods and problems. It uses local information only and is therefore particularly suitable for implementation in a parallel or network computing environment. Numerical examples are given for some second-order problems in two and three dimensions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Grosz:2000:HVA, author = "Lutz Grosz", title = "How to Vectorize the Algebraic Multi-level Iteration", journal = j-TOMS, volume = "26", number = "2", pages = "293--309", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.353483", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider the algebraic multilevel iteration (AMLI) for the solution of systems of linear equations as they arise form a finite-difference discretization on a rectangular grid. Key operation is the matrix-vector product, which can efficiently be executed on vector and parallel-vector computer architectures if the nonzero entries of the matrix are concentrated in a few diagonals. In order to maintain this structure for all matrices on all levels coarsening in alternating directions is used. In some cases it is necessary to introduce additional dummy grid hyperplanes. The data movements in the restriction and prolongation are crucial, as they produce massive memory conflicts on vector architectures. By using a simple performance model the best of the possible vectorization strategies is automatically selected at runtime. Examples show that on a Fujitsu VPP300 the presented implementation of AMLI reaches about 85\% of the useful performance, and scalability with respect to computing time can be achieved.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ward:2000:ASM, author = "William A. {Ward, Jr.}", title = "{Algorithm 803}: a Simpler Macro Processor", journal = j-TOMS, volume = "26", number = "2", pages = "310--319", month = jun, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/353474.353484", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Macro processors have been in the computing tool chest since the late 1950's. Their use, though perhaps not what it was in the heyday of assembly language programming, is still widespread. In the past, producing a full-featured macro processor has required significant effort, similar to that required to implement the front-end to a compiler augmented by appropriate text substitution capabilities. The tool described here adopts a different approach. The text containing macro definitions and substitutions is, in a sense, ``compiled'' to produce a program, and this program must then be executed to produce the final output.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", for = "Special issue dedicated to John Rice on his 65th birthday.", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Enright:2000:SIC, author = "Wayne H. Enright and Ramanan Sivasothinathan", title = "Superconvergent interpolants for collocation methods applied to mixed-order {BVODEs}", journal = j-TOMS, volume = "26", number = "3", pages = "323--351", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358410", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Continuous approximations to boundary value problems in ordinary differential equations (BVODEs), constructed using collocation at Gauss points, are more accurate at the mesh points than at off-mesh points. From these approximations, it is possible to construct improved continuous approximations by extending the high accuracy that is available at the mesh points to off-mesh points. One possibility is the bootstrap approach, which improves the accuracy of the approximate solution at the off-mesh points in a sequence of steps until the accuracy at the mesh points and off-mesh points is consistent. A bootstrap approach for systems of mixed-order BVODEs is developed to improve approximate solutions produced by COLNEW, a Gauss-collocation-based software package. An implementation of this approach is discussed and numerical results presented which confirm that the improved approximations satisfy the predicted error bounds and are relatively inexpensive to construct.", accepted = "24 Nov 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Liepelt:2000:RAN, author = "Michael Liepelt and Klaus Schittkowski", title = "Remark on Algorithm 746: new features of {PCOMP}: a {Fortran} Code for Automatic Differentiation", journal = j-TOMS, volume = "26", number = "3", pages = "352--362", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358412", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The software system PCOMP uses automatic differentiation to calculate derivatives of functions that are defined by the user in a modeling language similar to Fortran. This symbolical representation is converted into an intermediate code, which can be interpreted to calculate function and derivative values at run-time within machine accuracy. Furthermore, it is possible to generate Fortran code for function and gradient evaluation, which has to be compiled and linked separately. The first version of PCOMP was introduced in Dobmann et al. [1995]. In this article, we describe a series of extensions and additional features that have been implemented in the meantime.", accepted = "20 dec 1999", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Marsaglia:2000:SMG, author = "George Marsaglia and Wai Wan Tsang", title = "A Simple Method for Generating Gamma Variables", journal = j-TOMS, volume = "26", number = "3", pages = "363--372", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358414", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We offer a procedure for generating a gamma variate as the cube of a suitably scaled normal variate. It is fast and simple, assuming one has a fast way to generate normal variables. In brief: generate a normal variate $x$ and a uniform variate $U$ until $\ln(U) < 0.5x^2 + d - dv + d\ln(v)$, then return $dv$. Here, the gamma parameter is $\alpha \geq 1$, and $v = (1 + x/\sqrt{9d})^3$ with $d = \alpha - 1/3$. The efficiency is high, exceeding 0.951, 0.981, 0.992, 0.996 at $\alpha = 1,2,4,8$. The procedure can be made to run faster by means of a simple squeeze that avoids the two logarithms most of the time; return $dv$ if $U < 1 - 0.0331x^4$. We give a short C program for any $\alpha \geq 1$, and show how to boost an $\alpha < 1$ into an $\alpha > 1$. The gamma procedure is particularly fast for C implementation if the normal variate is generated in-line, via the {\tt \#define} feature. We include such an inline version, based on our ziggurat method. With it, and an inline uniform generator, gamma variates can be produced in 400MHz CPUs at better than 1.3 million per second, with the parameter $\alpha$ changing from call to call.", accepted = "14 Jan 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kearfott:2000:SCV, author = "R. B. Kearfott and G. W. Walster", title = "On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms", journal = j-TOMS, volume = "26", number = "3", pages = "373--389", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358418", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Traditionally, iterative methods for nonlinear systems use heuristic domain and range stopping criteria to determine when accuracy tolerances have been met. However, such heuristics can cause stopping at points far from actual solutions, and can be unreliable due to the effects of roundoff error or inaccuracies in data.\par In verified computations, rigorous determination of when a set of bounds has met a tolerance can be done analogously to the traditional approximate setting. Nonetheless, the range tolerance possibly cannot be met. If the criteria are used to determine when to stop subdivision of $n$-dimensional bounds into subregions, then failure of a range tolerance results in excessive, unnecessary subdivision, and could make the algorithm impractical.\par On the other hand, interval techniques can detect when inaccuracies or roundoff will not permit residual bounds to be narrowed. These techniques can be incorporated into {\it range thickness\/} stopping criteria that complement the range stopping criteria. In this note, the issue is first introduced and illustrated with a simple example. The thickness stopping criterion is then formally introduced and analyzed. Third, inclusion of the criterion within a general verified global optimization algorithm is studied. An industrial example is presented. Finally, consequences and implications are discussed.", accepted = "21 Mar 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alhargan:2000:ACA, author = "Fayez A. Alhargan", title = "Algorithms for the Computation of all {Mathieu} Functions of Integer Orders", journal = j-TOMS, volume = "26", number = "3", pages = "390--407", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358420", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$).", accepted = "19 May 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alhargan:2000:ASC, author = "Fayez A. Alhargan", title = "{Algorithm 804}: subroutines for the computation of {Mathieu} functions of integer orders", journal = j-TOMS, volume = "26", number = "3", pages = "408--414", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358422", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.", accepted = "19 May 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kolda:2000:ACU, author = "Tamara G. Kolda and Dianne P. O'Leary", title = "{Algorithm 805}: computation and uses of the semidiscrete matrix decomposition", journal = j-TOMS, volume = "26", number = "3", pages = "415--435", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358424", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We derive algorithms for computing a semidiscrete approximation to a matrix in the Frobenius and weighted norms. The approximation is formed as a weighted sum of outer products of vectors whose elements are $\pm 1$ or 0, so the storage required by the approximation is quite small. We also present a related algorithm for approximation of a tensor. Applications of the algorithms are presented to data compression, and information retrieval, and software is provided in C and in Matlab.", accepted = "18 May 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mascagni:2000:ASS, author = "Michael Mascagni and Ashok Srinivasan", title = "{Algorithm 806}: {SPRNG}: a scalable library for pseudorandom number generation", journal = j-TOMS, volume = "26", number = "3", pages = "436--461", month = sep, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/358407.358427", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See correction \cite{Mascagni:2000:CAS}.", abstract = "In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by briefly presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We briefly describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality in parallel applications. SPRNG was designed around the uniform implementation of different families of parameterized random number generators. We then present a short description of SPRNG. The description contained within this document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with installing and using SPRNG on scalable systems is available at the URL \path=http://www.ncsa.uiuc.edu/Apps/SPRNG=. In our description of SPRNG we discuss the random number library as well as the suite of tests of randomness that is an integral part of SPRNG. Random number tools for parallel Monte Carlo applications must be subjected to classical as well as new types of empirical tests of randomness to eliminate generators that show defects when used in scalable environments.", accepted = "26 may 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weideman:2000:MDM, author = "J. A. C. Weideman and S. C. Reddy", title = "A {MATLAB} Differentiation Matrix Suite", journal = j-TOMS, volume = "26", number = "4", pages = "465--519", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365727", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.", accepted = "15 March 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kaufman:2000:OBS, author = "Linda Kaufman", title = "An Observation on Bisection Software for the Symmetric Tridiagonal Eigenvalue Problem", journal = j-TOMS, volume = "26", number = "4", pages = "520--526", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365728", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this paper we discuss a small modification of the bisection routines in EISPACK and LAPACK for finding a few of the eigenvalues of a symmetric tridiagonal matrix A. When the principal minors of the matrix A yield good approximations to the desired eigenvalues, these modifications can yield about 30 percent reduction in the computation times.", accepted = "27 June 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Filippone:2000:PLP, author = "Salvatore Filippone and Michele Colajanni", title = "{PSBLAS}: a Library for Parallel Linear Algebra Computation on Sparse Matrices", journal = j-TOMS, volume = "26", number = "4", pages = "527--550", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365732", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Many computationally intensive problems in engineering and science give rise to the solution of large, sparse, linear systems of equations. Fast and efficient methods for their solution are very important because these systems usually occur in the innermost loop of the computational scheme. Parallelization is often necessary to achieve an acceptable level of performance. This paper presents the design, implementation, and interface of a library of Basic Linear Algebra Subroutines for sparse matrices (PSBLAS) which is specifically tailored to distributed memory computers. PSBLAS enables easy, efficient and portable implementations of parallel iterative solvers for linear systems. The interface keeps in view a Single Program Multiple Data programming model on distributed memory machines. However, the architecture of the library does not exclude an implementation in different paradigms, such as those based on the shared memory model.", accepted = "5 July 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kaufman:2000:BRA, author = "Linda Kaufman", title = "Band Reduction Algorithms Revisited", journal = j-TOMS, volume = "26", number = "4", pages = "551--567", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365733", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this paper we explain some of the changes that have been incorporated in the latest version of the LAPACK subroutine for reducing a symmetric banded matrix to tridiagonal form. These modifications improve the performance for larger-bandwidth problems and reduce the number of operations when accumulating the transformations onto the identity matrix, by taking advantage of the structure of the initial matrix. We show that similar modifications can be made to the LAPACK subroutines for reducing a symmetric positive definite generalized eigenvalue problem to a standard symmetric banded eigenvalue problem and for reducing a general banded matrix to bidiagonal form to facilitate the computation of the singular values of the matrix.", accepted = "3 Aug 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ramakrishnan:2000:NGE, author = "Naren Ramakrishnan and Ra{\'u}l E. Vald{\'e}s-P{\'e}rez", title = "Note on Generalization in Experimental Algorithmics", journal = j-TOMS, volume = "26", number = "4", pages = "568--580", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365734", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A recurring theme in mathematical software evaluation is the generalization of rankings of algorithms on test problems to build knowledge-based recommender systems for algorithm selection. A key issue is to {\em profile} algorithms in terms of the qualitative characteristics of benchmark problems. In this methodological note, we adapt a novel all-pairs algorithm for the profiling task --- Given performance rankings for $m$ algorithms on $n$ problem instances, each described with $p$ features, identify a (minimal) subset of $p$ that is useful for assessing the selective superiority of an algorithm over another, for all pairs of the $m$ algorithms. We show how techniques presented in the mathematical software literature are inadequate for such profiling purposes. In conclusion, we also address various statistical issues underlying the effective application of this technique.", accepted = "3 Aug 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bischof:2000:FSB, author = "Christian H. Bischof and Bruno Lang and Xiaobai Sun", title = "A Framework for Symmetric Band Reduction", journal = j-TOMS, volume = "26", number = "4", pages = "581--601", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365735", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We develop an algorithmic framework for reducing the bandwidth of symmetric matrices via orthogonal similarity transformations. This framework includes the reduction of full matrices to banded or tridiagonal form and the reduction of banded matrices to narrower banded or tridiagonal form, possibly in multiple steps. Our framework leads to algorithms that require fewer floating-point operations than do standard algorithms, if only the eigenvalues are required. In addition, it allows for space--time tradeoffs and enables or increases the use of blocked transformations.", accepted = "29 May 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bischof:2000:AST, author = "Christian H. Bischof and Bruno Lang and Xiaobai Sun", title = "{Algorithm 807}: {The SBR Toolbox}---software for successive band reduction", journal = j-TOMS, volume = "26", number = "4", pages = "602--616", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365736", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a software toolbox for symmetric band reduction via orthogonal transformations, together with a testing and timing program. The toolbox contains drivers and computational routines for the reduction of full symmetric matrices to banded form and the reduction of banded matrices to narrower banded or tridiagonal form, with optional accumulation of the orthogonal transformations, as well as repacking routines for storage rearrangement. The functionality and the calling sequences of the routines are described, with a detailed discussion of the ``control'' parameters that allow adaptation of the codes to particular machine and matrix characteristics. We also briefly describe the testing and timing program included in the toolbox.", accepted = "29 May 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anderson:2000:RAF, author = "Stuart Anderson", title = "Remark on {Algorithm 723}: {Fresnel} integrals", journal = j-TOMS, volume = "26", number = "4", pages = "617--617", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365737", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", accepted = "16 October 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mascagni:2000:CAS, author = "Michael Mascagni and Ashok Srinivasan", title = "Corrigendum: {Algorithm 806}: {SPRNG}: a scalable library for pseudorandom number generation", journal = j-TOMS, volume = "26", number = "4", pages = "618--619", month = dec, year = "2000", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/365723.365738", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Mascagni:2000:ASS}.", abstract = "In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods such as the leap-frog or blocking methods. We describe, in detail, parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We briefly describe the methods, detail some advantages and disadvantages of each method, and recount results from number theory that impact our understanding of their quality of parallel applications. SPRNG was designed around the uniform implementation of different families of parameterized random number generators. We then present a short description of SPRNG. The description contained within this document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with putting and using SPRNG on scalable systems is available at http://sprng.cs.fsu.edu. In this description of SPRNG we discuss the random-number generator library as well as the suite of tests of randomness that is an integral part of SPRNG. Random-number tools for parallel Monte Carlo applications must be subjected to classical as well as new types of empirical tests of randomness to eliminate generators that show defects when used in scalable environments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; Design; Documentation; Experimentation; lagged-Fibonacci generator; linear congruential generator; parallel random-number generators; Performance; random-number software; random-number tests; Reliability; Standardization", subject = "Primary Classification: D. Software D.3 PROGRAMMING LANGUAGES Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Nouns: FORTRAN; C++ G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Efficiency; Documentation; Parallel and vector implementations; Algorithm design and analysis; Reliability and robustness", } @Article{Langtangen:2001:SSP, author = "Hans Petter Langtangen and Otto Munthe", title = "Solving Systems of Partial Differential Equations using Object-Oriented Programming Techniques with Coupled Heat and Fluid Flow as Example", journal = j-TOMS, volume = "27", number = "1", pages = "1--26", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382045", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper exploits object-oriented implementation techniques to facilitate the development of computer codes for solving systems of coupled partial differential equations. We show how to build a simulator for equation systems by merging independent solvers for each equation that enters the system. The main goal is to obtain a rapid, robust, and reliable software development process with extensive reuse of implemented code. Coupled heat and fluid flow in pipes is used as example for illustrating the implementation techniques. We also present some results for the particular case of temperature-dependent generalized Newtonian fluid flow between two nonconcentric cylinders. The general applicability of the approach is discussed.", accepted = "5 July 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "C++; coupled heat-fluid; diffpack; finite elements; Languages, Measurement, Performance, Theory; non-Newtonian fluids; object-oriented programming; software development; systems of partial differential equations", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.8 Partial Differential Equations Subjects: Finite element methods Additional Classification: D. Software D.1 PROGRAMMING TECHNIQUES D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Nouns: C++ I. Computing Methodologies I.6 SIMULATION AND MODELING K. Computing Milieux K.6 MANAGEMENT OF COMPUTING AND INFORMATION SYSTEMS K.6.3 Software Management Subjects: Software development", } @Article{Neumaier:2001:EPE, author = "Arnold Neumaier and Tapio Schneider", title = "Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models", journal = j-TOMS, volume = "27", number = "1", pages = "27--57", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382304", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Dynamical characteristics of a complex system can often be inferred from analyses of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregressive (AR) models of first order. This paper describes the estimation of eigenmodes of AR models of arbitrary order. AR processes of any order can be decomposed into eigenmodes with characteristic oscillation periods, damping times, and excitations. Estimated eigenmodes and confidence intervals for the eigenmodes and their oscillation periods and damping times can be computed from estimated model parameters. As a computationally efficient method of estimating the parameters of AR models from high-dimensional data, a stepwise least squares algorithm is proposed. This algorithm computes model coefficients and evaluates criteria for the selection of the model order stepwise for AR models of successively decreasing order. Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients are estimated reliably and that the approximate 95\% confidence intervals for the coefficients and eigenmodes are rough approximations of the confidence intervals inferred from the simulations.", accepted = "10 October 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Schneider:2001:AAM, author = "Tapio Schneider and Arnold Neumaier", title = "{Algorithm 808}: {ARfit}---a {Matlab} package for the estimation of parameters and eigenmodes of multivariate autoregressive models", journal = j-TOMS, volume = "27", number = "1", pages = "58--65", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382316", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\sc ARfit} is a collection of Matlab modules for modeling and analyzing multivariate time series with autoregressive (AR) models. {\sc ARfit} contains modules for fitting AR models to given time series data, for analyzing eigenmodes of a fitted model, and for simulating AR processes. {\sc ARfit} estimates the parameters of AR models from given time series data with a stepwise least squares algorithm that is computationally efficient, in particular when the data are high-dimensional. {\sc ARfit} modules construct approximate confidence intervals for the estimated parameters and compute statistics with which the adequacy of a fitted model can be assessed. Dynamical characteristics of the modeled time series can be examined by means of a decomposition of a fitted AR model into eigenmodes and associated oscillation periods, damping times, and excitations. The {\sc ARfit} module that performs the eigendecomposition of a fitted model also constructs approximate confidence intervals for the eigenmodes and their oscillation periods and damping times.", accepted = "10 October 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Leydold:2001:SUG, author = "Josef Leydold", title = "A simple universal generator for continuous and discrete univariate {$T$}-concave distributions", journal = j-TOMS, volume = "27", number = "1", pages = "66--82", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382322", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions. The algorithms can be implemented in a few lines of high-level language code. In opposition to other black-box algorithms hardly any setup step is required, and thus it is superior in the changing-parameter case.", accepted = "27 November 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morales:2001:APF, author = "Jos{\'e} Luis Morales and Jorge Nocedal", title = "{Algorithm 809}: {PREQN}: {Fortran 77} subroutines for preconditioning the conjugate gradient method", journal = j-TOMS, volume = "27", number = "1", pages = "83--91", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382343", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems $A_i x=b_i, \,\, i=1,\dots,t$, where the coefficient matrices $A_i$ are symmetric and positive definite and vary slowly. The preconditioners are based on limited memory quasi-Newton updating and are recommended for problems in which: (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form $A_i v$ can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.", accepted = "26 October 2000", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Verdonk:2001:PRIa, author = "Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren", title = "A precision- and range-independent tool for testing floating-point arithmetic {I}: basic operations, square root, and remainder", journal = j-TOMS, volume = "27", number = "1", pages = "92--118", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382404", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.win.ua.ac.be/~cant/ieeecc754.html", abstract = "This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.", accepted = "23 February 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "arithmetic; floating-point testing; IEEE floating-point standard; multiprecision; validation; Verification", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic\\ Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards", } @Article{Verdonk:2001:PRIb, author = "Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren", title = "A precision- and range-independent tool for testing floating-point arithmetic {II}: conversions", journal = j-TOMS, volume = "27", number = "1", pages = "119--140", month = mar, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/382043.382405", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.win.ua.ac.be/~cant/ieeecc754.html", abstract = "The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems and compilers to programming languages (see especially section 8). Part I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision independent syntax.\par In Part I we have covered the testing of the basic operations +, -, $ \times $, /, the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values and last but not least binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversions between the bases 2 and 10 can be tested for a number of precisions ranging from single (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precision and a proper multiprecision (240 bits) format.\par We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.", accepted = "23 February 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "decimal floating-point arithmetic; floating-point testing", } @Article{Bailey:2001:ASS, author = "P. B. Bailey and W. N. Everitt and A. Zettl", title = "{Algorithm 810}: The {SLEIGN2 Sturm--Liouville} Code", journal = j-TOMS, volume = "27", number = "2", pages = "143--192", month = jun, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/383738.383739", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The SLEIGN2 code is based on the ideas and methods of the original SLEIGN code of 1979. The main purpose of the SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular Sturm--Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. The code uses a number of different algorithms, some of which are new, and has a user-friendly interface. In this paper the algorithms and their implementation are discussed, and the class of problems to which each algorithm applies is identified.", accepted = "14 February 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Luksan:2001:ANA, author = "Ladislav Luk{\v{s}}an and Jan Vl{\v{c}}ek", title = "{Algorithm 811}: {NDA}: algorithms for nondifferentiable optimization", journal = j-TOMS, volume = "27", number = "2", pages = "193--213", month = jun, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/383738.383740", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present four basic Fortran subroutines for nondifferentiable optimization with simple bounds and general linear constraints. Subroutine PMIN, intended for minimax optimization, is based on a sequential quadratic programming variable metric algorithm. Subroutine PBUN and PNEW, intended for general non-smooth problems, are based on bundle type methods. Subroutine PVAR is based on special nonsmooth variable metric methods. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of this approach.", accepted = "14 February 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "minimax optimization, discrete Chebychev approximation, sequential quadratic programming methods, variable metric methods, general linear constraints", } @Article{Andersen:2001:RFC, author = "Bjarne S. Andersen and Jerzy Wa{\'s}niewski and Fred G. Gustavson", title = "A recursive formulation of {Cholesky} factorization of a matrix in packed storage", journal = j-TOMS, volume = "27", number = "2", pages = "214--244", month = jun, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/383738.383741", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new compact way to store a symmetric or triangular matrix called RPF for Recursive Packed Format is fully described. Novel ways to transform RPF to and from standard packed format are included. A new algorithm, called RPC for Recursive Packed Cholesky, that operates on the RPG format is presented. Algorithm RPC is basd on level-3 BLAS and requires variants of algorithms TRSM and SYRK that work on RPF. We call these RP\_TRSM and RP\_SYRK and find that they do most of their work by calling GEMM. It follows that most of the execution time of RPC lies in GEMM. The advantage of this storage scheme compared to traditional packed and full storage is demonstrated. First, the RPC storage format uses the minimal amount of storage for the symmetric or triangular matrix. Second, RPC gives a level-3 implementation of Cholesky factorization whereas standard packed implementations are only level 2. Hence, the performance of our RPC implementation is decidedly superior. Third, unlike fixed block size algorithms, RPC, requires no block size tuning parameter. We present performance measurements on several current architectures that demonstrate improvements over the traditional packed routines. Also MSP parallel computations on the IBM SMP computer are made. The graphs that are attached in Section 7 show that the RPC algorithms are superior by a factor between 1.6 and 7.4 for order around 1000, and between 1.9 and 10.3 for order around 3000 over the traditional packed algorithms. For some architectures, the RPC performance results are almost the same or even better than the traditional full-storage algorithms results.", accepted = "15 March 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cash:2001:ACS, author = "J. R. Cash and G. Moore and R. W. Wright", title = "An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems", journal = j-TOMS, volume = "27", number = "2", pages = "245--266", month = jun, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/383738.383742", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In a recent paper, the present authors derived an automatic continuation algorithm for the solution of linear singular perturbation problems. The algorithm was incorporated into two general-purpose codes for solving boundary value problems, and it was shown to deal effectively with a large test set of linear problems. The present paper describes how the continuation algorithm for linear problems can be extended to deal with the nonlinear case. The results of extensive numerical testing on a set of nonlinear singular perturbation problems are given, and these clearly demonstrate the efficacy of continuation for solving such problems.", accepted = "9 April 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tsai:2001:ABO, author = "Yi-Feng Tsai and Rida T. Farouki", title = "{Algorithm 812}: {BPOLY}: an object-oriented library of numerical algorithms for polynomials in {Bernstein} form", journal = j-TOMS, volume = "27", number = "2", pages = "267--296", month = jun, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/383738.383743", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The design, implementation, and testing of a C++ software library for univariate polynomials in Bernstein form is described. By invoking the class environment and operator overloading, each polynomial in an expression is interpreted as an object compatible with the arithmetic operations and other common functions (subdivision, degree elevation, differentiation and integration, composition, greatest common divisor, real-root solving, etc.) for polynomials in Bernstein form. The library allows compact and intuitive implementation of lengthy manipulations of Bernstein-form polynomials, which often arise in computer graphics and computer-aided design and manufacturing applications. A series of empirical tests indicate that the library functions are typically very accurate and reliable, even for polynomials of surprisingly high degree.", accepted = "4 May 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kierzenka:2001:BSB, author = "Jacek Kierzenka and Lawrence F. Shampine", title = "A {BVP} solver based on residual control and the {Matlab PSE}", journal = j-TOMS, volume = "27", number = "3", pages = "299--316", month = sep, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/502800.502801", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Our goal was to make it as easy as possible to solve a large class of boundary value problems (BVPs) for ordinary differential equations in the Matlab problem solving environment (PSE). We present here theoretical and software developments resulting in bvp4c, a capable BVP solver that is exceptionally easy to use.", accepted = "1 May 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Yang:2001:CPD, author = "Dow-Yung Yang and Ananth Grama and Vivek Sarin and Naren Ramakrishnan", title = "Compression of particle data from hierarchical approximate methods", journal = j-TOMS, volume = "27", number = "3", pages = "317--339", month = sep, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/502800.502802", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents an analytical and computational framework for the compression of particle data resulting from hierarchical approximate treecodes such as the {\em Barnes--Hut} and {\em Fast Multipole Methods}. Due to approximations introduced by hierarchical methods, various parameters (such as position, velocity, acceleration, potential) associated with a particle can be bounded by distortion radii. Using this distortion radii, we develop storage schemes that guarantee error bounds while maximizing compression. Our schemes make extensive use of spatial and temporal coherence of particle behavior and yield compression ratios higher than 12:1 over raw data, and 6:1 over gzipped (LZ) raw data for selected simulation instances. We demonstrate that for uniform distributions with 2M particles, storage requirements can be reduced from 24 MB to about 1.8 MB (about 7 bits per particle per timestep) for storing particle positions. This is significant because it enables faster storage/retrieval, better temporal resolution, and improved analysis. Our results are shown to scale from small systems (2K particles) to much larger systems (over 2M particles). The associated algorithm is asymptotically optimal in computation time ($O(n)$) with a small constant. Our implementations are demonstrated to run extremely fast---much faster than the time it takes to compute a single time-step advance. In addition, our compression framework relies on a natural hierarchical representation upon which other analysis tasks such as segmented and window retrieval can be built.", accepted = "23 July 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Astrophysics; Barnes--Hut; data compression and analysis; Fast Multipole Method; materials simulation; molecular dynamics; particle dynamics", } @Article{Birgin:2001:ASS, author = "Ernesto G. Birgin and Jos{\'e} Mario Mart{\'\i}nez and Marcos Raydan", title = "{Algorithm 813}: {SPG}---Software for {Convex-Constrained Optimization}", journal = j-TOMS, volume = "27", number = "3", pages = "340--349", month = sep, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/502800.502803", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fortran 77 software implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line-search strategy. The user provides objective function and gradient values, and projections onto the feasible set. Some recent numerical tests are reported on very large location problems, indicating that SPG is substantially more efficient than existing general-purpose software on problems for which projections can be computed efficiently.", accepted = "6 July 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Bound constrained problems; large-scale problems; nonmonotone line search; projected gradients; spectral gradient method", subject = "Primary Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Additional Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Gradient methods G.4 MATHEMATICAL SOFTWARE", } @Article{Azulay:2001:RSM, author = "David-Olivier Azulay and Jean-Fran{\c{c}}ois Pique", title = "A revised simplex method with integer {$Q$}-matrices", journal = j-TOMS, volume = "27", number = "3", pages = "350--360", month = sep, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/502800.502804", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a modification of the simplex formulas in which Q-matrices are used to implement exact computations with an integer multiprecision library. Our motivation comes from the need for efficient and exact incremental solvers in the implementation of constraint solving languages such as Prolog. We explain how to reformulate the problem and the different steps of the simplex algorithm. We compare some measurements obtained with integer and rational computations.", accepted = "26 July 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Benson:2001:CSP, author = "Steven J. Benson and Lois Curfman McInnes and Jorge J. Mor{\'e}", title = "A case study in the performance and scalability of optimization algorithms", journal = j-TOMS, volume = "27", number = "3", pages = "361--376", month = sep, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/502800.502805", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving bound-constrained convex quadratic problems. Our implementation of the GPCG algorithm within the Toolkit for Advanced Optimization (TAO) is available for a wide range of high-performance architectures and has been tested on problems with over 2.5 million variables. We analyze the performance as a function of the number of variables, the number of free variables, and the preconditioner. In addition, we discuss how the software design facilitates algorithmic comparisons.", accepted = "10 August 2001", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Smith:2001:AFS, author = "David M. Smith", title = "{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions", journal = j-TOMS, volume = "27", number = "4", pages = "377--387", month = dec, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/504210.504211", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A collection of Fortran 90 routines for evaluating the Gamma function and related functions using the FM multiple-precision arithmetic package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amestoy:2001:ACT, author = "Patrick R. Amestoy and Iain S. Duff and Jean-Yves L'Excellent and Xiaoye S. Li", title = "Analysis and Comparison of Two General Sparse Solvers for Distributed Memory Computers", journal = j-TOMS, volume = "27", number = "4", pages = "388--421", month = dec, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/504210.504212", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper provides a comprehensive study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-scale distributed-memory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called superLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512-processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gunnels:2001:FFL, author = "John A. Gunnels and Fred G. Gustavson and Greg M. Henry and Robert A. van de Geijn", title = "{FLAME}: {Formal Linear Algebra Methods Environment}", journal = j-TOMS, volume = "27", number = "4", pages = "422--455", month = dec, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/504210.504213", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Since the advent of high-performance distributed-memory parallel computing, the need for intelligible code has become ever greater. The development and maintenance of libraries for these architectures is simply too complex to be amenable to conventional approaches to implementation. Attempts to employ traditional methodology have led, in our opinion, to the production of an abundance of anfractuous code that is difficult to maintain and almost impossible to upgrade. Having struggled with these issues for more than a decade, we have concluded that a solution is to apply a technique from theoretical computer science, formal derivation, to the development of high-performance linear algebra libraries. We think the resulting approach results in aesthetically pleasing, coherent code that greatly facilitates intelligent modularity and high performance while enhancing confidence in its correctness. Since the technique is language-independent, it lends itself equally well to a wide spectrum of programming languages (and paradigms) ranging from C and Fortran to C++ and Java. In this paper, we illustrate our observations by looking at the Formal Linear Algebra Methods Environment (FLAME), a framework that facilitates the derivation and implementation of linear algebra algorithms on sequential architectures. This environment demonstrates that lessons learned in the distributed-memory world can guide us toward better approaches even in the sequential world. We present performance experiments on the Intel (R) Pentium (R) III processor that demonstrate that high performance can be attained by coding at a high level of abstraction.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Festa:2001:AFS, author = "Paola Festa and Panos M. Pardalos and Mauricio G. C. Resende", title = "{Algorithm 815}: {FORTRAN} subroutines for computing approximate solutions of feedback set problems using {GRASP}", journal = j-TOMS, volume = "27", number = "4", pages = "456--464", month = dec, year = "2001", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/504210.504214", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We propose FORTRAN subroutines for approximately solving the feedback vertex and arc set problems on directed graphs using a Greedy Randomized Adaptive Search Procedure (GRASP). Implementation and usage of the package is outlined and computational experiments are reported illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; Combinatorial optimization; feedback set problems; FORTRAN subroutines; graph bipartization; GRASP; local search; Performance", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Integer programming Additional Classification: G. Mathematics of Computing G.2 DISCRETE MATHEMATICS G.2.1 Combinatorics Subjects: Combinatorial algorithms G.m MISCELLANEOUS", } @Article{Engelborghs:2002:NBA, author = "K. Engelborghs and T. Luzyanina and D. Roose", title = "Numerical bifurcation analysis of delay differential equations using {DDE-BIFTOOL}", journal = j-TOMS, volume = "28", number = "1", pages = "1--21", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513002", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe {DDE-BIFTOOL}, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gockenbach:2002:EAI, author = "Mark S. Gockenbach and Daniel R. Reynolds and Peng Shen and William W. Symes", title = "Efficient and automatic implementation of the adjoint state method", journal = j-TOMS, volume = "28", number = "1", pages = "22--44", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513003", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Combination of object-oriented programming with automatic differentiation techniques facilitates the solution of data fitting, control, and design problems driven by explicit time stepping schemes for initial-boundary value problems. The C++ class {\tt fdtd} takes a complete specification of a single step, along with some associated code, and assembles from it a complete simulator, along with the linearized and adjoint simulations. The result is a (nonlinear) operator in the sense of the Hilbert Class Library (HCL), a C++ software package for optimization. The HCL operator so produced links directly with any of the HCL optimization algorithms. Moreover, the performance of simulators constructed in this way is equivalent to that of optimized Fortran implementations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gansterer:2002:EDC, author = "Wilfried N. Gansterer and Robert C. Ward and Richard P. Muller", title = "An Extension of the Divide-and-Conquer Method for a Class of Symmetric Block-Tridiagonal Eigenproblems", journal = j-TOMS, volume = "28", number = "1", pages = "45--58", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513004", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A divide-and-conquer method for computing eigenvalues and eigenvectors of a block-tridiagonal matrix with rank-one off-diagonal blocks is presented. The implications of unbalanced merging operations due to unequal block sizes are analyzed and illustrated with numerical examples. It is shown that an unfavorable order for merging blocks in the synthesis phase of the algorithm may lead to a significant increase of the arithmetic complexity. A strategy to determine a good merging order which is at least close to optimal in all cases is given. The method has been implemented and applied to test problems from a Quantum Chemistry application.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hopkins:2002:RCA, author = "Tim Hopkins", title = "Renovating the {Collected Algorithms from ACM}", journal = j-TOMS, volume = "28", number = "1", pages = "59--74", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513005", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Since 1960 the Association for Computing Machinery has published a series of refereed algorithm implementations known as the Collected Algorithms of the ACM (CALGO). Most of those published since 1975 are mathematical algorithms, and many of them remain useful today. In this paper we describe measures that have been taken to bring some 400 of these latter codes to an up-to-date and consistent state.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Robinson:2002:ARA, author = "Ian Robinson and Michael Hill", title = "{Algorithm 816}: {\em r2d2lri\/}: an algorithm for automatic two-dimensional cubature", journal = j-TOMS, volume = "28", number = "1", pages = "75--100", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513006", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\em r2d2lri} is a non-adaptive algorithm implemented in C++ for performing automatic cubature over a wide variety of finite and non-finite two-dimensional domains. The core integrator uses a sixth-order Sidi transformation applied to a sequence of embedded lattice rules in such a fashion as to incur virtually no computational overhead. Even for integrals over non-finite domains, for which several non-finite to finite transformations may be attempted, the algorithm remains very fast. Performance data is presented which demonstrates both the effectiveness and efficiency of {\em r2d2lri}, taking into account the number of function evaluations needed and the execution speed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bertolazzi:2002:APG, author = "Enrico Bertolazzi and Gianmarco Manzini", title = "{Algorithm 817}: {P2MESH}: generic object-oriented interface between {$2$-D} unstructured meshes and {FEM\slash FVM}-based {PDE} solvers", journal = j-TOMS, volume = "28", number = "1", pages = "101--132", month = mar, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/513001.513007", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The software interface P2MESH is a collection of C++ class templates suitable for developing prototypes of high-performance PDE solvers on unstructured 2-D meshes. P2MESH supports several discretization methods on triangles and quadrilaterals, such as Finite Volumes or Finite Elements. The design philosophy of P2MESH does not consider neither specific model problems nor built-in approximation algorithms. The software package is of general purpose and it may also be used as a building block in the implementation of numerical both for engineering applications and mathematical problems.", accepted = "21 March 2002", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boisvert:2002:PSI, author = "Ronald F. Boisvert and Jack J. Dongarra", title = "Preface to the special issue on the {Basic Linear Algebra Subprograms (BLAS)}", journal = j-TOMS, volume = "28", number = "2", pages = "133--134", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567812", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Blackford:2002:USB, author = "L. Susan Blackford and James Demmel and Jack Dongarra and Iain Duff and Sven Hammarling and Greg Henry and Michael Heroux and Linda Kaufman and Andrew Lumsdaine and Antoine Petitet and Roldan Pozo and Karin Remington and R. Clint Whaley", title = "An updated set of {Basic Linear Algebra Subprograms (BLAS)}", journal = j-TOMS, volume = "28", number = "2", pages = "135--151", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567807", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper expands the specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS.\par Numerical linear algebra, particularly the solution of linear systems of equations, linear least squares problems, eigenvalue problems and singular value problems, is fundamental to most calculations in scientific computing, and is often the computationally intense part of such calculations. Designers of computer programs involving linear algebraic operations have frequently chosen to implement certain low level operations, such as the dot product or the matrix vector product, as separate subprograms. This may be observed both in many published codes and in codes written for specific applications at many computer installations.\par A major aim of the standards defined in this paper is to enable linear algebra libraries (both public domain and commercial) to interoperate efficiently, reliably and easily.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2002:DIT, author = "Xiaoye S. Li and James W. Demmel and David H. Bailey and Greg Henry and Yozo Hida and Jimmy Iskandar and William Kahan and Suh Y. Kang and Anil Kapur and Michael C. Martin and Brandon J. Thompson and Teresa Tung and Daniel J. Yoo", title = "Design, implementation and testing of extended and mixed precision {BLAS}", journal = j-TOMS, volume = "28", number = "2", pages = "152--205", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567808", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper describes the design rationale, a C implementation, and conformance testing of a subset of the new Standard for the BLAS (Basic Linear Algebra Subroutines): Extended and Mixed Precision BLAS. Permitting higher internal precision and mixed input\slash output types and precisions allows us to implement some algorithms that are simpler, more accurate, and sometimes faster than possible without these features. The new BLAS are challenging to implement and test because there are many more subroutines than in the existing Standard, and because we must be able to assess whether a higher precision is used for internal computations than is used for either input or output variables. We have therefore developed an automated process of generating and systematically testing these routines. Our methodology is applicable to languages besides C. In particular, our algorithms used in the testing code will be valuable to all other BLAS implementors. Our extra precision routines achieve excellent performance---close to half of the machine peak Megaflop rate even for the Level 2 BLAS, when the data access is stride one.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accurate floating-point summation", } @Article{Bindel:2002:CGR, author = "David Bindel and James Demmel and William Kahan and Osni Marques", title = "On computing {Givens} rotations reliably and efficiently", journal = j-TOMS, volume = "28", number = "2", pages = "206--238", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567809", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider the efficient and accurate computation of Givens rotations. When $f$ and $g$ are positive real numbers, this simply amounts to computing the values of $c = f/\sqrt{f^2+g^2}$, $s = g/\sqrt{f^2+g^2}$, and $r = \sqrt{f^2+g^2}$. This apparently trivial computation merits closer consideration for the following three reasons. First, while the definitions of $c$, $s$ and $r$ seem obvious in the case of two nonnegative arguments $f$ and $g$, there is enough freedom of choice when one or more of $f$ and $g$ are negative, zero or complex that LAPACK auxiliary routines SLARTG, CLARTG, SLARGV and CLARGV can compute rather different values of $c$, $s$ and $r$ for mathematically identical values of $f$ and $g$. To eliminate this unnecessary ambiguity, the BLAS Technical Forum chose a single consistent definition of Givens rotations that we will justify here. Second, computing accurate values of $c$, $s$ and $r$ as efficiently as possible and reliably despite over/underflow is surprisingly complicated. For complex Givens rotations, the most efficient formulas require only one real square root and one real divide (as well as several much cheaper additions and multiplications), but a reliable implementation using only working precision has a number of cases. On a Sun Ultra-10, the new implementation is slightly faster than the previous LAPACK implementation in the most common case, and 2.7 to 4.6 times faster than the corresponding vendor, reference or ATLAS routines. It is also more reliable; all previous codes occasionally suffer from large inaccuracies due to over/underflow. For real Givens rotations there are also improvements in speed and accuracy, though not as striking. Third, the design process that led to this reliable implementation is quite systematic, and could be applied to the design of similarly reliable subroutines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:2002:OSB, author = "Iain S. Duff and Michael A. Heroux and Roldan Pozo", title = "An overview of the {Sparse Basic Linear Algebra Subprograms}: {The} new standard from the {BLAS Technical Forum}", journal = j-TOMS, volume = "28", number = "2", pages = "239--267", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567810", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss the interface design for the Sparse Basic Linear Algebra Subprograms (BLAS), the kernels in the recent standard from the BLAS Technical Forum that are concerned with unstructured sparse matrices. The motivation for such a standard is to encourage portable programming while allowing for library-specific optimizations. In particular, we show how this interface can shield one from concern over the specific storage scheme for the sparse matrix. This design makes it easy to add further functionality to the sparse BLAS in the future. We illustrate the use of the Sparse BLAS with examples in the three supported programming languages, Fortran 95, Fortran 77, and C.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:2002:ARM, author = "Iain S. Duff and Christof V{\"o}mel", title = "{Algorithm 818}: a reference model implementation of the {Sparse BLAS} in {Fortran 95}", journal = j-TOMS, volume = "28", number = "2", pages = "268--283", month = jun, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/567806.567811", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Basic Linear Algebra Subprograms for sparse matrices (Sparse BLAS) as defined by the BLAS Technical Forum are a set of routines providing basic operations for sparse matrices and vectors. A principal goal for the Sparse BLAS standard is to aid in the development of iterative solvers for large sparse systems by specifying on the one hand interfaces for a high-level description of vector and matrix operations for the algorithm developer and on the other hand leaving enough freedom for vendors to provide the most efficient implementation of the underlying algorithms for their specific architectures.\par The Sparse BLAS standard defines interfaces and bindings for the three target languages: C, Fortran 77 and Fortran 95. We describe here our Fortran 95 implementation intended as a reference model for the Sparse BLAS. We identify the underlying complex issues of the representation and the handling of sparse matrices and give suggestions to other implementors of how to address them.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hopkins:2002:CPT, author = "Tim Hopkins", title = "A comment on the presentation and testing of {CALGO} codes and a remark on {Algorithm 639}: {To} integrate some infinite oscillating tails", journal = j-TOMS, volume = "28", number = "3", pages = "285--300", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569148", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We report on a number of coding problems that occur frequently in published CALGO software and are still appearing in new algorithm submissions. Using Algorithm 639 as an extended example, we describe how these types of faults may be almost entirely eliminated using available commercial compilers and software tools. We consider the levels of testing required to instill confidence that code performs reliably. Finally, we look at how the source code may be re-engineered, and thus made more maintainable, by taking account of advances in hardware and language development.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gupta:2002:RAD, author = "Anshul Gupta", title = "Recent Advances in Direct Methods for Solving Unsymmetric Sparse Systems of Linear Equations", journal = j-TOMS, volume = "28", number = "3", pages = "301--324", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569149", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 11:26:40 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms, Performance; Multifrontal Method; Parallel Sparse Solvers; Sparse LU Decomposition; Sparse Matrix Factorization", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra", } @Article{Gil:2002:AAB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77} routines for the computation of complex {Airy} functions", journal = j-TOMS, volume = "28", number = "3", pages = "325--336", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569150", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $Ai(z)$, $Bi(z)$ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ferrando:2002:AFI, author = "Sebastian E. Ferrando and Lawrence A. Kolasa and Natasha Kova{\v{c}}evi{\'c}", title = "{Algorithm 820}: a flexible implementation of matching pursuit for {Gabor} functions on the interval", journal = j-TOMS, volume = "28", number = "3", pages = "337--353", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569151", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The matching pursuit algorithm of Mallat et al. is discussed in the context of discretized Gabor functions on an interval. Results from frame theory are used to introduce corresponding finite dictionaries. We then proceed to describe two software implementations based on these dictionaries. One implementation allows for users to have great flexibility in the Gabor dictionary to be used. This is a useful improvement over other implementations which only allow for a fixed dictionary. The other implementation takes advantage of the FFT algorithm and is faster. These implementations are written in C++, and can be used in many practical situations given its flexibility and generality.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hanson:2002:AFI, author = "Richard J. Hanson and Clay P. Breshears and Henry A. Gabb", title = "{Algorithm 821}: a {Fortran} interface to {POSIX} threads", journal = j-TOMS, volume = "28", number = "3", pages = "354--371", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569152", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Pthreads is the library of POSIX standard functions for concurrent, multithreaded programming. The POSIX standard only defines an application programming interface (API) to the C programming language, not to Fortran. Many scientific and engineering applications are written in Fortran. Also, many of these applications exhibit functional, or task-level, concurrency. They would benefit from multithreading, especially on symmetric multiprocessors (SMP). We present here an interface to that part of the Pthreads library that is compatible with standard Fortran. The contribution consists of two primary source files: a Fortran module and a collection of C wrappers to Pthreads functions. The Fortran module defines the data structures, interface and initialization routines used to manage threads. The stability and portability of the Fortran API to Pthreads is demonstrated using common mathematical computations on three different systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hopkins:2002:RAF, author = "Tim Hopkins", title = "Remark on {Algorithm 705}: a {Fortran-77} software package for solving the {Sylvester} matrix equation {$AXB^T + CXD^T = E$}", journal = j-TOMS, volume = "28", number = "3", pages = "372--375", month = sep, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/569147.569153", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Gardiner:1992:AFS}.", abstract = "We present a number of corrections to Algorithm 705 [Gardiner et al. 1992].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reid:2002:IHE, author = "John K. Reid and Jennifer A. Scott", title = "Implementing {Hager}'s exchange methods for matrix profile reduction", journal = j-TOMS, volume = "28", number = "4", pages = "377--391", month = dec, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/592843.592844", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Hager recently introduced down and up exchange methods for reducing the profile of a sparse matrix with a symmetric sparsity pattern. The methods are particularly useful for refining orderings that have been obtained using a standard profile reduction algorithm, such as the Sloan method. The running times for the exchange algorithms reported by Hager suggested their cost could be prohibitive for practical applications. We examine how to implement the exchange algorithms efficiently. For a range of real test problems, it is shown that the cost of running our new implementation does not add a prohibitive overhead to the cost of the original reordering.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jonsson:2002:RBAa, author = "Isak Jonsson and Bo K{\aa}gstr{\"o}m", title = "Recursive blocked algorithms for solving triangular systems: {Part I}: one-sided and coupled {Sylvester}-type matrix equations", journal = j-TOMS, volume = "28", number = "4", pages = "392--415", month = dec, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/592843.592845", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Triangular matrix equations appear naturally in estimating the condition numbers of matrix equations and different eigenspace computations, including block-diagonalization of matrices and matrix pairs and computation of functions of matrices. To solve a triangular matrix equation is also a major step in the classical Bartels--Stewart method for solving the standard continuous-time Sylvester equation ($AX - XB = C$). We present novel recursive blocked algorithms for solving one-sided triangular matrix equations, including the continuous- time Sylvester and Lyapunov equations, and a generalized coupled Sylvester equation. The main parts of the computations are performed as level-3 general matrix multiply and add (GEMM) operations. In contrast to explicit standard blocking techniques, our recursive approach leads to an automatic variable blocking that has the potential of matching the memory hierarchies of today's HPC systems. Different implementation issues are discussed, including when to terminate the recursion, the design of new optimized superscalar kernels for solving leaf-node triangular matrix equations efficiently, and how parallelism is utilized in our implementations. Uniprocessor and SMP parallel performance results of our recursive blocked algorithms and corresponding routines in the state-of-the-art libraries LAPACK and SLICOT are presented. The performance improvements of our recursive algorithms are remarkable, including 10-fold speedups compared to standard algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; automatic blocking; GEMM-based; generalized coupled Sylvester; LAPACK; level-3 BLAS; Matrix equations; Performance; recursion; SLICOT; SMP parallelization; standard Sylvester and Lyapunov; superscalar", subject = "Primary Classification: G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis Additional Classification: F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra Subjects: Conditioning; Linear systems (direct and iterative methods) G.4 MATHEMATICAL SOFTWARE Subjects: Parallel and vector implementations; Efficiency; Reliability and robustness", } @Article{Jonsson:2002:RBAb, author = "Isak Jonsson and Bo K{\aa}gstr{\"o}m", title = "Recursive Blocked Algorithms for Solving Triangular Systems: {Part II}: Two-Sided and Generalized {Sylvester} and {Lyapunov} Matrix Equations", journal = j-TOMS, volume = "28", number = "4", pages = "416--435", month = dec, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/592843.592846", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We continue our study of high-performance algorithms for solving triangular matrix equations. They appear naturally in different condition estimation problems for matrix equations and various eigenspace computations, and as reduced systems in standard algorithms. Building on our successful recursive approach applied to one-sided matrix equations (Part I), we now present novel recursive blocked algorithms for two-sided matrix equations, which include matrix product terms such as AXBT. Examples are the discrete-time standard and generalized Sylvester and Lyapunov equations. The means for achieving high performance is the recursive variable blocking, which has the potential of matching the memory hierarchies of today's high-performance computing systems, and level-3 computations which mainly are performed as GEMM operations. Different implementation issues are discussed, including the design of efficient new algorithms for two-sided matrix products. We present uniprocessor and SMP parallel performance results of recursive blocked algorithms and routines in the state-of-the-art SLICOT library. Although our recursive algorithms with optimized kernels for the two-sided matrix equations perform more operations, the performance improvements are remarkable, including 10-fold speedups or more, compared to standard algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; automatic blocking; Design; generalized Sylvester and Lyapunov; LAPACK; level-3 BLAS; Matrix equations; Performance GEMM-based; recursion; SLICOT; SMP parallelization; standard discrete-time Sylvester and Lyapunov; superscalar", subject = "Primary Classification: G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis Additional Classification: F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra Subjects: Linear systems (direct and iterative methods); Conditioning G.4 MATHEMATICAL SOFTWARE Subjects: Parallel and vector implementations; Reliability and robustness; Efficiency", } @Article{Gil:2002:AGH, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77 routines for the computation of complex {Scorer} functions", journal = j-TOMS, volume = "28", number = "4", pages = "436--447", month = dec, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/592843.592847", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $Gi(z)$, $Hi(z)$ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Edlund:2002:SPS, author = "Ove Edlund", title = "A software package for sparse orthogonal factorization and updating", journal = j-TOMS, volume = "28", number = "4", pages = "448--482", month = dec, year = "2002", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/592843.592848", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Though there is good software for sparse QR factorization, there is little support for updating and downdating---something that is absolutely essential in some linear programming algorithms, for example. This paper describes an implementation of sparse LQ factorization, including block triangularization, approximate minimum degree ordering, symbolic factorization, multifrontal factorization, {\em and\/} updating and downdating. The factor $Q$ is not retained. The updating algorithm expands the nonzero pattern of the factor $L$, which is reflected in the dynamic representation of $L$. The block triangularization is used as an ``ordering for sparsity'' rather than as a prerequisite for block backward substitution. In the symbolic factorization, something called ``element counters'' is introduced to reduce the overestimation of the number of nonzeros that the commonly used methods do. Both the approximate minimum degree ordering and the symbolic factorization are done without explicitly forming the nonzero pattern of the symmetric matrix in the corresponding normal equations.\par Tests show that the average time used for a single update or downdate is essentially the same as the time used for a single forward or backward substitution. Other parts of the implementation show the same range of performance as existing code, but cannot be replaced because of the special character of the systems that are solved.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Soderlind:2003:DFA, author = "Gustaf S{\"o}derlind", title = "Digital filters in adaptive time-stepping", journal = j-TOMS, volume = "29", number = "1", pages = "1--26", month = mar, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/641876.641877", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Adaptive time-stepping based on linear digital control theory has several advantages: the algorithms can be analyzed in terms of stability and adaptivity, and they can be designed to produce smoother stepsize sequences resulting in significantly improved regularity and computational stability. Here, we extend this approach by viewing the closed-loop transfer map $H\phi: \log \phi \mapsto \log h$ as a digital filter, processing the signal $log \phi$ (the principal error function) in the frequency domain, in order to produce a smooth stepsize sequence $\log h$. The theory covers all previously considered control structures and offers new possibilities to construct stepsize selection algorithms in the asymptotic stepsize-error regime. Without incurring extra computational costs, the controllers can be designed for special purposes such as higher order of adaptivity (for smooth ODE problems) or a stronger ability to suppress high-frequency error components (nonsmooth problems, stochastic ODEs). Simulations verify the controllers' ability to produce stepsize sequences resulting in improved regularity and computational stability.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Adaptivity; algorithm analysis; algorithms; control theory; digital filters; error control; mathematical software; stepsize control; theory", subject = "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.7 Ordinary Differential Equations Subjects: Initial value problems", } @Article{Nievergelt:2003:SFM, author = "Yves Nievergelt", title = "Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit", journal = j-TOMS, volume = "29", number = "1", pages = "27--48", month = mar, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/641876.641878", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "68W99 (65Y99 68M99)", MRnumber = "MR2001452", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Combined with doubly compensated summation, scalar fused multiply-add instructions redefine the concept of floating-point arithmetic, because they allow for the computation of sums of real or complex matrix products accurate to the penultimate digit. Particular cases include complex arithmetic, dot products, cross products, residuals of linear systems, determinants of small matrices, discriminants of quadratic, cubic, or quartic equations, and polynomials.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accurate floating-point summation; algorithms; design; doubly compensated summation; floating-point arithmetic; fused multiply-add instruction; languages; matrix arithmetic; provable accuracy; rounding error; standardization; theory", subject = "Primary Classification: B. Hardware, B.2 ARITHMETIC AND LOGIC STRUCTURES, B.2.0 General; Additional Classification: B. Hardware, B.7 INTEGRATED CIRCUITS B.7.1 Types and Design Styles Subjects: Algorithms implemented in hardware B.8 Performance and Reliability B.8.2 Performance Analysis and Design Aids C. Computer Systems Organization C.0 GENERAL Subjects: Instruction set design (e.g., RISC, CISC, VLIW) F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic; Multiple precision arithmetic; Numerical algorithms; Error analysis G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis; Certification and testing; Reliability and robustness", } @Article{Joe:2003:RAI, author = "Stephen Joe and Frances Y. Kuo", title = "Remark on {Algorithm 659}: {Implementing} {Sobol}'s quasirandom sequence generator", journal = j-TOMS, volume = "29", number = "1", pages = "49--57", month = mar, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/641876.641879", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and ``direction numbers'' so as to allow the generation of Sobol' sequences to approximate integrals in up to 1111 dimensions. The direction numbers given generate Sobol' sequences that satisfy Sobol's so-called Property A.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; Low-discrepancy sequences; primitive polynomials; quasirandom sequences; Sobol' sequences", subject = "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.4 Quadrature and Numerical Differentiation Subjects: Multidimensional (multiple) quadrature", } @Article{Gertz:2003:OOS, author = "E. Michael Gertz and Stephen J. Wright", title = "Object-oriented software for quadratic programming", journal = j-TOMS, volume = "29", number = "1", pages = "58--81", month = mar, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/641876.641880", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The object-oriented software package OOQP for solving convex quadratic programming problems (QP) is described. The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular applications. The OOQP distribution contains default implementations that solve several important QP problem types, including general sparse and dense QPs, bound-constrained QPs, and QPs arising from support vector machines and Huber regression. The implementations supplied with the OOQP distribution are based on such well known linear algebra packages as MA27/57, LAPACK, and PETSc. OOQP demonstrates the usefulness of object-oriented design in optimization software development, and establishes standards that can be followed in the design of software packages for other classes of optimization problems. A number of the classes in OOQP may also be reusable directly in other codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; Design; Interior-Point Methods; Object-Oriented Software; Quadratic Programming", subject = "Primary Classification: D. Software D.2 SOFTWARE ENGINEERING D.2.2 Design Tools and Techniques Additional Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Quadratic programming methods G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis", } @Article{Wenzel:2003:IWD, author = "Lothar Wenzel and Ram Rajagopal and Dinesh Nair", title = "Induced well-distributed sets in {Riemannian} spaces", journal = j-TOMS, volume = "29", number = "1", pages = "82--94", month = mar, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/641876.641881", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The concept of Riemannian geometries is used to construct induced homogeneous point sets on manifolds that are based on well-distributed point sets in unit cubes of an appropriately chosen Euclidean space. These well-distributed point sets in unit cubes are based on standard low-discrepancy sequences. The approach is algorithmic, that is, the methods developed in this article have been implemented and tested. Applications in image processing, graph theory and measurement-based exploration are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; image processing; low-discrepancy sequences; Measurement; Riemannian geometry; Theory; well-distributed point sets", subject = "J. Computer Applications J.2 PHYSICAL SCIENCES AND ENGINEERING", } @Article{Hong:2003:AIS, author = "Hee Sun Hong and Fred J. Hickernell", title = "{Algorithm 823}: {Implementing} scrambled digital sequences", journal = j-TOMS, volume = "29", number = "2", pages = "95--109", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779360", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Random scrambling of deterministic $(t, m, s)$-nets and $(t, s)$-sequences eliminates their inherent bias while retaining their low-discrepancy properties. This article describes an implementation of two types of random scrambling, one proposed by Owen and another proposed by Faure and Tezuka. The four different constructions of digital sequences implemented are those proposed by Sobol', Faure, Niederreiter, and Niederreiter and Xing. Because the random scrambling involves manipulating all digits of each point, the code must be written carefully to minimize the execution time. Computed root mean square discrepancies of the scrambled sequences are compared to known theoretical results. Furthermore, the performances of these sequences on various test problems are discussed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2003:SSD, author = "Xiaoye S. Li and James W. Demmel", title = "{SuperLU\_DIST}: a scalable distributed-memory sparse direct solver for unsymmetric linear systems", journal = j-TOMS, volume = "29", number = "2", pages = "110--140", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779361", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the main algorithmic features in the software package SuperLU\_DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software's parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on large-scale distributed machines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dhooge:2003:MMP, author = "A. Dhooge and W. Govaerts and Yu. A. Kuznetsov", title = "{MATCONT}: {A MATLAB} package for numerical bifurcation analysis of {ODEs}", journal = j-TOMS, volume = "29", number = "2", pages = "141--164", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779362", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore--Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Henrion:2003:GGO, author = "Didier Henrion and Jean-Bernard Lasserre", title = "{GloptiPoly}: {Global} optimization over polynomials with {Matlab} and {SeDuMi}", journal = j-TOMS, volume = "29", number = "2", pages = "165--194", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779363", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "GloptiPoly is a Matlab\slash SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally nonconvex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality, or integer constraints. It generates a series of lower bounds monotonically converging to the global optimum without any problem splitting. Global optimality is detected and isolated optimal solutions are extracted automatically. Numerical experiments show that for most of the small-scale problems described in the literature, the global optimum is reached at low computational cost.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sarra:2003:SSP, author = "Scott A. Sarra", title = "The spectral signal processing suite", journal = j-TOMS, volume = "29", number = "2", pages = "195--217", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779364", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A software suite written in the Java programming language for the postprocessing of Chebyshev approximations to discontinuous functions is presented. It is demonstrated how to use the package to remove the effects of the Gibbs--Wilbraham phenomenon from Chebyshev approximations of discontinuous functions. Additionally, the package is used to postprocess Chebyshev collocation and Chebyshev super spectral viscosity approximations of hyperbolic partial differential equations. The postprocessing method is the Gegenbauer reconstruction procedure. The Spectral Signal Processing Suite is the first publicly available package that implements the procedure. State-of-the-art techniques are used to implement the algorithms with efficiency while reducing round-off error.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Quintana-Orti:2003:FDA, author = "Enrique S. Quintana-Ort{\'\i} and Robert A. van de Geijn", title = "Formal derivation of algorithms: {The} triangular {Sylvester} equation", journal = j-TOMS, volume = "29", number = "2", pages = "218--243", month = jun, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/779359.779365", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 13:56:17 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this paper we apply a formal approach for the derivation of dense linear algebra algorithms to the triangular Sylvester equation. The result is a large family of provably correct algorithms. By using a coding style that reflects the algorithms as they are naturally presented, the correctness of the algorithms carries through to the correctness of the implementations. Analytically motivated heuristics are used to subsequently choose members from the family that can be expected to yield high performance. Finally, we report performance on the Intel (R) Pentium (R) III processor that is competitive with that of recursive algorithms reported previously in the literature for this operation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Martins:2003:CSD, author = "Joaquim R. R. A. Martins and Peter Sturdza and Juan J. Alonso", title = "The complex-step derivative approximation", journal = j-TOMS, volume = "29", number = "3", pages = "245--262", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838251", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Eble:2003:ASP, author = "Ingo Eble and Markus Neher", title = "{ACETAF}: a software package for computing validated bounds for {Taylor} coefficients of analytic functions", journal = j-TOMS, volume = "29", number = "3", pages = "263--286", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838252", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents methods for practical computation of verified bounds for Taylor coefficients of analytic functions. These bounds are constructed from Cauchy's estimate and from some of its modifications. Interval arithmetic is used to obtain rigorous results.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cools:2003:ACP, author = "Ronald Cools and Ann Haegemans", title = "{Algorithm 824}: {\em {CUBPACK}\/}: a package for automatic cubature; framework description", journal = j-TOMS, volume = "29", number = "3", pages = "287--296", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838253", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "CUBPACK aims to offer a collection of re-usable code for automatic $n$-dimensional ($n \geq 1$) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows this region to consist of a union of $n$-simplices and $n$-parallelepipeds. The framework of CUBPACK is described as well as its user interface. The functionality of several well known routines is embedded. New features include integration algorithms using the $\epsilon$-algorithm for extrapolation for regions other than triangles and the implementation of a new type of subdivision for 3-cubes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Genz:2003:ANC, author = "Alan Genz and Ronald Cools", title = "An adaptive numerical cubature algorithm for simplices", journal = j-TOMS, volume = "29", number = "3", pages = "297--308", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838254", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A globally adaptive algorithm for numerical cubature of a vector of functions over a collection of $n$-dimensional simplices is described. The algorithm is based on a subdivision strategy that chooses for subdivision at each stage the subregion (of the input simplices) with the largest estimated error. This subregion is divided into two, three or four equal volume subregions by cutting selected edges. These edges are selected using information about the smoothness of the integrands in the edge directions. The algorithm allows a choice from several embedded cubature rule sequences for approximate integration and error estimation. A Fortran 95 implementation as a part of CUBPACK is also discussed. Testing of the algorithm is described.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shellman:2003:ADC, author = "Spencer Shellman and K. Sikorski", title = "{Algorithm 825}: a deep-cut bisection envelope algorithm for fixed points", journal = j-TOMS, volume = "29", number = "3", pages = "309--325", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838255", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the BEDFix (Bisection Envelope Deep-cut Fixed point) algorithm for the problem of approximating a fixed point of a function of two variables. The function must be Lipschitz continuous with constant 1 with respect to the infinity norm; such functions are commonly found in economics and game theory. The computed approximation satisfies a residual criterion given a specified error tolerance. The BEDFix algorithm improves the BEFix algorithm presented in Shellman and Sikorski [2002] by utilizing ``deep cuts,'' that is, eliminating additional segments of the feasible domain which cannot contain a fixed point. The upper bound on the number of required function evaluations is the same for BEDFix and BEFix, but our numerical tests indicate that BEDFix significantly improves the average-case performance. In addition, we show how BEDFix may be used to solve the absolute criterion fixed point problem with significantly better performance than the simple iteration method, when the Lipschitz constant is less than but close to 1. BEDFix is highly efficient when used to compute residual solutions for bivariate functions, having a bound on function evaluations that is twice the logarithm of the reciprocal of the tolerance. In the tests described in this article, the number of evaluations performed by the method averaged 31 percent of this worst-case bound. BEDFix works for nonsmooth continuous functions, unlike methods that require gradient information; also, it handles functions with minimum Lipschitz constants equal to 1, whereas the complexity of simple iteration approaches infinity as the minimum Lipschitz constant approaches 1. When BEDFix is used to compute absolute criterion solutions, the worst-case complexity depends on the logarithm of the reciprocal of $1-q$, where $q$ is the Lipschitz constant, as well as on the logarithm of the reciprocal of the tolerance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fahey:2003:APE, author = "Mark R. Fahey", title = "{Algorithm 826}: a parallel eigenvalue routine for complex {Hessenberg} matrices", journal = j-TOMS, volume = "29", number = "3", pages = "326--336", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838256", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be directly computed using a parallel QR algorithm. This parallel complex Schur decomposition routine was developed to fill a void in the ScaLAPACK library and was based on the parallel real Schur decomposition routine already in ScaLAPACK. The real-arithmetic version was appropriately modified to make it work with complex arithmetic and implement a complex multiple bulge QR algorithm. This also required the development of new auxiliary routines that perform essential operations for the complex Schur decomposition, and that will provide additional linear algebra computation capability to the parallel numerical library community.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Baglama:2003:AIM, author = "J. Baglama and D. Calvetti and L. Reichel", title = "{Algorithm 827}: {{\tt irbleigs}}: {A MATLAB} program for computing a few eigenpairs of a large sparse {Hermitian} matrix", journal = j-TOMS, volume = "29", number = "3", pages = "337--348", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838257", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\tt irbleigs} is a MATLAB program for computing a few eigenvalues and associated eigenvectors of a sparse Hermitian matrix of large order $n$. The matrix is accessed only through the evaluation of matrix-vector products. Working space of only a few n-vectors is required. The program implements a restarted block-Lanczos method. Judicious choices of acceleration polynomials make it possible to compute approximations of a few of the largest eigenvalues, a few of the smallest eigenvalues, or a few eigenvalues in the vicinity of a user-specified point on the real axis. {\tt irbleigs} also can be applied to certain large generalized eigenproblems as well as to the computation of a few nearby singular values and associated right and left singular vectors of a large general matrix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hopkins:2003:RAF, author = "Tim Hopkins", title = "Remark on {Algorithm 769}: {Fortran} subroutines for approximate solution of sparse quadratic assignment problems using {GRASP}", journal = j-TOMS, volume = "29", number = "3", pages = "349--351", month = sep, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/838250.838258", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 7 14:01:48 MDT 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a number of corrections and improvements to Algorithm 769 [Pardalos et al. 1997].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2003:GLT, author = "Nicholas I. M. Gould and Dominique Orban and Philippe L. Toint", title = "{GALAHAD}, a library of thread-safe {Fortran 90} packages for large-scale nonlinear optimization", journal = j-TOMS, volume = "29", number = "4", pages = "353--372", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962438", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for large-scale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set algorithms, as well as tools for preprocessing problems prior to solution. It also contains an updated version of the venerable nonlinear programming package, LANCELOT.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2003:CSC, author = "Nicholas I. M. Gould and Dominique Orban and Philippe L. Toint", title = "{CUTEr} and {SifDec}: a constrained and unconstrained testing environment, revisited", journal = j-TOMS, volume = "29", number = "4", pages = "373--394", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962438", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The initial release of CUTE, a widely used testing environment for optimization software, was described by Bongartz, et al. [1995]. A new version, now known as CUTEr, is presented. Features include reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for Unix systems. The environment is fully backward compatible with its predecessor, and offers support for Fortran 90/95 and a general C/C++ Application Programming Interface. The SIF decoder, formerly a part of CUTE, has become a separate tool, easily callable by various packages. It features simple extensions to the SIF test problem format and the generation of files suited to automatic differentiation packages.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2003:PFS, author = "Jennifer A. Scott", title = "Parallel frontal solvers for large sparse linear systems", journal = j-TOMS, volume = "29", number = "4", pages = "395--417", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962440", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Many applications in science and engineering give rise to large sparse linear systems of equations that need to be solved as efficiently as possible. As the size of the problems of interest increases, it can become necessary to consider exploiting multiprocessors to solve these systems. We report on the design and development of parallel frontal solvers for the numerical solution of large sparse linear systems. Three codes have been developed for the mathematical software library HSL (www.cse.clrc.ac.uk/Activity/HSL). The first is for unsymmetric finite-element problems; the second is for symmetric positive definite finite-element problems; and the third is for highly unsymmetric linear systems such as those that arise in chemical process engineering. In each case, the problem is subdivided into a small number of loosely connected subproblems and a frontal method is then applied to each of the subproblems in parallel. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate the performance using problems arising from real applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bradbury:2003:FCS, author = "Emma L. Bradbury and Wayne H. Enright", title = "Fast contouring of solutions to partial differential equations", journal = j-TOMS, volume = "29", number = "4", pages = "418--439", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962441", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The application of Differential Equation Interpolants (DEIs) to the visualization of the solutions to Partial Differential Equations (PDEs) is investigated. In particular, we describe how a DEI can be used to generate a fine mesh approximation from a coarse mesh approximation; this fine mesh approximation can then be used by a standard contouring function to render an accurate contour plot of the surface. However, the standard approach has a time complexity equivalent to that of rendering a surface plot, $O(fm^2)$ for each element of the coarse mesh, (where $fm$ is the ratio of the width of the coarse mesh to the fine mesh). To address this concern three fast contouring algorithms are proposed that compute accurate contour lines directly from the DEI, and have time complexity at most $O(fm)$ for each coarse mesh element.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bucker:2003:MPI, author = "H. Martin B{\"u}cker and Arno Rasch", title = "Modeling the performance of interface contraction", journal = j-TOMS, volume = "29", number = "4", pages = "440--457", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962442", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Automatic differentiation is a technique used to transform a computer code implementing some mathematical function into another program capable of evaluating the function and its derivatives. Compared to numerical differentiation, the derivatives obtained from applying automatic differentiation are free from truncation error, and their computation often requires less time. To increase the efficiency of a black box approach of automatic differentiation, a technique called interface contraction may be used. Interface contraction exploits the local structure of a code to temporarily reduce the global number of derivatives propagated through the code. Two performance models are introduced to predict the potential improvement in the execution time of a program making use of interface contraction compared to a program generated by a black box approach of automatic differentiation. The performance models are validated by numerical experiments carried out on different computing platforms. The computer codes used in the experiments stem from the application areas of neutron scattering and biostatistics.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:2003:ADD, author = "Robert J. Renka", title = "{Algorithm 828}: {DNSPLIN1}: discrete nonlinear spline interpolation", journal = j-TOMS, volume = "29", number = "4", pages = "458--468", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962443", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a new method and a Fortran-77 code for constructing discrete approximations to nonparametric interpolating nonlinear spline curves. Our approach consists of minimizing the discretized strain energy by a descent method with a Sobolev gradient in place of the standard gradient. It serves as a demonstration of the Sobolev gradient method, which is much more generally applicable. The effectiveness of the method in rapidly producing smooth interpolatory curves is demonstrated by test results for several challenging data sets.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gaviano:2003:ASG, author = "Marco Gaviano and Dmitri E. Kvasov and Daniela Lera and Yaroslav D. Sergeyev", title = "{Algorithm 829}: {Software} for generation of classes of test functions with known local and global minima for global optimization", journal = j-TOMS, volume = "29", number = "4", pages = "469--480", month = dec, year = "2003", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/962437.962444", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 5 17:18:49 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gonzalez--Pinto:2004:TSE, author = "S. Gonz{\'a}lez--Pinto and J. I. Montijano and S. P{\'e}rez--Rodr{\'\i}guez", title = "Two-step error estimators for implicit {Runge--Kutta} methods applied to stiff systems", journal = j-TOMS, volume = "30", number = "1", pages = "1--18", month = mar, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/974781.974782", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:45:13 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This paper is concerned with local error estimation in the numerical integration of stiff systems of ordinary differential equations by means of Runge--Kutta methods. With implicit Runge--Kutta methods it is often difficult to embed a local error estimate with the appropriate order and stability properties. In this paper local error estimation based on the information from the last two integration steps (that are supposed to have the same steplength) is proposed. It is shown that this technique, applied to Radau IIA methods, lets us get estimators with proper order and stability properties. Numerical examples showing that the proposed estimate improves the efficiency of the integration codes are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rotkin:2004:DIN, author = "Vladimir Rotkin and Sivan Toledo", title = "The design and implementation of a new out-of-core sparse {Cholesky} factorization method", journal = j-TOMS, volume = "30", number = "1", pages = "19--46", month = mar, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/974781.974783", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:45:13 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a new out-of-core sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtree-scheduling algorithm, and both right-looking and left-looking updates. The implementation of the new method is efficient and robust. On a 2 GHz personal computer with 768 MB of main memory, the code can easily factor matrices with factors of up to 48 GB, usually at rates above 1 Gflop/s. For example, the code can factor audikw, currently the largest matrix in any matrix collection (factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-140 mesh in about 12 hours (factor size around 27 GB).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Vaz:2004:SSI, author = "A. Ismael F. Vaz and Edite M. G. P. Fernandes and M. Paula S. F. Gomes", title = "{SIPAMPL}: {Semi-infinite} programming with {AMPL}", journal = j-TOMS, volume = "30", number = "1", pages = "47--61", month = mar, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/974781.974784", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:45:13 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SIPAMPL is an environment for coding semi-infinite programming (SIP) problems. This environment includes a database containing a set of SIP problems that have been collected from the literature and a set of routines. It allows users to code their own SIP problems in AMPL, to use any problem already in the database, and to develop and test any SIP solver. The SIPAMPL routines support the interface between a potential SIP solver and test problems coded in AMPL. SIPAMPL also provides a tool that allows the selection of problems from the database with specified characteristics. As a concept demonstration, we show how MATLAB can use SIPAMPL to solve the problems in the database. The Linux and Microsoft Windows versions together with the database of coded problems are freely available via the web.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bartlett:2004:VRT, author = "Roscoe A. Bartlett and Bart G. {Van Bloemen Waanders} and Michael A. Heroux", title = "Vector reduction\slash transformation operators", journal = j-TOMS, volume = "30", number = "1", pages = "62--85", month = mar, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/974781.974785", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:45:13 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Development of flexible linear algebra interfaces is an increasingly critical issue. Efficient and expressive interfaces are well established for some linear algebra abstractions, but not for vectors. Vectors differ from other abstractions in the diversity of necessary operations, sometimes requiring dozens for a given algorithm (e.g. interior-point methods for optimization). We discuss a new approach based on operator objects that are transported to the underlying data by the linear algebra library implementation, allowing developers of abstract numerical algorithms to easily extend the functionality regardless of computer architecture, application or data locality\slash organization. Numerical experiments demonstrate efficient implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hanson:2004:AAV, author = "Richard J. Hanson and Tim Hopkins", title = "{Algorithm 830}: {Another} visit with standard and modified {Givens} transformations and a remark on {Algorithm 539}", journal = j-TOMS, volume = "30", number = "1", pages = "86--94", month = mar, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/974781.974786", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 20 13:45:13 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL}.", abstract = "First we report on a correction and improvement to the Level 1 BLAS routine {\tt srotmg} for computing the Modified Givens Transformation (MG). We then, in the light of the performance of the code on modern compiler\slash hardware combinations, reconsider the strategy of supplying separate routines to compute and apply the transformation. Finally, we show that the apparent savings in multiplies obtained by using MG rather than the Standard Givens Transformation (SG) do not always translate into reductions in execution time.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:2004:PDS, author = "Iain S. Duff and Jennifer A. Scott", title = "A parallel direct solver for large sparse highly unsymmetric linear systems", journal = j-TOMS, volume = "30", number = "2", pages = "95--117", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992201", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The need to solve large sparse linear systems of equations efficiently lies at the heart of many applications in computational science and engineering. For very large systems when using direct factorization methods of solution, it can be beneficial and sometimes necessary to use multiple processors, because of increased memory availability as well as reduced factorization time. We report on the development of a new parallel code that is designed to solve linear systems with a highly unsymmetric sparsity structure using a modest number of processors (typically up to about 16). The problem is first subdivided into a number of loosely connected subproblems and a variant of sparse Gaussian elimination is then applied to each of the subproblems in parallel. An interface problem in the variables on the boundaries of the subproblems must also be factorized. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate its performance on an SGI Origin 2000, a Cray T3E, and a 2-processor Compaq DS20, using problems arising from real applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:2004:MCS, author = "Iain S. Duff", title = "{MA57}---a code for the solution of sparse symmetric definite and indefinite systems", journal = j-TOMS, volume = "30", number = "2", pages = "118--144", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992202", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with $2 \times 2$ pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2004:CSM, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing solutions of the modified {Bessel} differential equation for imaginary orders and positive arguments", journal = j-TOMS, volume = "30", number = "2", pages = "145--158", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992203", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' + xw' + (a^2 - x^2)w = 0$. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2004:AMB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 831}: {Modified} {Bessel} functions of imaginary order and positive argument", journal = j-TOMS, volume = "30", number = "2", pages = "159--164", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992204", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $x^2 w'' + xw' + (a^2 - x^2)w = 0$. The code also computes exponentially scaled functions. The range of computation is $(x, a) \in (0,1500] \times [-1500, 1500]$ when scaled functions are considered and it is larger than $(0,500] \times [-400, 400]$ for standard IEEE double precision arithmetic. The relative accuracy is better than $10^{-13}$ in the range $(0,200] \times [-200, 200]$ and close to $10^{-12}$ in $(0, 1500] \times [-1500, 1500]$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2004:CPO, author = "Timothy A. Davis", title = "A column pre-ordering strategy for the unsymmetric-pattern multifrontal method", journal = j-TOMS, volume = "30", number = "2", pages = "165--195", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992205", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-in and then refined during numerical factorization (while preserving the bound). Pivot rows are selected to maintain numerical stability and to preserve sparsity. The method analyzes the matrix and automatically selects one of three pre-ordering and pivoting strategies. The number of nonzeros in the LU factors computed by the method is typically less than or equal to those found by a wide range of unsymmetric sparse LU factorization methods, including left-looking methods and prior multifrontal methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2004:AUV, author = "Timothy A. Davis", title = "{Algorithm 832}: {UMFPACK V4.3}---an unsymmetric-pattern multifrontal method", journal = j-TOMS, volume = "30", number = "2", pages = "196--199", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992206", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations. The simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as $x = A \backslash b$ when $A$ is sparse and unsymmetric.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:2004:ACI, author = "Robert J. Renka", title = "{Algorithm 833}: {CSRFPACK}---interpolation of scattered data with a {$C^1$} convexity-preserving surface", journal = j-TOMS, volume = "30", number = "2", pages = "200--211", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992207", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a Fortran-77 software package for constructing a $C^1$ convex surface that interpolates a convex data set consisting of data values at arbitrarily distributed points in the plane (nodes) such that there exists a triangulation of the nodes for which the triangle-based piecewise linear interpolant is convex. The method consists of constructing this data-dependent triangulation, computing a set of nodal gradients for which there exists a convex piecewise linear Hermite interpolant $H$ of the nodal values and gradients, and applying convolution smoothing to $H$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renka:2004:AGI, author = "Robert J. Renka", title = "{Algorithm 834}: {{\tt glsurf}} --- an interactive surface plotting program using {OpenGL}", journal = j-TOMS, volume = "30", number = "2", pages = "212--217", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992208", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe an interactive surface visualization tool implemented in C, OpenGL, and GLUT. The surface is represented by a set of triangles in Euclidean 3-space, thus allowing for unrestricted topology. Capabilities include color-filled contour plots (for the graph of a bivariate function) and surface perspective plots with lighting and smooth shading. Interactive zooms and axis rotations are executed with a single keypress or mouse motion. The advantage of this code over the many alternatives is that it is small, simple, portable, easy to install and use, and the source code is available if the user wishes to change defaults, add light sources, or whatever.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zeng:2004:AMM, author = "Zhonggang Zeng", title = "{Algorithm 835}: {MultRoot}---a {Matlab} package for computing polynomial roots and multiplicities", journal = j-TOMS, volume = "30", number = "2", pages = "218--236", month = jun, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/992200.992209", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 10 07:24:58 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Matthey:2004:POO, author = "Thierry Matthey and Trevor Cickovski and Scott Hampton and Alice Ko and Qun Ma and Matthew Nyerges and Troy Raeder and Thomas Slabach and Jes{\'u}s A. Izaguirre", title = "{ProtoMol}, an object-oriented framework for prototyping novel algorithms for molecular dynamics", journal = j-TOMS, volume = "30", number = "3", pages = "237--265", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024075", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "ProtoMol is a high-performance framework in C++ for rapid prototyping of novel algorithms for molecular dynamics and related applications. Its flexibility is achieved primarily through the use of inheritance and design patterns (object-oriented programming). Performance is obtained by using templates that enable generation of efficient code for sections critical to performance (generic programming). The framework encapsulates important optimizations that can be used by developers, such as parallelism in the force computation. Its design is based on domain analysis of numerical integrators for molecular dynamics (MD) and of fast solvers for the force computation, particularly due to electrostatic interactions. Several new and efficient algorithms are implemented in ProtoMol. Finally, it is shown that ProtoMol's sequential performance is excellent when compared to a leading MD program, and that it scales well for moderate number of processors. Binaries and source codes for Windows, Linux, Solaris, IRIX, HP-UX, and AIX platforms are available under open source license at http://protomol.sourceforge.net.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Forth:2004:JCG, author = "Shaun A. Forth and Mohamed Tadjouddine and John D. Pryce and John K. Reid", title = "{Jacobian} code generated by source transformation and vertex elimination can be as efficient as hand-coding", journal = j-TOMS, volume = "30", number = "3", pages = "266--299", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024076", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents the first extended set of results from EliAD, a source-transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and Reese, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, 1991, pp. 126--135). We introduce the necessary theory in terms of well known algorithms of numerical linear algebra applied to the linear, extended Jacobian system that prescribes the relationship between the derivatives of all variables in the function code. Using an example, we highlight the potential for numerical instability in vertex-elimination. We describe the source transformation implementation of our tool EliAD and present results from five test cases, four of which are taken from the MINPACK-2 collection (Averick et al, Report ANL/MCS-TM-150, 1992) and for which hand-coded Jacobian codes are available. On five computer/compiler platforms, we show that the Jacobian code obtained by EliAD is as efficient as hand-coded Jacobian code. It is also between 2 to 20 times more efficient than that produced by current, state of the art, Automatic Differentiation tools even when such tools make use of sophisticated techniques such as sparse Jacobian compression. We demonstrate the effectiveness of reverse-ordered pre-elimination from the (successively updated) extended Jacobian system of all intermediate variables used once. Thereafter, the monotonic forward/reverse ordered eliminations of all other intermediates is shown to be very efficient. On only one test case were orderings determined by the Markowitz or related VLR heuristics found superior. A re-ordering of the statements of the Jacobian code, with the aim of reducing reads and writes of data from cache to registers, was found to have mixed effects but could be very beneficial.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2004:NEH, author = "Nicholas I. M. Gould and Jennifer A. Scott", title = "A numerical evaluation of {HSL} packages for the direct solution of large sparse, symmetric linear systems of equations", journal = j-TOMS, volume = "30", number = "3", pages = "300--325", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024077", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In recent years, a number of new direct solvers for the solution of large sparse, symmetric linear systems of equations have been added to the mathematical software library HSL. These include solvers that are designed for the solution of positive-definite systems as well as solvers that are principally intended for solving indefinite problems. The available choice can make it difficult for users to know which solver is the most appropriate for their use. In this study, we use performance profiles as a tool for evaluating and comparing the performance of the HSL solvers on an extensive set of test problems taken from a range of practical applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bai:2004:BTE, author = "Yihua Bai and Wilfried N. Gansterer and Robert C. Ward", title = "Block tridiagonalization of ``effectively'' sparse symmetric matrices", journal = j-TOMS, volume = "30", number = "3", pages = "326--352", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024078", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A block tridiagonalization algorithm is proposed for transforming a sparse (or ``effectively'' sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero or ``effectively zero'' (with respect to the given accuracy tolerance) elements. In the light of a recently developed block tridiagonal divide-and-conquer eigensolver [Gansterer, Ward, Muller, and Goddard, III, SIAM J. Sci. Comput. 25 (2003), pp. 65--85], for which block tridiagonalization may be needed as a preprocessing step, the algorithm also provides an option for attempting to produce at least a few very small diagonal blocks in the block tridiagonal matrix. This leads to low time complexity of the last merging operation in the block divide-and-conquer method. Numerical experiments are presented and various block tridiagonalization strategies are compared.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2004:CAM, author = "Timothy A. Davis and John R. Gilbert and Stefan I. Larimore and Esmond G. Ng", title = "A column approximate minimum degree ordering algorithm", journal = j-TOMS, volume = "30", number = "3", pages = "353--376", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024079", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Sparse Gaussian elimination with partial pivoting computes the factorization $PAQ = LU$ of a sparse matrix $A$, where the row ordering $P$ is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, $Q$, based solely on the nonzero pattern of $A$, that limits the worst-case number of nonzeros in the factorization. The fill-in also depends on $P$, but $Q$ is selected to reduce an upper bound on the fill-in for any subsequent choice of $P$. The choice of $Q$ can have a dramatic impact on the number of nonzeros in $L$ and $U$. One scheme for determining a good column ordering for $A$ is to compute a symmetric ordering that reduces fill-in in the Cholesky factorization of $A^T A$. A conventional minimum degree ordering algorithm would require the sparsity structure of $A^T A$ to be computed, which can be expensive both in terms of space and time since $A^T A$ may be much denser than $A$. An alternative is to compute $Q$ directly from the sparsity structure of $A$; this strategy is used by MATLAB's COLMMD preordering algorithm. A new ordering algorithm, COLAMD, is presented. It is based on the same strategy but uses a better ordering heuristic. COLAMD is faster and computes better orderings, with fewer nonzeros in the factors of the matrix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2004:ACC, author = "Timothy A. Davis and John R. Gilbert and Stefan I. Larimore and Esmond G. Ng", title = "{Algorithm 836}: {COLAMD}, a column approximate minimum degree ordering algorithm", journal = j-TOMS, volume = "30", number = "3", pages = "377--380", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024080", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 29 06:31:52 MDT 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation of both the rows and columns of the matrix being factorized. These orderings are computed by COLAMD and SYMAMD, respectively. The ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices of the form $A^T A$ and $A A^T$, such as those that arise in least-squares problems and interior point methods for linear programming problems. The two routines are available both in MATLAB and C-callable forms. They appear as built-in routines in MATLAB Version 6.0.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amestoy:2004:AAA, author = "Patrick R. Amestoy and Timothy A. Davis and Iain S. Duff", title = "{Algorithm 837}: {AMD}, an approximate minimum degree ordering algorithm", journal = j-TOMS, volume = "30", number = "3", pages = "381--388", month = sep, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1024074.1024081", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (05C85)", MRnumber = "MR2124398", bibdate = "Mon Jan 2 09:11:24 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "AMD is a set of routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. There are versions written in both C and Fortran 77. A MATLAB interface is included.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algorithms; Experimentation; Linear equations; minimum degree; ordering methods; Performance; sparse", } @Article{Priest:2004:ESC, author = "Douglas M. Priest", title = "Efficient scaling for complex division", journal = j-TOMS, volume = "30", number = "4", pages = "389--401", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.109814", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We develop a simple method for scaling to avoid overflow and harmful underflow in complex division. The method guarantees that no overflow will occur unless at least one component of the quotient must overflow, otherwise the normwise error in the computed result is at most a few units in the last place. Moreover, the scaling requires only four floating point multiplications and a small amount of integer arithmetic to compute the scale factor. Thus, on many modern CPUs, our method is both safer and faster than Smith's widely used algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "complex division", } @Article{Nievergelt:2004:AAP, author = "Yves Nievergelt", title = "Analysis and applications of {Priest}'s distillation", journal = j-TOMS, volume = "30", number = "4", pages = "402--433", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039815", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Correcting an infinite loop in Douglas M. Priest's renormalization algorithm, the theory proved here supports streamlined algorithms to resolve the tablemaker's dilemma for the floating-point computation of real and complex sums and dot-products, properly rounded to the ultimate digit. Applications include computations of areas, volumes, and intersections.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Whittle:2004:AIK, author = "Jon Whittle and Johann Schumann", title = "Automating the implementation of {Kalman} filter algorithms", journal = j-TOMS, volume = "30", number = "4", pages = "434--453", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039816", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\tt autofilter} is a tool that generates implementations that solve state estimation problems using Kalman filters. From a high-level, mathematics-based description of a state estimation problem, {\tt autofilter} automatically generates code that computes a statistically optimal estimate using one or more of a number of well-known variants of the Kalman filter algorithm. The problem description may be given in terms of continuous or discrete, linear or nonlinear process and measurement dynamics. From this description, {\tt autofilter} automates many common solution methods (e.g., linearization, discretization) and generates C or Matlab code fully automatically. {\tt autofilter} surpasses toolkit-based programming approaches for Kalman filters because it requires no low-level programming skills (e.g., to ``glue'' together library function calls). {\tt autofilter} raises the level of discourse to the mathematics of the problem at hand rather than the details of what algorithms, data structures, optimizations and so on are required to implement it. An overview of {\tt autofilter} is given along with an example of its practical application to deep space attitude estimation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wang:2004:BBS, author = "R. Wang and P. Keast and P. Muir", title = "{BACOL}: {B}-spline adaptive collocation software for {$1$-D} parabolic {PDEs}", journal = j-TOMS, volume = "30", number = "4", pages = "454--470", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039817", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "BACOL is a new, high quality, robust software package in Fortran 77 for solving one-dimensional parabolic PDEs, which has been shown to be significantly more efficient than any other widely available software package of the same class (to our knowledge), especially for problems with solutions exhibiting rapid spatial variation. A novel feature of this package is that it employs high order, adaptive methods in both time and space, controlling and balancing both spatial and temporal error estimates. The software implements a spline collocation method at Gaussian points, with a B-spline basis, for the spatial discretization. The time integration is performed using a modification of the popular DAE solver, DASSL. Based on the computation of a second, higher order, global solution, a high quality a posteriori spatial error estimate is obtained after each successful time step. The spatial error is controlled by a sophisticated new mesh selection algorithm based on an equidistribution principle. In this article we describe the overall structure of the BACOL package, and in particular the modifications to the DASSL package that improve its performance within BACOL. An example is provided in the online Appendix to illustrate the use of the package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fabijonas:2004:CCA, author = "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver", title = "Computation of complex {Airy} functions and their zeros using asymptotics and the differential equation", journal = j-TOMS, volume = "30", number = "4", pages = "471--490", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039818", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fabijonas:2004:AAF, author = "B. R. Fabijonas", title = "{Algorithm 838}: {Airy} Functions", journal = j-TOMS, volume = "30", number = "4", pages = "491--501", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039819", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2004:AFN, author = "Robert C. Kirby", title = "{Algorithm 839}: {FIAT}, a new paradigm for computing finite element basis functions", journal = j-TOMS, volume = "30", number = "4", pages = "502--516", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039820", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bientinesi:2005:SDD, author = "Paolo Bientinesi and John A. Gunnels and Margaret E. Myers and Enrique S. Quintana-Ort{\'\i} and Robert A. van de Geijn", title = "The science of deriving dense linear algebra algorithms", journal = j-TOMS, volume = "31", number = "1", pages = "1--26", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055532", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we present a systematic approach to the derivation of families of high-performance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is generated. The article is structured so that it can be used as a tutorial for novices. However, the method has been shown to yield new high-performance algorithms for well-studied linear algebra operations and should also be of interest to those who wish to produce best-in-class high-performance codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bientinesi:2005:RLA, author = "Paolo Bientinesi and Enrique S. Quintana-Ort{\'\i} and Robert A. van de Geijn", title = "Representing linear algebra algorithms in code: the {FLAME} application program interfaces", journal = j-TOMS, volume = "31", number = "1", pages = "27--59", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055533", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article, we present a number of Application Program Interfaces (APIs) for coding linear algebra algorithms. On the surface, these APIs for the MATLAB M-script and C programming languages appear to be simple, almost trivial, extensions of those languages. Yet with them, the task of programming and maintaining families of algorithms for a broad spectrum of linear algebra operations is greatly simplified. In combination with our Formal Linear Algebra Methods Environment (FLAME) approach to deriving such families of algorithms, dozens of algorithms for a single linear algebra operation can be derived, verified to be correct, implemented, and tested, often in a matter of minutes per algorithm. Since the algorithms are expressed in code much like they are explained in a classroom setting, these APIs become not just a tool for implementing libraries, but also a valuable tool for teaching the algorithms that are incorporated in the libraries. In combination with an extension of the Parallel Linear Algebra Package (PLAPACK) API, the approach presents a migratory path from algorithm to MATLAB implementation to high-performance sequential implementation to parallel implementation. Finally, the APIs are being used to create a repository of algorithms and implementations for linear algebra operations, the FLAME Interface REpository (FIRE), which already features hundreds of algorithms for dozens of commonly encountered linear algebra operations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gunter:2005:PCC, author = "Brian C. Gunter and Robert A. {Van De Geijn}", title = "Parallel out-of-core computation and updating of the {QR} factorization", journal = j-TOMS, volume = "31", number = "1", pages = "60--78", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055534", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article discusses the high-performance parallel implementation of the computation and updating of QR factorizations of dense matrices, including problems large enough to require out-of-core computation, where the matrix is stored on disk. The algorithms presented here are scalable both in problem size and as the number of processors increases. Implementation using the Parallel Linear Algebra Package (PLAPACK) and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) is discussed. The methods are shown to attain excellent performance, in some cases attaining roughly 80\% of the ``realizable'' peak of the architectures on which the experiments were performed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:2005:UAS, author = "L. F. Shampine and Robert Ketzscher and Shaun A. Forth", title = "Using {AD} to solve {BVPs} in {MATLAB}", journal = j-TOMS, volume = "31", number = "1", pages = "79--94", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055535", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The MATLAB program {\tt bvp4c} solves two--point boundary value problems (BVPs) of considerable generality. The numerical method requires partial derivatives of several kinds. To make solving BVPs as easy as possible, the default in {\tt bvp4c} is to approximate these derivatives with finite differences. The solver is more robust and efficient if analytical derivatives are supplied. In this article we investigate how to use automatic differentiation (AD) to obtain the advantages of analytical derivatives without giving up the convenience of finite differences. In {\tt bvp4cAD} we have approached this ideal by a careful use of the MAD AD tool and some modification of {\tt bvp4c}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dercole:2005:SAD, author = "Fabio Dercole and Yuri A. Kuznetsov", title = "{SlideCont}: an {AUTO97} driver for bifurcation analysis of {Filippov} systems", journal = j-TOMS, volume = "31", number = "1", pages = "95--119", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055536", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SLIDECONT, an AUTO97 driver for sliding bifurcation analysis of discontinuous piecewise-smooth autonomous systems, known as Filippov systems, is described in detail. Sliding bifurcations are those in which some sliding on the discontinuity boundary is critically involved. The software allows for detection and continuation of codimension-1 sliding bifurcations as well as detection of some codimension-2 singularities, with special attention to planar systems ($n = 2$). Some bifurcations are also supported for $n$-dimensional systems. This article gives a brief introduction to Filippov systems, describes the structure of SLIDECONT and all computations supported by SLIDECONT 2.0. Several examples, which are distributed together with the source code of SLIDECONT, are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jin:2005:SFE, author = "Guohua Jin and John Mellor-Crummey", title = "{SFCGen}: a framework for efficient generation of multi-dimensional space-filling curves by recursion", journal = j-TOMS, volume = "31", number = "1", pages = "120--148", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055537", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Because they are continuous and self-similar, space-filling curves have been widely used in mathematics to transform multi-dimensional problems into one-dimensional forms. For scientific applications, reordering computation by certain space-filling curves can significantly improve data reuse because of the locality properties of these curves. However, when space-filling curves are used in programs for reordering data, traversal or indexing of the curves must be efficient. To address this problem, we present the table-driven framework SFCGen to efficiently generate multi-dimensional space-filling curves on the fly. The framework is general and easy enough to be used in any application that can be partitioned recursively in multiple dimensions. We describe a movement specification table, a universal turtle algorithm to enumerate points along a space-filling curve, a table-based indexing algorithm to transform coordinates of a point into its position along the curve and an algorithm to pregenerate the table automatically. As examples, we show how high-dimensional Hilbert, Morton, and Peano curves and a two-dimensional Sierpi{\'n}ski curve can be generated with our algorithms. We present performance results for Hilbert, Morton, and Peano curves and compare the efficiency of our curve generation algorithm with the most recent work on generating Hilbert curves. Our experimental results on three modern microprocessor-based platforms show that SFCGen performs up to 63\% faster than the most recent recursive algorithm on 2D curve generation and up to a factor of 132 faster than two previous byte-oriented non-recursive implementations. On curve indexing, SFCGen performs as much as a factor of three faster than the byte-oriented implementation. Our results on 4D space-filling curves also show that SFCGen scales very well with curve level for higher dimensional spaces.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boyd:2005:ACG, author = "John P. Boyd", title = "{Algorithm 840}: Computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions---prolate elements", journal = j-TOMS, volume = "31", number = "1", pages = "149--165", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055538", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "High order domain decomposition methods using a basis of Legendre polynomials, known variously as ``spectral elements'' or ``$p$-type finite elements,'' have become very popular. Recent studies suggest that accuracy and efficiency can be improved by replacing Legendre polynomials by prolate spheroidal wave functions of zeroth order. In this article, we explain the practicalities of computing all the numbers needed to switch bases: the grid points $x_j$, the quadrature weights $w_j$, and the values of the prolate functions and their derivatives at the grid points. The prolate functions themselves are computed by a Legendre--Galerkin discretization of the prolate differential equation; this yields a symmetric tridiagonal matrix. The prolate functions are then defined by Legendre series whose coefficients are the eigenfunctions of the matrix eigenproblem. The grid points and weights are found simultaneously through a Newton iteration. For large $N$ and $c$, the iteration diverges from a first guess of the Legendre--Lobatto points and weights. Fortunately, the variations of the $x_j$ and $w_j$ with $c$ are well-approximated by a symmetric parabola over the whole range of interest. This makes it possible to bypass the continuation procedures of earlier authors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Howell:2005:ABG, author = "Gary W. Howell and Nadia Diaa", title = "{Algorithm 841}: {BHESS}: {Gaussian} reduction to a similar banded {Hessenberg} form", journal = j-TOMS, volume = "31", number = "1", pages = "166--185", month = mar, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1055531.1055539", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "BHESS uses Gaussian similarity transformations to reduce a general real square matrix to similar upper Hessenberg form. Multipliers are bounded in root mean square by a user-supplied parameter. If the input matrix is not highly nonnormal and the user-supplied tolerance on multipliers is of a size greater than ten, the returned matrix usually has small upper bandwidth. In such a case, eigenvalues of the returned matrix can be determined by the bulge-chasing BR iteration or by Rayleigh quotient iteration. BHESS followed by BR iteration determines a complete spectrum in about one-fifth the time required for orthogonal reduction to Hessenberg form followed by QR iterations. The FORTRAN 77 code provided for BHESS runs efficiently on a cache-based architecture.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Xin:2005:IHB, author = "Jianguo Xin and Katia Pinchedez and Joseph E. Flaherty", title = "Implementation of hierarchical bases in {FEMLAB} for simplicial elements", journal = j-TOMS, volume = "31", number = "2", pages = "187--200", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067968", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the implementation of well-conditioned hierarchical bases for one-dimensional, triangular and tetrahedral elements in finite element FEMLAB software. Using the domain mesh information provided by FEMLAB, we found an easy way to maintain the continuity of solution across the interelement boundaries. The conditionings of the global stiffness matrices of several standard problems are compared with the Lagrange bases and are smaller for all cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Andersen:2005:FPH, author = "Bjarne S. Andersen and John A. Gunnels and Fred G. Gustavson and John K. Reid and Jerzy Wa{\'s}niewski", title = "A fully portable high performance minimal storage hybrid format {Cholesky} algorithm", journal = j-TOMS, volume = "31", number = "2", pages = "201--227", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067969", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code but substantially outperforms it. Furthermore, it compares favorably to using conventional full format (LAPACK) and using the recursive format of Andersen et al. [2001].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fraysse:2005:ASG, author = "Val\'rie Frayss{\'e} and Luc Giraud and Serge Gratton and Julien Langou", title = "{Algorithm 842}: a set of {GMRES} routines for real and complex arithmetics on high performance computers", journal = j-TOMS, volume = "31", number = "2", pages = "228--238", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067970", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and efficiency the GMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning and the dot product computations. For distributed memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, which is a well-known bottleneck of efficiency for the Krylov methods. Either implicit or explicit calculation of the residual at restart are possible depending on the actual cost of the matrix-vector product. Finally the implemented stopping criterion is based on a normwise backward error.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Driscoll:2005:AIS, author = "Tobin A. Driscoll", title = "{Algorithm 843}: {Improvements} to the {Schwarz--Christoffel} toolbox for {MATLAB}", journal = j-TOMS, volume = "31", number = "2", pages = "239--251", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067971", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Schwarz--Christoffel Toolbox (SC Toolbox) for MATLAB, first released in 1994, made possible the interactive creation and visualization of conformal maps to regions bounded by polygons. The most recent release supports new features, including an object-oriented command-line interface model, new algorithms for multiply elongated and multiple-sheeted regions, and a module for solving Laplace's equation on a polygon with Dirichlet and homogeneous Neumann conditions. Brief examples are given to demonstrate the new capabilities.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Berry:2005:ACS, author = "Michael W. Berry and Shakhina A. Pulatova and G. W. Stewart", title = "{Algorithm 844}: {Computing} sparse reduced-rank approximations to sparse matrices", journal = j-TOMS, volume = "31", number = "2", pages = "252--269", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067972", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix $A$. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi-Gram--Schmidt-algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form $(XR11^{-1})(R11 R12)$, where $X$ consists of columns of $A$. The second, the SCR approximation, is of the form the form $A \approx XTYT$, where $X$ and $Y$ consist of columns and rows $A$, and $T$ is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Money:2005:AEM, author = "James H. Money and Qiang Ye", title = "{Algorithm 845}: {EIGIFP}: a {MATLAB} program for solving large symmetric generalized eigenvalue problems", journal = j-TOMS, volume = "31", number = "2", pages = "270--279", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067973", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\tt eigifp} is a MATLAB program for computing a few extreme eigenvalues and eigenvectors of the large symmetric generalized eigenvalue problem $Ax = \lambda Bx$. It is a black-box implementation of an inverse free preconditioned Krylov subspace projection method developed by Golub and Ye [2002]. It has important features that allow it to solve some difficult problems without any input from users. It is particularly suitable for problems where preconditioning by the standard shift-and-invert transformation is not feasible.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boisvert:2005:ISI, author = "Ronald F. Boisvert and L. A. Drummond and Osni A. Marques", title = "Introduction to the special issue on the {Advanced CompuTational Software (ACTS)} collection", journal = j-TOMS, volume = "31", number = "3", pages = "281--281", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089015", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drummond:2005:OAC, author = "L. A. Drummond and O. A. Marques", title = "An overview of the {Advanced CompuTational Software (ACTS)} collection", journal = j-TOMS, volume = "31", number = "3", pages = "282--301", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089016", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The ACTS Collection brings together a number of general-purpose computational tools that were developed by independent research projects mostly funded and supported by the U.S. Department of Energy. These tools tackle a number of common computational issues found in many applications, mainly implementation of numerical algorithms, and support for code development, execution, and optimization. In this article, we introduce the numerical tools in the collection and their functionalities, present a model for developing more complex computational applications on top of ACTS tools, and summarize applications that use these tools. Last, we present a vision of the ACTS project for deployment of the ACTS Collection by the computational sciences community.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2005:OSA, author = "Xiaoye S. Li", title = "An overview of {SuperLU}: {Algorithms}, implementation, and user interface", journal = j-TOMS, volume = "31", number = "3", pages = "302--325", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089017", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We give an overview of the algorithms, design philosophy, and implementation techniques in the software SuperLU, for solving sparse unsymmetric linear systems. In particular, we highlight the differences between the sequential SuperLU (including its multithreaded extension) and parallel SuperLU\_DIST. These include the numerical pivoting strategy, the ordering strategy for preserving sparsity, the ordering in which the updating tasks are performed, the numerical kernel, and the parallelization strategy. Because of the scalability concern, the parallel code is drastically different from the sequential one. We describe the user interfaces of the libraries, and illustrate how to use the libraries most efficiently depending on some matrix characteristics. Finally, we give some examples of how the solver has been used in large-scale scientific applications, and the performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Falgout:2005:PSH, author = "Robert D. Falgout and Jim E. Jones and Ulrike Meier Yang", title = "Pursuing scalability for {\em hypre\/}'s conceptual interfaces", journal = j-TOMS, volume = "31", number = "3", pages = "326--350", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089018", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The software library {\em hypre\/} provides high-performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers as well as conceptual interfaces that allow users to access the library in the way they naturally think about their problems. These interfaces include a stencil-based structured interface (Struct); a semistructured interface (semiStruct), which is appropriate for applications that are mostly structured, for example, block structured grids, composite grids in structured adaptive mesh refinement applications, and overset grids; and a finite element interface (FEI) for unstructured problems, as well as a conventional linear-algebraic interface (IJ). It is extremely important to provide an efficient, scalable implementation of these interfaces in order to support the scalable solvers of the library, especially when using tens of thousands of processors. This article describes the data structures, parallel implementation, and resulting performance of the IJ, Struct and semiStruct interfaces. It investigates their scalability, presents successes as well as pitfalls of some of the approaches and suggests ways of dealing with them.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hernandez:2005:SSF, author = "Vicente Hernandez and Jose E. Roman and Vicente Vidal", title = "{SLEPc}: a scalable and flexible toolkit for the solution of eigenvalue problems", journal = j-TOMS, volume = "31", number = "3", pages = "351--362", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089019", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same programming paradigm. The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic.SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem, and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hindmarsh:2005:SSN, author = "Alan C. Hindmarsh and Peter N. Brown and Keith E. Grant and Steven L. Lee and Radu Serban and Dan E. Shumaker and Carol S. Woodward", title = "{SUNDIALS}: {Suite} of nonlinear and differential\slash algebraic equation solvers", journal = j-TOMS, volume = "31", number = "3", pages = "363--396", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089020", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton--Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Heroux:2005:OTP, author = "Michael A. Heroux and Roscoe A. Bartlett and Vicki E. Howle and Robert J. Hoekstra and Jonathan J. Hu and Tamara G. Kolda and Richard B. Lehoucq and Kevin R. Long and Roger P. Pawlowski and Eric T. Phipps and Andrew G. Salinger and Heidi K. Thornquist and Ray S. Tuminaro and James M. Willenbring and Alan Williams and Kendall S. Stanley", title = "An overview of the {Trilinos} project", journal = j-TOMS, volume = "31", number = "3", pages = "397--423", month = sep, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1089014.1089021", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 5 07:43:35 MDT 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking. Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates high-quality software engineering practices that are increasingly required from simulation software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Castillo:2005:FOO, author = "Paul Castillo and Robert Rieben and Daniel White", title = "{FEMSTER}: an object-oriented class library of high-order discrete differential forms", journal = j-TOMS, volume = "31", number = "4", pages = "425--457", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114269", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FEMSTER is a modular finite element class library for solving three-dimensional problems arising in electromagnetism. The library was designed using a modern geometrical approach based on differential forms (or p-forms) and can be used for high-order spatial discretizations of well-known H(div)- and H(curl)-conforming finite element methods. The software consists of a set of abstract interfaces and concrete classes, providing a framework in which the user is able to add new schemes by reusing the existing classes or by incorporating new user-defined data types.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Naumann:2005:DEF, author = "Uwe Naumann and Jan Riehme", title = "A differentiation-enabled {Fortran 95} compiler", journal = j-TOMS, volume = "31", number = "4", pages = "458--474", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114270", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The availability of first derivatives of vector functions is crucial for the robustness and efficiency of a large number of numerical algorithms. An upcoming new version of the differentiation-enabled NAGWare Fortran 95 compiler is described that uses programming language extensions and a semantic code transformation known as automatic differentiation to provide Jacobians of numerical programs with machine accuracy. We describe a new user interface as well as the relevant algorithmic details. In particular, we focus on the source transformation approach that generates locally optimal gradient code for single assignments by vertex elimination in the linearized computational graph. Extensive tests show the superiority of this method over the current overloading-based approach. The robustness and convenience of the new compiler-feature is illustrated by various case studies.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tang:2005:DNI, author = "Ping Tak Peter Tang", title = "{DFTI} --- a new interface for {Fast Fourier Transform} libraries", journal = j-TOMS, volume = "31", number = "4", pages = "475--507", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114271", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Fast Fourier Transform (FFT) algorithm that calculates the Discrete Fourier Transform (DFT) is one of the major breakthroughs in scientific computing and is now an indispensable tool in a vast number of fields. Unfortunately, software applications that provide fast computation of DFT via FFT differ vastly in functionality and lack uniformity. A widely accepted Applications Programmer Interface (API) for DFT would advance the field of scientific computing significantly. In this article, we present the specification of DFTI, a new interface that combines functionality with ease of use. This API is our strawman proposal toward a common interface for DFT calculations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mu:2005:PMN, author = "Mo Mu", title = "{PDE.Mart}: a network-based problem-solving environment for {PDEs}", journal = j-TOMS, volume = "31", number = "4", pages = "508--531", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114272", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "PDE.Mart is a network-based problem-solving environment (PSE) for solving partial differential equations (PDEs) in numerical simulations and academic research, as well as in educational settings. The client-server protocol consists of a Web-browser-enabled graphical user interface, PDE-GUI, that runs on client machines to manage the server connection, geometric and model specifications, computational method selection, and postprocessing; a server system, PDE-Server, to build computational engines and provide PDE solution services on the host machine; and a library, PDE-LIB, that contains building blocks for developing network-based and PDE-oriented PSEs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ledoux:2005:MMP, author = "V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}", title = "{MATSLISE}: {A MATLAB} package for the numerical solution of {Sturm--Liouville} and {Schr{\"o}dinger} equations", journal = j-TOMS, volume = "31", number = "4", pages = "532--554", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114273", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "MATSLISE is a graphical MATLAB software package for the interactive numerical study of regular Sturm--Liouville problems, one-dimensional Schr{\"o}dinger equations, and radial Schr{\"o}dinger equations with a distorted Coulomb potential. It allows the fast and accurate computation of the eigenvalues and the visualization of the corresponding eigenfunctions. This is realized by making use of the power of high-order piecewise constant perturbation methods, a technique described by Ixaru. For a well-outlined class of problems, the implemented algorithms are more efficient than the well-established SL-solvers SL02f, SLEDGE, SLEIGN, and SLEIGN2, which are included by Pryce in the SLDRIVER code that has been built on top of SLTSTPAK.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gao:2005:AMS, author = "Tangan Gao and T. Y. Li and Mengnien Wu", title = "{Algorithm 846}: {MixedVol}: a software package for mixed-volume computation", journal = j-TOMS, volume = "31", number = "4", pages = "555--560", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114274", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "MixedVol is a C++ software package that computes the mixed volume of n finite subsets of $\mathbb{Z}^n$ or the support of a system of n polynomials in $n$ variables. The software produces the mixed volume as well as the mixed cells. The mixed cells are crucial for solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes for mixed-volume computation in speed by a substantial margin and its memory requirement is very low.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Klimke:2005:ASP, author = "Andreas Klimke and Barbara Wohlmuth", title = "{Algorithm 847}: {Spinterp}: piecewise multilinear hierarchical sparse grid interpolation in {MATLAB}", journal = j-TOMS, volume = "31", number = "4", pages = "561--579", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114275", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic factor. We describe three possible piecewise multilinear hierarchical interpolation schemes in detail and conduct a numerical comparison. Furthermore, we document the features of our sparse grid interpolation software package {\tt spinterp} for MATLAB.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shellman:2005:ARF, author = "Spencer Shellman and K. Sikorski", title = "{Algorithm 848}: a recursive fixed-point algorithm for the infinity-norm case", journal = j-TOMS, volume = "31", number = "4", pages = "580--586", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114276", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications in economics, game theory, and the solution of partial differential equations. PFix computes an approximation that satisfies the residual error criterion, and can also compute an approximation satisfying the absolute error criterion when the Lipschitz constant is less than 1. For functions defined on all rectangular domains, the worst-case complexity of PFix has order equal to the logarithm of the reciprocal of the tolerance, raised to the power of the dimension. Dividing this order expression by the factorial of the dimension yields the order of the worst-case bound for the case of the unit hypercube. PFix is a recursive algorithm, in that it uses solutions to a d-dimensional problem to compute a solution to a $(d + 1)$-dimensional problem. A full analysis of PFix may be found in Shellman and Sikorski [2003b], and a C implementation is available through ACM ToMS.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2005:ACS, author = "Timothy A. Davis", title = "{Algorithm 849}: a concise sparse {Cholesky} factorization package", journal = j-TOMS, volume = "31", number = "4", pages = "587--591", month = dec, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1114268.1114277", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 16 11:39:20 MST 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 executable lines of code. The package is written in C, and includes a MATLAB interface.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Panneton:2006:ILP, author = "Fran{\c{c}}ois Panneton and Pierre L'Ecuyer and Makoto Matsumoto", title = "Improved long-period generators based on linear recurrences modulo $2$", journal = j-TOMS, volume = "32", number = "1", pages = "1--16", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132974", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo $2$. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite optimal in this respect. In this article, we propose new generators of that form with better equidistribution and ``bit-mixing'' properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Guermouche:2006:CMM, author = "Abdou Guermouche and Jean-Yves L'Excellent", title = "Constructing memory-minimizing schedules for multifrontal methods", journal = j-TOMS, volume = "32", number = "1", pages = "17--32", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132975", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We are interested in the memory usage of multifrontal methods. Starting from the algorithms introduced by Liu, we propose new schedules to allocate and process tasks that improve memory usage. This generalizes two existing factorization and memory-allocation schedules by allowing a more flexible task allocation together with a specific tree traversal. We present optimal algorithms for this new class of schedules, and demonstrate experimentally their benefit for some real-world matrices from sparse matrix collections where either the active memory or the total memory is minimized.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Koyuturk:2006:NDB, author = "Mehmet Koyut{\"u}rk and Ananth Grama and Naren Ramakrishnan", title = "Nonorthogonal decomposition of binary matrices for bounded-error data compression and analysis", journal = j-TOMS, volume = "32", number = "1", pages = "33--69", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132976", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents the design and implementation of a software tool, PROXIMUS, for error-bounded approximation of high-dimensional binary attributed datasets based on nonorthogonal decomposition of binary matrices. This tool can be used for analyzing data arising in a variety of domains ranging from commercial to scientific applications. Using a combination of innovative algorithms, novel data structures, and efficient implementation, PROXIMUS demonstrates excellent accuracy, performance, and scalability to large datasets. We experimentally demonstrate these on diverse applications in association rule mining and DNA microarray analysis. In limited beta release, PROXIMUS currently has over 300 installations in over 10 countries.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2006:CRP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing the real parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "70--101", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132977", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Methods for the computation of real parabolic cylinder functions $U(a, x)$, and $V(a, x)$ and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of the order $a$ and the variable $x$ except for the overflow\slash underflow limitations. By factoring the dominant exponential factor, scaled functions can be computed without practical overflow\slash underflow limitations. In an accompanying article we describe the precise domains for these methods and we present the Fortran 90 codes for the computation of these functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2006:ARP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 850}: {Real} parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "102--112", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132978", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions $U(a, x)$, $V(a, x)$ and their derivatives for real $a$ and $x (x \geq 0)$. The code also computes scaled functions. The range of computation for scaled PCFs is practically unrestricted. The aimed relative accuracy for scaled functions is better than $5 \times 10^{14}$. Exceptions to this accuracy are the evaluation of the functions near their zeros and the error caused by the evaluation of trigonometric functions of large arguments when $|a| > x$. The routines always give values for which the Wronskian relation for scaled functions is verified with a relative accuracy better than $5 \times 10^{14}$. The accuracy of the unscaled functions is also better than $5 \times 10^{14}$ for moderate values of $x$ and $a$ (except close to the zeros), while for large $x$ and $a$ the error is dominated by exponential and trigonometric function evaluations. For IEEE standard double precision arithmetic, the accuracy is better than $5 \times 10^{13}$ in the computable range of unscaled PCFs (except close to the zeros).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hager:2006:ACD, author = "William W. Hager and Hongchao Zhang", title = "{Algorithm 851}: {CG\_DESCENT}, a conjugate gradient method with guaranteed descent", journal = j-TOMS, volume = "32", number = "1", pages = "113--137", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132979", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition $g^T_k d_k \leq -7/8 ||g_k||^2$ and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Granvilliers:2006:ARI, author = "Laurent Granvilliers and Fr{\'e}d{\'e}ric Benhamou", title = "{Algorithm 852}: {RealPaver}: an interval solver using constraint satisfaction techniques", journal = j-TOMS, volume = "32", number = "1", pages = "138--156", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132980", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.sciences.univ-nantes.fr/info/perso/permanents/granvil/papers/gbtoms05.pdf", abstract = "RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or nonsquare, sparse or dense, linear, polynomial, or involving transcendental functions. The modeling language permits stating constraint models and tuning parameters of solving algorithms which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, and 3B) are implemented. The distribution includes C sources, executables for different machine architectures, documentation, and benchmarks. The portability is ensured by the GNU C compiler.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Foster:2006:AEA, author = "Leslie Foster and Rajesh Kommu", title = "{Algorithm 853}: an efficient algorithm for solving rank-deficient least squares problems", journal = j-TOMS, volume = "32", number = "1", pages = "157--165", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132981", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require {$O(m n^2)$} operations to solve $\min ||b - Ax||$ where $A$ is an $m$ by $n$ matrix. We present a modification of the LAPACK routine xGELSY that requires $O(m n k)$ operations where $k$ is the effective numerical rank of the matrix $A$. For low rank matrices the modification is an order of magnitude faster than the LAPACK code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hasselman:2006:RAF, author = "Berend Hasselman", title = "Remark on {Algorithm 815}: {FORTRAN} subroutines for computing approximate solutions of feedback set problems using {GRASP}", journal = j-TOMS, volume = "32", number = "1", pages = "166--168", month = mar, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1132973.1132982", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri May 26 06:32:19 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We show that the Fortran source code for Algorithm 815 contains an error and we propose a correction. The error may cause the algorithm to generate incorrect results. We also show that the performance of the corrected algorithm can be improved by a minor adjustment in the code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Joffrain:2006:AHT, author = "Thierry Joffrain and Tze Meng Low and Enrique S. Quintana-Ort{\'\i} and Robert van de Geijn and Field G. {Van Zee}", title = "Accumulating {Householder} transformations, revisited", journal = j-TOMS, volume = "32", number = "2", pages = "169--179", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141886", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A theorem related to the accumulation of Householder transformations into a single orthogonal transformation known as the compact WY transform is presented. It provides a simple characterization of the computation of this transformation and suggests an alternative algorithm for computing it. It also suggests an alternative transformation, the UT transform, with the same utility as the compact WY Transform which requires less computation and has similar stability properties. That alternative transformation was first published over a decade ago but has gone unnoticed by the community.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Quintana-Orti:2006:IPR, author = "Gregorio Quintana-Ort{\'\i} and Robert van de Geijn", title = "Improving the performance of reduction to {Hessenberg} form", journal = j-TOMS, volume = "32", number = "2", pages = "180--194", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141887", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article, a modification of the blocked algorithm for reduction to Hessenberg form is presented that improves performance by shifting more computation from less efficient matrix-vector operations to highly efficient matrix-matrix operations. Significant performance improvements are reported relative to the performance achieved by the current LAPACK implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Forth:2006:EOI, author = "Shaun A. Forth", title = "An efficient overloaded implementation of forward mode automatic differentiation in {MATLAB}", journal = j-TOMS, volume = "32", number = "2", pages = "195--222", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141888", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Mad package described here facilitates the evaluation of first derivatives of multidimensional functions that are defined by computer codes written in MATLAB. The underlying algorithm is the well-known forward mode of automatic differentiation implemented via operator overloading on variables of the class fmad. The main distinguishing feature of this MATLAB implementation is the separation of the linear combination of derivative vectors into a separate derivative vector class derivvec. This allows for the straightforward performance optimization of the overall package. Additionally, by internally using a matrix (two-dimensional) representation of arbitrary dimension directional derivatives, we may utilize MATLAB's sparse matrix class to propagate sparse directional derivatives for MATLAB code which uses arbitrary dimension arrays. On several examples, the package is shown to be more efficient than Verma's ADMAT package [Verma 1998a].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2006:OFL, author = "Robert C. Kirby", title = "Optimizing {FIAT} with {Level 3 BLAS}", journal = j-TOMS, volume = "32", number = "2", pages = "223--235", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141889", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Our previous work on FIAT (Finite Element Automatic Tabulator) developed a ``computational representation theory'' that allowed us to construct arbitrary order instances of a wide range of finite elements, many of which are infrequently used owing to their associated code complexity. In our present work, we further hone this theory by rephrasing most of the internal operations as linear transformations over finite-dimensional Banach spaces. This additional insight has led to increased code granularity and allowed the use of level 3 BLAS operations. This is both a conceptual and a practical development; as the run-time performance of FIAT has been improved multiple orders of magnitude.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brisebarre:2006:CME, author = "Nicolas Brisebarre and Jean-Michel Muller and Arnaud Tisserand", title = "Computing machine-efficient polynomial approximations", journal = j-TOMS, volume = "32", number = "2", pages = "236--256", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141890", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Polynomial approximations are almost always used when implementing functions on a computing system. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite---and sometimes small---number of bits. This is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-$i$ coefficient has at most $m_i$ fractional bits; in other words, it is a rational number with denominator $2^{m_i}$. We provide a general and efficient method for finding the best polynomial approximation under this constraint. Moreover, our method also applies if some other constraints (such as requiring some coefficients to be equal to some predefined constants or minimizing relative error instead of absolute error) are required.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kolonko:2006:SRS, author = "M. Kolonko and D. W{\"a}sch", title = "Sequential reservoir sampling with a nonuniform distribution", journal = j-TOMS, volume = "32", number = "2", pages = "257--273", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141891", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a simple algorithm that allows sampling from a stream of data items without knowing the number of items in advance and without having to store all items in main memory. The sampling distribution may be general, that is, the probability of selecting a data item i may depend on the individual item. The main advantage of the algorithms is that they have to pass through the data items only once to produce a sample of arbitrary size $n$. We give different variants of the algorithm for sampling with and without replacement and analyze their complexity. We generalize earlier results of Knuth on reservoir sampling with a uniform sampling distribution. The general distribution considered here allows us to sample an item with a probability equal to the relative weight (or fitness) of the data item within the whole set of items. Applications include heuristic optimization procedures such as genetic algorithms where solutions are sampled from a population with probability proportional to their fitness.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cameron:2006:MPA, author = "Frank Cameron", title = "A {Matlab} package for automatically generating {Runge--Kutta} trees, order conditions, and truncation error coefficients", journal = j-TOMS, volume = "32", number = "2", pages = "274--298", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141892", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In designing parts of Runge--Kutta methods, order conditions and truncation error coefficients (TECs) are needed. Order conditions and TECs are typically presented as a set of trees combined with rules for producing algebraic expressions from the trees. The tree sets are defined recursively and can be generated by hand only for low orders. This article describes a package of Matlab routines for automatically generating Runge--Kutta trees, order conditions, and TECs. The routines are capable of generating Maple code, Matlab code, or \LaTeX{} expressions for ODEs or DAEs of index 1 and 2. In producing the package, two theoretical problems are tackled: (a) avoiding the repeated generation of the same tree and (b) the efficient storage of TECs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lerch:2006:FFI, author = "Michael Lerch and German Tischler and J{\"u}rgen Wolff Von Gudenberg and Werner Hofschuster and Walter Kr{\"a}mer", title = "{FILIB++}, a fast interval library supporting containment computations", journal = j-TOMS, volume = "32", number = "2", pages = "299--324", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141893", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "filib++ is an extension of the interval library filib originally developed at the University of Karlsruhe. The most important aim of filib is the fast computation of guaranteed bounds for interval versions of a comprehensive set of elementary functions. filib++ extends this library in two aspects. First, it adds a second mode, the extended mode, that extends the exception-free computation mode (using special values to represent infinities and NaNs known from the IEEE floating-point standard 754) to intervals. In this mode, the so-called containment sets are computed to enclose the topological closure of a range of a function over an interval. Second, our new design uses templates and traits classes to obtain an efficient, easily extendable, and portable C++ library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", author-dates = "1952--2014 (WK)", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Demmel:2006:EBE, author = "James Demmel and Yozo Hida and William Kahan and Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy", title = "Error bounds from extra-precise iterative refinement", journal = j-TOMS, volume = "32", number = "2", pages = "325--351", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141894", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the design and testing of an algorithm for iterative refinement of the solution of linear equations where the residual is computed with extra precision. This algorithm was originally proposed in 1948 and analyzed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems. However, two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard has essentially removed the first obstacle. To overcome the second obstacle, we show how the application of iterative refinement can be used to compute an error bound in any norm at small cost and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound. We report extensive test results on over $6.2$ million matrices of dimensions $5$, $10$, $100$, and $1000$. As long as a normwise (componentwise) condition number computed by the algorithm is less than $1/max\{10,\sqrt{n}\}\varepsilon_w$, the computed normwise (componentwise) error bound is at most $2 max\{10, \sqrt{n}\} \cdot \varepsilon_w$, and indeed bounds the true error. Here, $n$ is the matrix dimension and $\varepsilon_w = 2^{-24}$ is the working precision. Residuals were computed in double precision (53 bits of precision). In other words, the algorithm always computed a tiny error at negligible extra cost for most linear systems. For worse conditioned problems (which we can detect using condition estimation), we obtained small correct error bounds in over 90\% of cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Benner:2006:AFS, author = "Peter Benner and Daniel Kressner", title = "{Algorithm 854}: {Fortran 77} subroutines for computing the eigenvalues of {Hamiltonian} matrices {II}", journal = j-TOMS, volume = "32", number = "2", pages = "352--373", month = jun, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1141885.1141895", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Aug 23 10:29:48 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sharp:2006:BSP, author = "Philip W. Sharp", title = "{$N$}-body simulations: {The} performance of some integrators", journal = j-TOMS, volume = "32", number = "3", pages = "375--395", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163642", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe four challenging $N$-body test problems involving the Sun and planets and use them to compare the performance of nine nonsymplectic and two symplectic integrators. Each problem has a long interval of integration and two have non-Newtonian gravitational interactions. The emphasis in our comparison is on the accuracy of the solution, including the phase information produced by nonsympletic methods; the symplectic methods have been included to provide a contrast. Long intervals of integration necessitate small local error tolerances for the nonsymplectic integrators. Among variable-stepsize integrators, RKNINT requires the least CPU time on the two problems with Newtonian interactions and DIVA the least CPU time on the other two problems for the intervals of integration we used. We find that the error growth on some integrations is noticeably slower than predicted by asymptotic analysis of the truncation and round-off error. Our comparisons suggest that the numerical solutions near the end of a billion year simulation in double precision with variable-stepsize nonsymplectic methods would have poor accuracy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sala:2006:OOF, author = "Marzio Sala", title = "An object-oriented framework for the development of scalable parallel multilevel preconditioners", journal = j-TOMS, volume = "32", number = "3", pages = "396--416", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163643", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the design of a high-performance object-oriented framework that enables the rapid development and usage of efficient, scalable, and portable implementations of multilevel preconditioners for distributed sparse real matrices, in both serial and (massively) parallel environments. The main feature of the proposed framework is the use of several programming paradigms for the different implementation layers, with a strong emphasis on object-oriented classes and operator overloading for the top layer, and optimized FORTRAN and C code for the layers underneath. We describe an implementation of the proposed framework that is based on the ML library, the algebraic multilevel preconditioning package of Trilinos, which supports state-of-the-art parallel smoothed aggregation methods, and can be used to define general algebraic and geometric multilevel and multigrid preconditioners and solvers. The article demonstrates that we can take advantage of object-oriented programming and operator overloading to obtain intuitive, easy-to-read, and easy-to-develop codes that are at the same time efficient and scalable. Several numerical experiments obtained on serial and parallel computers show that the overhead required by the object-oriented layer is very modest, therefore allowing developers to focus on the new algorithms they are developing and testing, rather than on implementation details.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2006:CVF, author = "Robert C. Kirby and Anders Logg", title = "A compiler for variational forms", journal = j-TOMS, volume = "32", number = "3", pages = "417--444", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163644", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS Form Compiler (FFC). We present benchmark results for a series of standard variational forms, including the incompressible Navier--Stokes equations and linear elasticity. The speedup compared to the standard quadrature-based approach is impressive; in some cases the speedup is as large as a factor of 1000.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meshar:2006:CSS, author = "Omer Meshar and Dror Irony and Sivan Toledo", title = "An out-of-core sparse symmetric-indefinite factorization method", journal = j-TOMS, volume = "32", number = "3", pages = "445--471", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163645", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a new out-of-core sparse symmetric-indefinite factorization algorithm. The most significant innovation of the new algorithm is a dynamic partitioning method for the sparse factor. This partitioning method results in very low I/O traffic and allows the algorithm to run at high computational rates, even though the factor is stored on a slow disk. Our implementation of the new code compares well with both high-performance in-core sparse symmetric-indefinite codes and a high-performance out-of-core sparse Cholesky code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alhargan:2006:ASC, author = "Fayez A. Alhargan", title = "{Algorithm 855}: {Subroutines} for the computation of {Mathieu} characteristic numbers and their general orders", journal = j-TOMS, volume = "32", number = "3", pages = "472--484", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163646", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A continued fraction function algorithm is developed to evaluate general-order Mathieu characteristic numbers, and a new technique is presented for evaluating the Mathieu determinant which can be used to compute the order directly. Approximate expressions are developed to estimate the orders and Mathieu characteristic numbers for the root, finding algorithms. The algorithms, with minor modifications, were used for computing Mathieu coefficients of general order. The algorithms can deal with a large range of Mathieu characteristic number $c$, real and complex order $\nu$, and parameter $h$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gray:2006:AAA, author = "Genetha A. Gray and Tamara G. Kolda", title = "{Algorithm 856}: {APPSPACK 4.0}: asynchronous parallel pattern search for derivative-free optimization", journal = j-TOMS, volume = "32", number = "3", pages = "485--507", month = sep, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1163641.1163647", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 27 05:51:43 MDT 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "APPSPACK is software for solving unconstrained and bound-constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed via a separate program or script; the code can be run serially or in parallel, regardless of whether the function evaluation itself is parallel; and the software is freely available. We describe the underlying algorithm, data structures, and features of APPSPACK version 4.0, as well as how to use and customize the software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{LEcuyer:2006:ISB, author = "Pierre L'Ecuyer and Richard Simard", title = "Inverting the symmetrical beta distribution", journal = j-TOMS, volume = "32", number = "4", pages = "509--520", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186786", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around $x = 0$ and two around $x = 1/2$) are used to approximate the distribution function, and its inverse is found via Newton's method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kressner:2006:BAR, author = "Daniel Kressner", title = "Block algorithms for reordering standard and generalized {Schur} forms", journal = j-TOMS, volume = "32", number = "4", pages = "521--532", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186787", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Block algorithms for reordering a selected set of eigenvalues in a standard or generalized Schur form are proposed. Efficiency is achieved by delaying orthogonal transformations and (optionally) making use of level 3 BLAS operations. Numerical experiments demonstrate that existing algorithms, as currently implemented in LAPACK, are outperformed by up to a factor of four.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dhillon:2006:DIM, author = "Inderjit S. Dhillon and Beresford N. Parlett and Christof V{\"o}mel", title = "The design and implementation of the {MRRR} algorithm", journal = j-TOMS, volume = "32", number = "4", pages = "533--560", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186788", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In the 1990's, Dhillon and Parlett devised the algorithm of multiple relatively robust representations (MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix $T$ with $O(n^2)$ cost. While previous publications related to MRRR focused on theoretical aspects of the algorithm, a documentation of software issues has been missing. In this article, we discuss the design and implementation of the new MRRR version STEGR that will be included in the next LAPACK release. By giving an algorithmic description of MRRR and identifying governing parameters, we hope to make STEGR more easily accessible and suitable for future performance tuning. Furthermore, this should help users understand design choices and tradeoffs when using the code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Su:2006:APP, author = "Hai-Jun Su and J. Michael McCarthy and Masha Sosonkina and Layne T. Watson", title = "{Algorithm 857}: {POLSYS\_GLP}---a parallel general linear product homotopy code for solving polynomial systems of equations", journal = j-TOMS, volume = "32", number = "4", pages = "561--579", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186789", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked and handling singular solutions have made probability-one homotopy methods even more practical. POLSYS\_GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95-derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS\_PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although finding the optimal GLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS\_GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different GLP structures and their corresponding B{\'e}zout numbers can be systematically explored before committing to root finding.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanDeun:2006:ACI, author = "Joris {Van Deun} and Ronald Cools", title = "{Algorithm 858}: {Computing} infinite range integrals of an arbitrary product of {Bessel} functions", journal = j-TOMS, volume = "32", number = "4", pages = "580--596", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186790", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present an algorithm to compute integrals of the form $\int_0^\infty x^m \prod^k_i = 1J_{\nu_i}(a_ix)dx$ with $J_{\nu_i}(x)$ the Bessel function of the first kind and (real) order $\nu_i$. The parameter $m$ is a real number such that $\sum_i \nu_i + m > -1$ and the coefficients $a_i$ are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for $J_{\nu_i}(x)$ and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function $\Gamma(a,z)$. Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amodio:2006:ABF, author = "Pierluigi Amodio and Giuseppe Romanazzi", title = "{Algorithm 859}: {BABDCR}---a {Fortran 90} package for the solution of bordered {ABD} linear systems", journal = j-TOMS, volume = "32", number = "4", pages = "597--608", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186791", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal structure with an additional block in the right upper corner. The algorithm implemented in the package performs cyclic reduction of the coefficient matrix in order to reduce the fill-in due to the corner block.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Goncalves:2006:ASE, author = "Eduardo N. Gon{\c{c}}alves and Reinaldo M. Palhares and Ricardo H. C. Takahashi and Renato C. Mesquita", title = "{Algorithm 860}: {SimpleS}---an extension of {Freudenthal}'s simplex subdivision", journal = j-TOMS, volume = "32", number = "4", pages = "609--621", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186792", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents a simple efficient algorithm for the subdivision of a $d$-dimensional simplex in $k^d$ simplices, where $k$ is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of $k^d$ subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Erricolo:2006:AFS, author = "Danilo Erricolo", title = "{Algorithm 861}: {Fortran 90} subroutines for computing the expansion coefficients of {Mathieu} functions using {Blanch}'s algorithm", journal = j-TOMS, volume = "32", number = "4", pages = "622--634", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186793", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A translation to Fortran 90 of Gertrude Blanch's algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bader:2006:AMT, author = "Brett W. Bader and Tamara G. Kolda", title = "{Algorithm 862}: {MATLAB} tensor classes for fast algorithm prototyping", journal = j-TOMS, volume = "32", number = "4", pages = "635--653", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186794", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Tensors (also known as multidimensional arrays or $N$-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor\_as\_matrix class supports the ``matricization'' of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp\_tensor and tucker\_tensor. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Enright:2007:RRD, author = "W. H. Enright and Wayne B. Hayes", title = "Robust and reliable defect control for {Runge--Kutta} methods", journal = j-TOMS, volume = "33", number = "1", pages = "1:1--1:19", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206041", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The quest for reliable integration of initial value problems (IVPs) for ordinary differential equations (ODEs) is a long-standing problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely with the user to ensure the stepsize chosen is adequate for the desired accuracy. At the other end of the reliability spectrum are rigorous interval-based methods, that can provide provably correct bounds on the error of a numerical solution. This rigour comes at a price, however: interval methods are generally two to three orders of magnitude more expensive than fixed stepsize floating-point methods. Along the spectrum between these two extremes lie various methods of different expense that estimate and control some measure of the local errors and adjust the stepsize accordingly. In this article, we continue previous investigations into a class of interpolants for use in Runge--Kutta methods that have a defect function whose qualitative behavior is asymptotically independent of the problem being integrated. In particular the point, in a step, where the maximum defect occurs as $ h \rightarrow 0 $ is known a priori. This property allows the defect to be monitored and controlled in an efficient and robust manner even for modestly large stepsizes. Our interpolants also have a defect with the highest possible order given the constraints imposed by the order of the underlying discrete formula. We demonstrate the approach on three Runge--Kutta methods of orders 5, 6, and 8, and provide Fortran and preliminary Matlab interfaces to these three new integrators. We also consider how sensitive such methods are to roundoff errors. Numerical results for four problems on a range of accuracy requests are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Neher:2007:CSF, author = "Markus Neher", title = "Complex standard functions and their implementation in the {CoStLy} library", journal = j-TOMS, volume = "33", number = "1", pages = "2:1--2:27", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206042", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The practical calculation of range bounds for some complex standard functions is addressed in this article. The functions under consideration are root and power functions, the exponential, trigonometric and hyperbolic functions, and their inverse functions. For such a function $f$ and a given rectangular complex interval $z$, some interval $w$ is computed that contains all function values of $f$ in $z$. This is done by expressing the real and the imaginary part of $f$ as compositions of real standard functions and then estimating the ranges of these compositions. In many cases, the inclusions are optimal, such that $w$ is the smallest rectangular interval containing the range of $f$. The algorithms presented in this article have been implemented in a C++ class library called CoStLy (Complex Standard Functions License), which is distributed under the conditions of the GNU General Public License.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2007:FFF, author = "Nicholas I. M. Gould and Philippe L. Toint", title = "{FILTRANE}, a {Fortran 95} filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems", journal = j-TOMS, volume = "33", number = "1", pages = "3:1--3:23", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206043", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FILTRANE, a new Fortran 95 package for finding vectors satisfying general sets of nonlinear equations and/or inequalities, is presented. Several algorithmic variants are discussed and extensively compared on a set of CUTEr test problems, indicating that the default variant is both reliable and efficient. This discussion provides a first experimental study of the parameters inherent in filter algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Berland:2007:EMP, author = "H{\aa}vard Berland and B{\aa}rd Skaflestad and Will M. Wright", title = "{EXPINT} --- a {MATLAB} package for exponential integrators", journal = j-TOMS, volume = "33", number = "1", pages = "4:1--4:17", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206044", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Recently, a great deal of attention has been focused on the construction of exponential integrators for semilinear problems. In this article we describe a MATLAB1 package which aims to facilitate the quick deployment and testing of exponential integrators, of Runge--Kutta, multistep, and general linear type. A large number of integrators are included in this package along with several well-known examples. The so-called $ \varphi $ functions and their evaluation is crucial for accuracy, stability, and efficiency of exponential integrators, and the approach taken here is through a modification of the scaling and squaring technique, the most common approach used for computing the matrix exponential.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morandini:2007:UDS, author = "Marco Morandini and Paolo Mantegazza", title = "Using dense storage to solve small sparse linear systems", journal = j-TOMS, volume = "33", number = "1", pages = "5:1--5:12", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206045", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A data structure is used to build a linear solver specialized for relatively small sparse systems. The proposed solver, optimized for run-time performance at the expense of memory footprint, outperforms widely used direct and sparse solvers for systems with between 100 and 3000 equations. A multithreaded version of the solver is shown to give some speedups for problems with medium fill-in, while it does not give any benefit for very sparse problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Demetriou:2007:ALF, author = "Ioannis C. Demetriou", title = "{Algorithm 863}: {L2WPMA}, a {Fortran 77} package for weighted least-squares piecewise monotonic data approximation", journal = j-TOMS, volume = "33", number = "1", pages = "6:1--6:19", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206046", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fortran software is developed that calculates a best piecewise monotonic approximation to $n$ univariate data contaminated by random errors. The underlying method minimizes the weighted sum of the squares of the errors by requiring $ k - 1 $ sign changes in the first divided differences of the approximation, where $k$ is a given positive integer. Hence, the piecewise linear interpolant to the fit consists of $k$ monotonic sections, alternately increasing and decreasing. This calculation can have about $ O(n^k) $ local minima, because the positions of the turning points of the fit are integer variables of the problem. The method, however, by employing a dynamic programming technique divides the data into at most $k$ disjoint sets of adjacent data and solves a $ k = 1 $ problem (monotonic fit or isotonic regression) for each set. So it calculates efficiently a global solution in only $ O(n \sigma + k \sigma^2) $ computer operations when $ k \geq 3 $, where $ \sigma $ is the number of local minima of the data, always bounded by $ n / 2 $. This complexity reduces to only $ O(n) $ when $ k = 1 $ or $ k = 2 $ (unimodal case). At the end of the calculation a spline representation of the solution and the corresponding Lagrange multipliers are provided. The software package has been tested on a variety of data sets showing a performance that does provide in practice shorter computation times than the complexity indicates in theory. An application of the method on identifying turning points and monotonic trends of data from 1947--1996 on the U.K. pound over the U.S. dollar exchange rate is presented. Generally, the method may have useful applications as, for example, in estimating the turning points of a function from some noisy measurements of its values, or in image and signal processing, or in providing a preliminary or complementary smoothing phase to further analyses of the data.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Martello:2007:AGR, author = "Silvano Martello and David Pisinger and Daniele Vigo and Edgar Den Boef and Jan Korst", title = "{Algorithm 864}: {General} and robot-packable variants of the three-dimensional bin packing problem", journal = j-TOMS, volume = "33", number = "1", pages = "7:1--7:12", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206047", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider the problem of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of three-dimensional rectangular bins. The problem is NP-hard in the strong sense and extremely difficult to solve in practice. We characterize relevant subclasses of packing and present an algorithm which is able to solve moderately large instances to optimality. Extensive computational experiments compare the algorithm for the three-dimensional bin packing when solving general orthogonal packings and when restricted to robot packings.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gustavson:2007:AFS, author = "Fred G. Gustavson and John K. Reid and Jerzy Wa{\'s}niewski", title = "{Algorithm 865}: {Fortran 95} subroutines for {Cholesky} factorization in block hybrid format", journal = j-TOMS, volume = "33", number = "1", pages = "8:1--8:5", month = mar, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1206040.1206048", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Apr 14 09:48:58 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into $ n(n + 1) / 2 $ real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage ($ n^2 $ variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zhang:2007:SSI, author = "Hong Zhang and Barry Smith and Michael Sternberg and Peter Zapol", title = "{SIPs}: Shift-and-invert parallel spectral transformations", journal = j-TOMS, volume = "33", number = "2", pages = "1--19", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236464", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SIPs is a new efficient and robust software package implementing multiple shift-and-invert spectral transformations on parallel computers. Built on top of SLEPc and PETSc, it can compute very large numbers of eigenpairs for sparse symmetric generalized eigenvalue problems. The development of SIPs is motivated by applications in nanoscale materials modeling, in which the growing size of the matrices and the pathological eigenvalue distribution challenge the efficiency and robustness of the solver. In this article, we present a parallel eigenvalue algorithm based on distributed spectrum slicing. We describe the object-oriented design and implementation techniques in SIPs, and demonstrate its numerical performance on an advanced distributed computer.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2007:NES, author = "Nicholas I. M. Gould and Jennifer A. Scott and Yifan Hu", title = "A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations", journal = j-TOMS, volume = "33", number = "2", pages = "1--32", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236465", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In recent years a number of solvers for the direct solution of large sparse symmetric linear systems of equations have been developed. These include solvers that are designed for the solution of positive definite systems as well as those that are principally intended for solving indefinite problems. In this study, we use performance profiles as a tool for evaluating and comparing the performance of serial sparse direct solvers on an extensive set of symmetric test problems taken from a range of practical applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Benson:2007:UGT, author = "Steven Benson and Manojkumar Krishnan and Lois Mcinnes and Jarek Nieplocha and Jason Sarich", title = "Using the {GA} and {TAO} toolkits for solving large-scale optimization problems on parallel computers", journal = j-TOMS, volume = "33", number = "2", pages = "1--21", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Challenges in the scalable solution of large-scale optimization problems include the development of innovative algorithms and efficient tools for parallel data manipulation. This article discusses two complementary toolkits from the collection of Advanced CompuTational Software (ACTS), namely, Global Arrays (GA) for parallel data management and the Toolkit for Advanced Optimization (TAO), which have been integrated to support large-scale scientific applications of unconstrained and bound constrained minimization problems. Most likely to benefit are minimization problems arising in classical molecular dynamics, free energy simulations, and other applications where the coupling among variables requires dense data structures. TAO uses abstractions for vectors and matrices so that its optimization algorithms can easily interface to distributed data management and linear algebra capabilities implemented in the GA library. The GA/TAO interfaces are available both in the traditional library mode and as components compliant with the Common Component Architecture (CCA). We highlight the design of each toolkit, describe the interfaces between them, and demonstrate their use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meza:2007:OPO, author = "J. C. Meza and R. A. Oliva and P. D. Hough and P. J. Williams", title = "{OPT++}: an object-oriented toolkit for nonlinear optimization", journal = j-TOMS, volume = "33", number = "2", pages = "1--27", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Object-oriented programming is a relatively new tool in the development of optimization software. The code extensibility and the rapid algorithm prototyping capability enabled by this programming paradigm promise to enhance the reliability, utility, and ease of use of optimization software. While the use of object-oriented programming is growing, there are still few examples of general purpose codes written in this manner, and a common approach is far from obvious. This paper describes OPT++, a C++ class library for nonlinear optimization. The design is predicated on the concept of distinguishing between an algorithm-independent class hierarchy for nonlinear optimization problems and a class hierarchy for nonlinear optimization methods that is based on common algorithmic traits. The interface is designed for ease of use while being general enough so that new optimization algorithms can be added easily to the existing framework. A number of nonlinear optimization algorithms have been implemented in OPT++ and are accessible through this interface. Furthermore, example applications demonstrate the simplicity of the interface as well as the advantages of a common interface in comparing multiple algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fousse:2007:MMP, author = "Laurent Fousse and Guillaume Hanrot and Vincent Lef{\`e}vre and Patrick P{\'e}lissier and Paul Zimmermann", title = "{MPFR}: a multiple-precision binary floating-point library with correct rounding", journal = j-TOMS, volume = "33", number = "2", pages = "1--15", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236468", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65G99", MRnumber = "MR2326955", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these strong semantics are achieved---with no significant slowdown with respect to other arbitrary-precision tools---and discuss a few applications where such a library can be useful.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Elman:2007:AIM, author = "Howard C. Elman and Alison Ramage and David J. Silvester", title = "{Algorithm 866}: {IFISS}, a {Matlab} toolbox for modelling incompressible flow", journal = j-TOMS, volume = "33", number = "2", pages = "1--18", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236469", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "IFISS is a graphical Matlab package for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions. The package can also be used as a computational laboratory for experimenting with state-of-the-art preconditioned iterative solvers for the discrete linear equation systems that arise in incompressible flow modelling. A unique feature of the package is its comprehensive nature; for each problem addressed, it enables the study of both discretization and iterative solution algorithms as well as the interaction between the two and the resulting effect on overall efficiency.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Crouse:2007:RAG, author = "David F. Crouse", title = "Remark on {Algorithm 515}: {Generation} of a vector from the lexicographical index combinations", journal = j-TOMS, volume = "33", number = "2", pages = "1--2", month = jun, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1236463.1236470", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jul 26 17:36:59 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a correction to Algorithm 515 [Buckles and Lybanon 1977].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rioux:2007:ANF, author = "J. Rioux and M. Halse and E. Aubanel and B. J. Balcom and J. Kaffanke and S. Romanzetti and T. Dierkes and N. J. Shah", title = "An accurate nonuniform {Fourier} transform for {SPRITE} magnetic resonance imaging data", journal = j-TOMS, volume = "33", number = "3", pages = "16:1--16:21", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268770", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new algorithm is proposed for computing the discrete Fourier Transform (DFT) of purely phase encoded data acquired during Magnetic Resonance Imaging (MRI) experiments. These experiments use the SPRITE (Single Point Ramped Imaging with $T_1$ Enhancement) method and multiple-point acquisition, sampling data in a nonuniform manner that prohibits reconstruction by fast Fourier transform. The chirp $z$-transform algorithm of Rabiner, Schafer, and Rader can be combined with phase corrections to compute the DFT of this data to extremely high accuracy. This algorithm outperforms the interpolation methods that are traditionally used to process nonuniform data, both in terms of execution time and in terms of accuracy as compared to the DFT.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2007:ECC, author = "Robert C. Kirby and Anders Logg", title = "Efficient compilation of a class of variational forms", journal = j-TOMS, volume = "33", number = "3", pages = "17:1--17:20", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268771", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2007:ESD, author = "Jennifer A. Scott and Yifan Hu", title = "Experiences of sparse direct symmetric solvers", journal = j-TOMS, volume = "33", number = "3", pages = "18:1--18:28", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We recently carried out an extensive comparison of the performance of state-of-the-art sparse direct solvers for the numerical solution of symmetric linear systems of equations. Some of these solvers were written primarily as research codes while others have been developed for commercial use. Our experiences of using the different packages to solve a wide range of problems arising from real applications were mixed. In this paper, we highlight some of these experiences with the aim of providing advice to both software developers and users of sparse direct solvers. We discuss key features that a direct solver should offer and conclude that while performance is an essential factor to consider when choosing a code, there are other features that a user should also consider looking for that vary significantly between packages.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ball:2007:EGR, author = "James S. Ball and Nelson H. F. Beebe", title = "Efficient {Gauss}-related quadrature for two classes of logarithmic weight functions", journal = j-TOMS, volume = "33", number = "3", pages = "19:1--19:21", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268773", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Integrals with logarithmic singularities are often difficult to evaluate by numerical methods. In this work, a quadrature method is developed that allows the exact evaluation (up to machine accuracy) of integrals of polynomials with two general types of logarithmic weights.\par The total work for the determination of $N$ nodes and points of the quadrature method is $O(N^2)$. Subsequently, integrals can be evaluated with $O(N)$ operations and function evaluations, so the quadrature is efficient.\par This quadrature method can then be used to generate the nonclassical orthogonal polynomials for weight functions containing logarithms and obtain Gauss and Gauss-related quadratures for these weights. Two algorithms for each of the two types of logarithmic weights that incorporate these methods are given in this paper.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Beebe:2007:AQP, author = "Nelson H. F. Beebe and James S. Ball", title = "{Algorithm 867}: {QUADLOG}---a package of routines for generating {Gauss}-related quadrature for two classes of logarithmic weight functions", journal = j-TOMS, volume = "33", number = "3", pages = "20:1--20:30", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A collection of subroutines and examples of their uses are described for the quadrature method developed in the companion article. These allow the exact evaluation (up to computer truncation and rounding errors) of integrals of polynomials with two general types of logarithmic weights, and also with the corresponding nonlogarithmic weights. The recurrence coefficients for the related nonclassical orthogonal polynomials with logarithmic weight functions can also be obtained. Tests of accuracy on various platforms are presented.\par The routines are usable from Fortran, C, and C++ programs conforming to any of at least six international programming-language standards.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Espelid:2007:AGD, author = "Terje O. Espelid", title = "{Algorithm 868}: {Globally} doubly adaptive quadrature---reliable {Matlab} codes", journal = j-TOMS, volume = "33", number = "3", pages = "21:1--21:21", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268769.1268775", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 5 14:34:54 MDT 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss how to modify a recently published Matlab code, {\tt coteglob}, so that the excellent performance this code demonstrates for low and intermediate accuracy requests is retained while the performance is improved for high accuracy requests. {\tt coteglob} is a globally adaptive code using a 5 and 9 point pair of Newton--Cotes rules. Combining an extended sequence of rules using 5, 9, 17 and 33 points with a doubly adaptive bisection strategy is the main focus of the paper. We also discuss local versus global adaptivity and conclude that globally adaptive codes are to be preferred. Based on this we develop several new globally adaptive codes that all compare favorably both with {\tt coteglob}, with Matlab's best currently available quadrature software {\tt quadl} and the general purpose QUADPACK codes {\tt dqk15} and {\tt dqk21}. We include the results from extensive testing using both a Lyness--Kaganove testing technique and a battery test.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{LEcuyer:2007:TCL, author = "Pierre L'Ecuyer and Richard Simard", title = "{TestU01}: {A C} library for empirical testing of random number generators", journal = j-TOMS, volume = "33", number = "4", pages = "22:1--22:40", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268777", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the article provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pesch:2007:HSF, author = "Lars Pesch and Alexander Bell and Henk Sollie and Vijaya R. Ambati and Onno Bokhove and Jaap J. W. {Van Der Vegt}", title = "{hpGEM} --- a software framework for discontinuous {Galerkin} finite element methods", journal = j-TOMS, volume = "33", number = "4", pages = "23:1--23:25", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268778", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods (FEMs), is described. We present data structures and methods that are common for many (discontinuous) FEMs and show how we have implemented the components as an object-oriented framework. This framework facilitates and accelerates the implementation of finite element programs, the assessment of algorithms, and their application to real-world problems. The article documents the status of the framework, exemplifies aspects of its philosophy and design, and demonstrates the feasibility of the approach with several application examples.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bangerth:2007:DIG, author = "W. Bangerth and R. Hartmann and G. Kanschat", title = "{deal.II} --- a general-purpose object-oriented finite element library", journal = j-TOMS, volume = "33", number = "4", pages = "24:1--24:27", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268779", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this approach, deal.II supports a large number of different applications covering a wide range of scientific areas, programming methodologies, and application-specific algorithms, without imposing a rigid framework into which they have to fit. A judicious use of programming techniques allows us to avoid the computational costs frequently associated with abstract object-oriented class libraries.\par The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools. Finally, some results obtained with applications built atop deal.II are shown to demonstrate the powerful capabilities of this toolbox.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bai:2007:PSB, author = "Yihua Bai and Robert C. Ward", title = "A parallel symmetric block-tridiagonal divide-and-conquer algorithm", journal = j-TOMS, volume = "33", number = "4", pages = "25:1--25:23", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268780", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigensolutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to achieve data distribution and workload balance. Numerical tests show that our implementation is efficient, scalable and computes eigenpairs to prescribed accuracy. We compare the performance of our parallel eigensolver with that of the ScaLAPACK divide-and-conquer eigensolver on block-tridiagonal matrices.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shampine:2007:AND, author = "L. F. Shampine", title = "Accurate numerical derivatives in {MATLAB}", journal = j-TOMS, volume = "33", number = "4", pages = "26:1--26:17", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268781", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Complex step differentiation (CSD) is a technique for computing very accurate numerical derivatives in languages that support complex arithmetic. We describe here the development of a CSD package in MATLAB called PMAD. We have extended work done in other languages for scalars to the arrays that are fundamental to MATLAB. This extension raises questions that we have been able to resolve in a satisfactory way. Our goal has been to make it as easy as possible to compute approximate Jacobians in MATLAB that are all but exact. Although PMAD has a fast option for the expert that implements CSD as in previous work, the default is an object-oriented implementation that asks very little of the user.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zwolak:2007:AOW, author = "Jason W. Zwolak and Paul T. Boggs and Layne T. Watson", title = "{Algorithm 869}: {ODRPACK95}: a weighted orthogonal distance regression code with bound constraints", journal = j-TOMS, volume = "33", number = "4", pages = "27:1--27:12", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268782", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and many more features. The foundation for the algorithm is a stable and efficient trust region Levenberg--Marquardt minimizer that exploits the structure of the orthogonal distance regression problem. ODRPACK95 was created to extend the functionality and usability of ODRPACK. ODRPACK95 adds bound constraints, uses the newer Fortran 95 language, and simplifies the interface to the user called subroutine.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kodama:2007:RA, author = "Masao Kodama", title = "Remark on {Algorithm 644}", journal = j-TOMS, volume = "33", number = "4", pages = "28:1--28:3", month = aug, year = "2007", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1268776.1268783", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Dec 17 18:09:13 MST 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Amos:1986:APP,Amos:1990:RPP,Amos:1995:RAP}.", abstract = "This remark details correction for errors in the functions which compute the modified Bessel function of the second kind and the log of the gamma function. In both cases these errors cause a loss of precision for a small range of values of the $\nu$ argument. These routines are used in the calculation of a number of other functions within the package whose accuracy is thus similarly affected.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kressner:2008:BVH, author = "Daniel Kressner", title = "Block variants of {Hammarling}'s method for solving {Lyapunov} equations", journal = j-TOMS, volume = "34", number = "1", pages = "1:1--1:15", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322437", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article is concerned with the efficient numerical solution of the Lyapunov equation $A^T X + XA = -C$ with a stable matrix $A$ and a symmetric positive semidefinite matrix $C$ of possibly small rank. We discuss the efficient implementation of Hammarling's method and propose among other algorithmic improvements a block variant, which is demonstrated to perform significantly better than existing implementations. An extension to the discrete-time Lyapunov equation $A^T X A - X = -C$ is also described.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rouson:2008:GFA, author = "Damian W. I. Rouson and Robert Rosenberg and Xiaofeng Xu and Irene Moulitsas and Stavros C. Kassinos", title = "A grid-free abstraction of the {Navier--Stokes} equations in {Fortran 95\slash 2003}", journal = j-TOMS, volume = "34", number = "1", pages = "2:1--2:33", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322438", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Computational complexity theory inspires a grid-free abstraction of the Navier--Stokes equations in Fortran 95/2003. A novel complexity analysis estimates that structured programming time grows at least quadratically with the number of program lines. Further analysis demonstrates how an object-oriented strategy focused on mathematical objects renders the quadratic estimate scale-invariant, so the time required for the limiting factor in program development (debugging) no longer grows as the code grows. Compared to the coordinate-free C++ programming of Grant et al. [2000], grid-free Fortran programming eliminates a layer of procedure calls, eliminates a related need for the C++ template construct, and offers a shorter migration path for Fortran programmers. The grid-free strategy is demonstrated by constructing a physical-space driver for a Fourier-space Navier--Stokes solver. Separating the expression of the continuous mathematical model from the discrete numerics clarifies issues that are otherwise easily conflated. A run-time profile suggests that grid-free design substantially reduces the fraction of the procedures that significantly impact runtime, freeing more code to be structured in ways that reduce development time. Applying Amdahl's law to the total solution time (development time plus run time) leads to a strategy that negligibly impacts development time but achieves 58\% of the maximum possible speedup.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Walther:2008:CSH, author = "Andrea Walther", title = "Computing sparse {Hessians} with automatic differentiation", journal = j-TOMS, volume = "34", number = "1", pages = "3:1--3:15", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322439", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new approach for computing a sparsity pattern for a Hessian is presented: nonlinearity information is propagated through the function evaluation yielding the nonzero structure. A complexity analysis of the proposed algorithm is given. Once the sparsity pattern is available, coloring algorithms can be applied to compute a seed matrix. To evaluate the product of the Hessian and the seed matrix, a vector version for evaluating second order adjoints is analysed. New drivers of ADOL-C are provided implementing the presented algorithms. Runtime analyses are given for some problems of the CUTE collection.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Linardakis:2008:ASG, author = "Leonidas Linardakis and Nikos Chrisochoides", title = "{Algorithm 870}: a static geometric {Medial Axis} domain decomposition in {$2$D} {Euclidean} space", journal = j-TOMS, volume = "34", number = "1", pages = "4:1--4:28", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322440", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a geometric domain decomposition method and its implementation, which produces good domain decompositions in terms of three basic criteria: (1) The boundary of the subdomains create good angles, that is, angles no smaller than a given tolerance $\Phi_0$, where the value of $\Phi_0$ is determined by the application which will use the domain decomposition. (2) The size of the separator should be relatively small compared to the area of the subdomains. (3) The maximum area of the subdomains should be close to the average subdomain area. The domain decomposition method uses an approximation of a Medial Axis as an auxiliary structure for constructing the boundary of the subdomains (separators). The N-way decomposition is based on the ``divide and conquer'' algorithmic paradigm and on a smoothing procedure that eliminates the creation of any new artifacts in the subdomains. This approach produces well shaped uniform and graded domain decompositions, which are suitable for parallel mesh generation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Schreppers:2008:ACC, author = "Walter Schreppers and Annie Cuyt", title = "{Algorithm 871}: a {C\slash C++} precompiler for autogeneration of multiprecision programs", journal = j-TOMS, volume = "34", number = "1", pages = "5:1--5:20", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322441", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In the past decade a number of libraries for multiprecision floating-point arithmetic have been developed. We describe an easy to use, generic C/C++ transcription program or precompiler for the conversion of C or C++ source code into new code that uses a C++ multiprecision library of choice. The precompiler can convert any type in the input source code to another type in the output source code. The input source can be either C or C++, while the output code generated by the precompiler and using the new types, is C++. The type conversion is based on a simple XML configuration file which is provided by either the developer of the multiprecision library or by the user of the precompiler. The precompiler can also convert to data types with additional features, which are not supported in the types of the source code. Applicability of the precompiler is shown with the successful conversion of large subsets of the GNU Scientific Library and Numerical Recipes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chernikov:2008:APC, author = "Andrey N. Chernikov and Nikos P. Chrisochoides", title = "{Algorithm 872}: {Parallel} {$2$D} constrained {Delaunay} mesh generation", journal = j-TOMS, volume = "34", number = "1", pages = "6:1--6:20", month = jan, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1322436.1322442", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Mar 12 17:39:58 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Delaunay refinement is a widely used method for the construction of guaranteed quality triangular and tetrahedral meshes. We present an algorithm and a software for the parallel constrained Delaunay mesh generation in two dimensions. Our approach is based on the decomposition of the original mesh generation problem into $N$ smaller subproblems which are meshed in parallel. The parallel algorithm is asynchronous with small messages which can be aggregated and exhibits low communication costs. On a heterogeneous cluster of more than 100 processors our implementation can generate over one billion triangles in less than 3 minutes, while the single-node performance is comparable to that of the fastest to our knowledge sequential guaranteed quality Delaunay meshing library (the Triangle).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sala:2008:PHP, author = "Marzio Sala and W. F. Spotz and M. A. Heroux", title = "{PyTrilinos}: {High-performance} distributed-memory solvers for {Python}", journal = j-TOMS, volume = "34", number = "2", pages = "7:1--7:33", month = mar, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1326548.1326549", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:47:31 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "PyTrilinos is a collection of Python modules that are useful for serial and parallel scientific computing. This collection contains modules that cover serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, domain decomposition and multilevel preconditioners, nonlinear solvers, and continuation algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms, and matrix generation. PyTrilinos vector objects are integrated with the popular NumPy Python module, gathering together a variety of high-level distributed computing operations with serial vector operations.\par PyTrilinos is a set of interfaces to existing, compiled libraries. This hybrid framework uses Python as front-end, and efficient precompiled libraries for all computationally expensive tasks. Thus, we take advantage of both the flexibility and ease of use of Python, and the efficiency of the underlying C++, C, and FORTRAN numerical kernels. Out numerical results show that, for many important problem classes, the overhead required by the Python interpreter is negligible.\par To run in parallel, PyTrilinos simply requires a standard Python interpreter. The fundamental MPI calls are encapsulated under an abstract layer that manages all interprocessor communications. This makes serial and parallel scripts using PyTrilinos virtually identical.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "direct solvers; multilevel preconditioners; nonlinear solvers; object-oriented programming; script languages", } @Article{Avron:2008:PUP, author = "Haim Avron and Gil Shklarski and Sivan Toledo", title = "Parallel unsymmetric-pattern multifrontal sparse {LU} with column preordering", journal = j-TOMS, volume = "34", number = "2", pages = "8:1--8:31", month = mar, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1326548.1326550", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:47:31 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a new parallel sparse LU factorization algorithm and code. The algorithm uses a column-preordering partial-pivoting unsymmetric-pattern multifrontal approach. Our baseline sequential algorithm is based on UMFPACK 4, but is somewhat simpler and is often somewhat faster than UMFPACK version 4.0. Our parallel algorithm is designed for shared-memory machines with a small or moderate number of processors (we tested it on up to 32 processors). We experimentally compare our algorithm with SuperLU\_MT, an existing shared-memory sparse LU factorization with partial pivoting. SuperLU\_MT scales better than our new algorithm, but our algorithm is more reliable and is usually faster. More specifically, on matrices that are costly to factor, our algorithm is usually faster on up to 4 processors, and is usually faster on 8 and 16. We were not able to run SuperLU\_MT on 32. The main contribution of this article is showing that the column-preordering partial-pivoting unsymmetric-pattern multifrontal approach, developed as a sequential algorithm by Davis in several recent versions of UMFPACK, can be effectively parallelized.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gaussian elimination; multifrontal; unsymmetric", } @Article{Sala:2008:DIS, author = "Marzio Sala and Kendall S. Stanley and Michael A. Heroux", title = "On the design of interfaces to sparse direct solvers", journal = j-TOMS, volume = "34", number = "2", pages = "9:1--9:22", month = mar, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1326548.1326551", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:47:31 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss the design of general, flexible, consistent, reusable, and efficient interfaces to software libraries for the direct solution of systems of linear equations on both serial and distributed memory architectures. We introduce a set of abstract classes to access the linear system matrix elements and their distribution, access vector elements, and control the solution of the linear system.\par We describe a concrete implementation of the proposed interfaces, and report examples of applications and numerical results showing that the overhead induced by the object-oriented design is negligible under typical conditions of usage. We include examples of applications, and we comment on the advantages and limitations of the design.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "direct solver libraries; distributed linear algebra; object-oriented design", } @Article{VanZee:2008:SPF, author = "Field G. {Van Zee} and Paolo Bientinesi and Tze Meng Low and Robert A. van de Geijn", title = "Scalable parallelization of {FLAME} code via the workqueuing model", journal = j-TOMS, volume = "34", number = "2", pages = "10:1--10:29", month = mar, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1326548.1326552", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:47:31 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss the OpenMP parallelization of linear algebra algorithms that are coded using the Formal Linear Algebra Methods Environment (FLAME) API. This API expresses algorithms at a higher level of abstraction, avoids the use loop and array indices, and represents these algorithms as they are formally derived and presented. We report on two implementations of the workqueuing model, neither of which requires the use of explicit indices to specify parallelism. The first implementation uses the experimental {\tt taskq} pragma, which may influence the adoption of a similar construct into OpenMP 3.0. The second workqueuing implementation is domain-specific to FLAME but allows us to illustrate the benefits of sorting tasks according to their computational cost prior to parallel execution. In addition, we discuss how scalable parallelization of dense linear algebra algorithms via OpenMP will require a two-dimensional partitioning of operands much like a 2D data distribution is needed on distributed memory architectures. We illustrate the issues and solutions by discussing the parallelization of the symmetric rank-$k$ update and report impressive performance on an SGI system with 14 Itanium2 processors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "FLAME; OpenMP; parallel; scalability; SMP; workqueuing", } @Article{Rojas:2008:ALM, author = "Marielba Rojas and Sandra A. Santos and Danny C. Sorensen", title = "{Algorithm 873}: {LSTRS}: {MATLAB} software for large-scale trust-region subproblems and regularization", journal = j-TOMS, volume = "34", number = "2", pages = "11:1--11:28", month = mar, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1326548.1326553", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:47:31 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A MATLAB 6.0 implementation of the LSTRS method is presented. LSTRS was described in Rojas et al. [2000]. LSTRS is designed for large-scale quadratic problems with one norm constraint. The method is based on a reformulation of the trust-region subproblem as a parameterized eigenvalue problem, and consists of an iterative procedure that finds the optimal value for the parameter. The adjustment of the parameter requires the solution of a large-scale eigenvalue problem at each step. LSTRS relies on matrix-vector products only and has low and fixed storage requirements, features that make it suitable for large-scale computations. In the MATLAB implementation, the Hessian matrix of the quadratic objective function can be specified either explicitly, or in the form of a matrix-vector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method. A description of the LSTRS method and of the MATLAB software, version 1.2, is presented. Comparisons with other techniques and applications of the method are also included. A guide for using the software and examples are provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ARPACK; constrained quadratic optimization; Lanczos method; MATLAB; regularization; trust-region", } @Article{Goto:2008:AHP, author = "Kazushige Goto and Robert A. van de Geijn", title = "Anatomy of high-performance matrix multiplication", journal = j-TOMS, volume = "34", number = "3", pages = "12:1--12:25", month = may, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1356052.1356053", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:53:20 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. Design decisions are justified by successively refining a model of architectures with multilevel memories. A simple but effective algorithm for executing this operation results. Implementations on a broad selection of architectures are shown to achieve near-peak performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Basic Linear Algebra Subprograms; linear algebra; matrix multiplication", } @Article{Piiroinen:2008:EDM, author = "Petri T. Piiroinen and Yuri A. Kuznetsov", title = "An event-driven method to simulate {Filippov} systems with accurate computing of sliding motions", journal = j-TOMS, volume = "34", number = "3", pages = "13:1--13:24", month = may, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1356052.1356054", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:53:20 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes how to use smooth solvers for simulation of a class of piecewise smooth systems of ordinary differential equations, called Filippov systems, with discontinuous vector fields. In these systems constrained motion along a discontinuity surface (so-called sliding) is possible and requires special treatment numerically. The introduced algorithms are based on an extension to Filippov's method to stabilize the sliding flow together with accurate detection of the entrance and exit of sliding regions. The methods are implemented in a general way in MATLAB and sufficient details are given to enable users to modify the code to run on arbitrary examples. Here, the method is used to compute the dynamics of three example systems, a dry-friction oscillator, a relay feedback system and a model of an oil well drill-string.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Filippov systems; Numerical simulation; piecewise-smooth differential equations; sliding solutions", } @Article{Howell:2008:CEB, author = "Gary W. Howell and James W. Demmel and Charles T. Fulton and Sven Hammarling and Karen Marmol", title = "Cache efficient bidiagonalization using {BLAS 2.5} operators", journal = j-TOMS, volume = "34", number = "3", pages = "14:1--14:33", month = may, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1356052.1356055", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:53:20 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "On cache based computer architectures using current standard algorithms, Householder bidiagonalization requires a significant portion of the execution time for computing matrix singular values and vectors. In this paper we reorganize the sequence of operations for Householder bidiagonalization of a general $m \times n$ matrix, so that two (\_GEMV) vector-matrix multiplications can be done with one pass of the unreduced trailing part of the matrix through cache. Two new BLAS operations approximately cut in half the transfer of data from main memory to cache, reducing execution times by up to 25 per cent. We give detailed algorithm descriptions and compare timings with the current LAPACK bidiagonalization algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bidiagonalization; BLAS 2.5; cache-efficient; Householder reflections; matrix factorization; singular values; SVD", } @Article{Wang:2008:ABS, author = "R. Wang and P. Keast and P. H. Muir", title = "{Algorithm 874}: {BACOLR}-spatial and temporal error control software for {PDEs} based on high-order adaptive collocation", journal = j-TOMS, volume = "34", number = "3", pages = "15:1--15:28", month = may, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1356052.1356056", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:53:20 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we discuss a new software package, BACOLR, for the numerical solution of a general class of time-dependent 1-D PDEs. This package employs high-order adaptive methods in time and space within a method-of-lines approach and provides tolerance control of the spatial and temporal errors. The DAEs resulting from the spatial discretization (based on B-spline collocation) are handled by a substantially modified version of the Runge--Kutta solver, RADAU5. For each time step, the RADAU5 code computes an estimate of the temporal error and requires it to satisfy the user tolerance. After each time step BACOLR then computes a high-order estimate of the spatial error and requires this error estimate to satisfy the user tolerance. BACOLR was developed through a substantial modification of the adaptive method-of-lines package, BACOL. In this article we introduce the BACOLR package and present numerical results to show that the performance of BACOLR is comparable to and in some cases significantly superior to that of BACOL, which was shown in previous work to be more efficient, reliable and robust than other existing codes, especially for problems with solutions exhibiting narrow spikes or boundary layers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "1-D PDEs; adaptive method-of-lines; differential-algebraic equations; Numerical software; Runge--Kutta methods; spatial error control", } @Article{Benson:2008:ADS, author = "Steven J. Benson and Yinyu Ye", title = "{Algorithm 875}: {DSDP5}-software for semidefinite programming", journal = j-TOMS, volume = "34", number = "3", pages = "16:1--16:20", month = may, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1356052.1356057", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 12 12:53:20 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "DSDP implements the dual-scaling algorithm for semidefinite programming. The source code for this interior-point algorithm, written entirely in ANSI C, is freely available under an open source license. The solver can be used as a subroutine library, as a function within the Matlab environment, or as an executable that reads and writes to data files. Initiated in 1997, DSDP has developed into an efficient and robust general-purpose solver for semidefinite programming. Its features include a convergence proof with polynomially bounded worst-case complexity, primal and dual feasible solutions when they exist, certificates of infeasibility when solutions do not exist, initial points that can be feasible or infeasible, relatively low memory requirements for an interior-point method, sparse and low-rank data structures, extensibility that allows applications to customize the solver and improve its performance, a subroutine library that enables it to be linked to larger applications, scalable performance for large problems on parallel architectures, and a well-documented interface and examples of its use. The package has been used in many applications and tested for efficiency, robustness, and ease of use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "conic programming; dual-scaling algorithm; interior-point methods; linear matrix inequalities; semidefinite programming", } @Article{Buttari:2008:UMP, author = "Alfredo Buttari and Jack Dongarra and Jakub Kurzak and Piotr Luszczek and Stanimir Tomov", title = "Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy", journal = j-TOMS, volume = "34", number = "4", pages = "17:1--17:22", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377597", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. These ideas can be applied to sparse multifrontal and supernodal direct techniques and sparse iterative techniques such as Krylov subspace methods. The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the Cell BE processor.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "floating point; iterative refinement; linear systems; precision", } @Article{Utke:2008:OFM, author = "Jean Utke and Uwe Naumann and Mike Fagan and Nathan Tallent and Michelle Strout and Patrick Heimbach and Chris Hill and Carl Wunsch", title = "{OpenAD\slash F}: a Modular Open-Source Tool for Automatic Differentiation of {Fortran} Codes", journal = j-TOMS, volume = "34", number = "4", pages = "18:1--18:36", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377598", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Open/ADF tool allows the evaluation of derivatives of functions defined by a Fortran program. The derivative evaluation is performed by a Fortran code resulting from the analysis and transformation of the original program that defines the function of interest. Open/ADF has been designed with a particular emphasis on modularity, flexibility, and the use of open source components. While the code transformation follows the basic principles of automatic differentiation, the tool implements new algorithmic approaches at various levels, for example, for basic block preaccumulation and call graph reversal. Unlike most other automatic differentiation tools, Open/ADF uses components provided by the Open/AD framework, which supports a comparatively easy extension of the code transformations in a language-independent fashion. It uses code analysis results implemented in the OpenAnalysis component. The interface to the language-independent transformation engine is an XML-based format, specified through an XML schema. The implemented transformation algorithms allow efficient derivative computations using locally optimized cross-country sequences of vertex, edge, and face elimination steps. Specifically, for the generation of adjoint codes, Open/ADF supports various code reversal schemes with hierarchical checkpointing at the subroutine level. As an example from geophysical fluid dynamics, a nonlinear time-dependent scalable, yet simple, barotropic ocean model is considered. OpenAD/F's reverse mode is applied to compute sensitivities of some of the model's transport properties with respect to gridded fields such as bottom topography as independent (control) variables.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "adjoint compiler; Automatic differentiation; source transformation", } @Article{Goldani-Moghaddam:2008:ECU, author = "Hassan Goldani-Moghaddam and Wayne H. Enright", title = "Efficient Contouring on Unstructured Meshes for Partial Differential Equations", journal = j-TOMS, volume = "34", number = "4", pages = "19:1--19:25", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377599", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce three fast contouring algorithms for visualizing the solution of partial differential equations based on the PCI (pure cubic interpolant). The PCI is a particular piecewise bicubic polynomial interpolant defined over an unstructured mesh. Unlike standard contouring approaches, our contouring algorithms do not need a fine-structured approximation and work efficiently with the original scattered data. The basic idea is to first identify the intersection points between contour curves and the sides of each triangle and then draw smooth contour curves connecting these points. We compare these contouring algorithms with the built-in Matlab {\em contour\/} procedure and other contouring algorithms. We demonstrate that our algorithms are both more accurate and faster than the others.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "contour; PDE; scattered data; unstructured mesh; Visualization", } @Article{Gao:2008:IEA, author = "Weiguo Gao and Xiaoye S. Li and Chao Yang and Zhaojun Bai", title = "An Implementation and Evaluation of the {AMLS} Method for Sparse Eigenvalue Problems", journal = j-TOMS, volume = "34", number = "4", pages = "20:1--20:28", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377600", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe an efficient implementation and present a performance study of an automated multi-level substructuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shift-and-invert Lanczos algorithm. Our eigenvalue problems come from two very different application areas: accelerator cavity design and normal-mode vibrational analysis of polyethylene particles. We show that the AMLS method, when implemented carefully, outperforms the traditional method in broad application areas when large numbers of eigenvalues are sought, with relatively low accuracy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "multilevel substructuring; performance evaluation; Sparse eigenvalue problems", } @Article{Atkinson:2008:ASF, author = "Kendall E. Atkinson and Lawrence F. Shampine", title = "{Algorithm 876}: Solving {Fredholm} Integral Equations of the Second Kind in {Matlab}", journal = j-TOMS, volume = "34", number = "4", pages = "21:1--21:20", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377601", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65R20", MRnumber = "MR2474526 (2010a:65281)", bibdate = "Tue Mar 30 17:06:44 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present here the algorithms and user interface of a Matlab program, Fie, that solves numerically Fredholm integral equations of the second kind on an interval $[a,b]$ to a specified, modest accuracy. The kernel function $K(s,t)$ is moderately smooth on $[a,b] \times [a,b]$ except possibly across the diagonal $s = t$. If the interval is finite, provides for kernel functions that behave in a variety of ways across the diagonal, that is, $K(s,t)$ may be smooth, have a discontinuity in a low-order derivative, have a logarithmic singularity, or have an algebraic singularity. Fie also solves a large class of integral equations with moderately smooth kernel function on $[0,\infty)$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Matlab; Numerical solution", } @Article{Kodama:2008:ASP, author = "Masao Kodama", title = "{Algorithm 877}: a Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument", journal = j-TOMS, volume = "34", number = "4", pages = "22:1--22:21", month = jul, year = "2008", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377596.1377602", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 16 11:30:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The algorithm presented provides a package of subroutines for calculating the cylindrical functions $J_\nu(x)$, $N_\nu(x)$, $H_\nu^{1}(x)$, $H_\nu^{2}(x)$ where the order $\nu$ is complex and the real argument $x$ is nonnegative. The algorithm is written in Fortran 95 and calculates the functions using single, double, or quadruple precision according to the value of a parameter defined in the algorithm. The methods of calculating the functions are based on a series expansion, Debye's asymptotic expansions, Olver's asymptotic expansions, and recurrence methods (Miller's algorithms). The relative errors of the functional values computed by this algorithm using double precision are less than $2.4 \times 10^{-13}$ in the region $0 \leq \mbox{Re}(\nu) \leq 64$, $0 \leq \mbox{Im}(\nu) \leq 63$, $0.024 \leq x \leq 97$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Bessel functions; complex order; Cylindrical functions; Debye's asymptotic expansions; Hankel functions; Miller's algorithms; Neumann functions; nonnegative argument; numerical calculation; Olver's asymptotic expansions", } @Article{Bartlett:2009:HDS, author = "Roscoe A. Bartlett and Bart G. {Van Bloemen Waanders} and Martin Berggren", title = "Hybrid differentiation strategies for simulation and analysis of applications in {C++}", journal = j-TOMS, volume = "35", number = "1", pages = "1:1--1:29", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377604", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Computationally efficient and accurate derivatives are important to the success of many different types of numerical methods. Automatic differentiation (AD) approaches compute truncation-free derivatives and can be efficient in many cases. Although present AD tools can provide a convenient implementation mechanism, the computational efficiency rarely compares to analytically derived versions that have been carefully implemented. The focus of this work is to combine the strength of these methods into a hybrid strategy that attempts to achieve an optimal balance of implementation and computational efficiency by selecting the appropriate components of the target algorithms for AD and analytical derivation. Although several AD approaches can be considered, our focus is on the use of template overloading forward AD tools in C++ applications. We demonstrate this hybrid strategy for a system of partial differential equations in gas dynamics. These methods apply however to other systems of differentiable equations, including DAEs and ODEs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; Euler equations; finite volume methods; hybrid differentiation methods; template overloading", } @Article{Naumann:2009:OVE, author = "Uwe Naumann and Yuxiao Hu", title = "Optimal vertex elimination in single-expression-use graphs", journal = j-TOMS, volume = "35", number = "1", pages = "2:1--2:20", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377605", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The source transformation tool for automatic differentiation of Fortran programs ADIFOR uses a preaccumulation technique to speed up tangent-linear codes significantly compared to the standard forward mode. Reverse mode automatic differentiation is applied to all scalar assignments to generate efficient code for the computation of local gradients. It has been well known for some time that reverse mode is not necessarily the optimal choice for the computation of these statement-level gradients as it does not minimize the number of operations required. This article presents an efficient algorithm for the solution of this combinatorial optimization problem. The corresponding software is freely available for downloading on our website. Developers of software for automatic differentiation are invited to integrate the algorithm into their tools.\par Gradients of scalar multivariate functions can be computed by elimination methods on the linearized computational graph. The combinatorial optimization problem that aims to minimize the number of arithmetic operations performed by the elimination algorithm is known to be NP-complete. In this article we present a polynomial algorithm for solving a relevant subclass of this problem's instances. The proposed method relies on the ability to compute vertex covers in bipartite graphs in polynomial time. A simplified version of this graph algorithm is used in a research prototype of the differentiation-enabled NAGWare Fortran compiler for the preaccumulation of local gradients of scalar assignments in the context of automatic generation of efficient tangent-linear code for numerical programs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "single-expression-use graph; vertex elimination", } @Article{Bientinesi:2009:FAR, author = "Paolo Bientinesi and Brian Gunter and Robert A. van de Geijn", title = "Families of algorithms related to the inversion of a {Symmetric Positive Definite} matrix", journal = j-TOMS, volume = "35", number = "1", pages = "3:1--3:22", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377606", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three ``sweeps'': a Cholesky factorization of the SPD matrix, the inversion of the resulting triangular matrix, and finally the multiplication of the inverted triangular matrix by its own transpose. We state different algorithms for each of these sweeps as well as algorithms that compute the result in a single sweep. One algorithm outperforms the current ScaLAPACK implementation by 20--30 percent due to improved load-balance on a distributed memory architecture.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "inversion; libraries; linear algebra; symmetric positive definite", } @Article{Goto:2009:HPI, author = "Kazushige Goto and Robert {Van De Geijn}", title = "High-performance implementation of the level-3 {BLAS}", journal = j-TOMS, volume = "35", number = "1", pages = "4:1--4:14", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377607", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A simple but highly effective approach for transforming high-performance implementations on cache-based architectures of matrix-matrix multiplication into implementations of other commonly used matrix-matrix computations (the level-3 BLAS) is presented. Exceptional performance is demonstrated on various architectures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "basic linear algebra subprograms; libraries; linear algebra; matrix-matrix operations", } @Article{Jonasson:2009:EEV, author = "Kristjan Jonasson and Sebastian E. Ferrando", title = "Evaluating exact {VARMA} likelihood and its gradient when data are incomplete", journal = j-TOMS, volume = "35", number = "1", pages = "5:1--5:16", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377608", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A detailed description of an algorithm for the evaluation and differentiation of the likelihood function for VARMA processes in the general case of missing values is presented. The method is based on combining the Cholesky decomposition method for complete data VARMA evaluation and the Sherman--Morrison--Woodbury formula. Potential saving for pure VAR processes is discussed and formulae for the estimation of missing values and shocks are provided. A theorem on the determinant of a low rank update is proved. Matlab implementation of the algorithm is in a companion article.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ARMA; determinant of low rank update; exact likelihood function; incomplete data; matrix derivative; matrix differentiation; missing values; VARMA; vector autoregressive moving average model", } @Article{Jonasson:2009:AEV, author = "Kristjan Jonasson", title = "{Algorithm 878}: {Exact VARMA} likelihood and its gradient for complete and incomplete data with {Matlab}", journal = j-TOMS, volume = "35", number = "1", pages = "6:1--6:11", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377609", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Matlab functions for the evaluation of the exact log-likelihood of VAR and VARMA time series models are presented (vector autoregressive moving average). The functions accept incomplete data, and calculate analytical gradients, which may be used in parameter estimation with numerical likelihood maximization. Allowance is made for possible savings when estimating seasonal, structured or distributed lag models. Also provided is a function for creating simulated VARMA time series that have an accurate distribution from term one (they are {\em spin-up\/} free). The functions are accompanied by a simple example driver, a program demonstrating their use for real parameter fitting, as well as a test suite for verifying their correctness and aid further development. The article concludes with description of numerical results obtained with the algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ARMA; exact likelihood function; incomplete data; missing values; VARMA; vector autoregressive moving average model", } @Article{Lee:2009:AET, author = "Che-Rung Lee and G. W. Stewart", title = "{Algorithm 879}: {EIGENTEST} --- a test matrix generator for large-scale eigenproblems", journal = j-TOMS, volume = "35", number = "1", pages = "7:1--7:11", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377610", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat $A$ of order $n$ requires only $O(n)$ storage for its representation. Auxiliary programs permit the computation of $(A - sI) b$, $(A - sI)^T b$, $(A - sI)^{-1} b$, and $(A - sI)^{-T} b$ in $O(n)$ operations. A special routine computes specified eigenvectors of an eigenmat and the condition of its eigenvalue. Thus eigenmats are suitable for testing algorithms based on Krylov sequences, as well as others based on matrix-vector products. This article introduces the eigenmat and describes implementations in Fortran 77, Fortran 95, C, and Matlab.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "eigensystem; test matrix generation", } @Article{Marques:2009:ATI, author = "Osni A. Marques and Christof V{\"o}mel and James W. Demmel and Beresford N. Parlett", title = "{Algorithm 880}: a testing infrastructure for symmetric tridiagonal eigensolvers", journal = j-TOMS, volume = "35", number = "1", pages = "8:1--8:13", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377611", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This article describes an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows for easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accuracy; design; eigenvalues; eigenvectors; implementation; LAPACK; numerical software; performance; symmetric matrix; test matrices; testing", } @Article{Huyer:2009:SSN, author = "Waltraud Huyer and Arnold Neumaier", title = "{SNOBFIT} -- {Stable Noisy Optimization by Branch and Fit}", journal = j-TOMS, volume = "35", number = "2", pages = "9:1--9:25", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377613", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The software package SNOBFIT for bound-constrained (and soft-constrained) noisy optimization of an expensive objective function is described. It combines global and local search by branching and local fits. The program is made robust and flexible for practical use by allowing for hidden constraints, batch function evaluations, change of search regions, etc.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "branch-and-bound; derivative-free; expensive function values; hidden constraints; noisy function values; parallel evaluation; soft constraints; surrogate model", } @Article{Kirby:2009:BDS, author = "Robert C. Kirby and Anders Logg", title = "Benchmarking Domain-Specific Compiler Optimizations for Variational Forms", journal = j-TOMS, volume = "35", number = "2", pages = "10:1--10:18", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377614", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We examine the effect of using complexity-reducing relations [Kirby et al. 2006] to generate optimized code for the evaluation of finite-element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as an optimizing backend to the FEniCS form compiler, FFC [Kirby and Logg 2006; 2007]. In some cases, FErari provides very little speedup, while in other cases we obtain reduced local operation counts by a factor of as much as 7.9 and speedups for the assembly of the global sparse matrix by as much as a factor of 2.8 (see Figure 9).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "compiler; complexity-reducing relations; FErari; FFC; finite element method; optimization; variational form", } @Article{Quintana-Orti:2009:ULF, author = "Enrique S. Quintana-Ort{\'\i} and Robert A. {Van De Geijn}", title = "Updating an {LU} Factorization with Pivoting", journal = j-TOMS, volume = "35", number = "2", pages = "11:1--11:16", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377615", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We show how to compute an LU factorization of a matrix when the factors of a leading principle submatrix are already known. The approach incorporates pivoting akin to partial pivoting, a strategy we call {\em incremental pivoting}. An implementation using the Formal Linear Algebra Methods Environment (FLAME) application programming interface (API) is described. Experimental results demonstrate practical numerical stability and high performance on an Intel Itanium2 processor-based server.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "linear systems; LU factorization; pivoting; updating", } @Article{Drmac:2009:FRR, author = "Zlatko Drma{\v{c}} and Zvonimir Bujanovi{\'c}", title = "On the Failure of Rank-Revealing {QR} Factorization Software -- a Case Study", journal = j-TOMS, volume = "35", number = "2", pages = "12:1--12:28", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377616", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger--Golub column pivoting. It is shown that, due to finite precision arithmetic, the software implementation of the factorization can catastrophically fail to produce a properly structured triangular factor, thus leading to a potentially severe underestimate of a matrix's numerical rank. The 30-year old problem, dating back to LINPACK, has (undetectedly) badly affected many computational routines and software packages, as well as the study of rank-revealing QR factorizations. We combine computer experiments and numerical analysis to isolate, analyze, and fix the problem. Our modification of the current LAPACK xGEQP3 routine is already included in the LAPACK 3.1.0 release. The modified routine is numerically more robust and with a negligible overhead. We also provide a new, equally efficient, and provably numerically safe partial-column norm-updating strategy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "pivoting; QR factorization; rank-revealing", } @Article{Fraysse:2009:ASF, author = "Val{\'e}rie Frayss{\'e} and Luc Giraud and Serge Gratton", title = "{Algorithm 881}: a Set of Flexible {GMRES} Routines for Real and Complex Arithmetics on High-Performance Computers", journal = j-TOMS, volume = "35", number = "2", pages = "13:1--13:12", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377617", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we describe our implementations of the FGMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared-memory, and distributed-memory computers. For the sake of portability, simplicity, flexibility, and efficiency, the FGMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning, and the dot-product computations. For distributed-memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot-product calculation, which is a well-known bottleneck of efficiency for Krylov methods. Furthermore, either implicit or explicit calculation of the residual at restart is possible depending on the actual cost of the matrix-vector product. Finally, the implemented stopping criterion is based on a normwise backward error.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "distributed memory; FGMRES; flexible Krylov methods; high-performance computing; linear systems; reverse communication", } @Article{VanDeun:2009:ANB, author = "Joris {Van Deun} and Karl Deckers and Adhemar Bultheel and J. A. C. Weideman", title = "{Algorithm 882}: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods", journal = j-TOMS, volume = "35", number = "2", pages = "14:1--14:21", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377618", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a numerical procedure to compute the nodes and weights in rational Gauss--Chebyshev quadrature formulas. Under certain conditions on the poles, these nodes are near best for rational interpolation with prescribed poles (in the same sense that Chebyshev points are near best for polynomial interpolation). As an illustration, we use these interpolation points to solve a differential equation with an interior boundary layer using a rational spectral method.\par The algorithm to compute the interpolation points (and, if required, the quadrature weights) is implemented as a Matlab program.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "quadrature; rational interpolation", } @Article{Waki:2009:ASS, author = "Hayato Waki and Sunyoung Kim and Masakazu Kojima and Masakazu Muramatsu and Hiroshi Sugimoto", title = "{Algorithm 883}: {SparsePOP} --- a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems", journal = j-TOMS, volume = "35", number = "2", pages = "15:1--15:13", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377619", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying ``a hierarchy of LMI relaxations of increasing dimensions'' Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "global optimization; Matlab software package; polynomial optimization problem; semidefinite programming relaxation; sparsity; sums-of-squares optimization", } @Article{Dominguez:2009:ASM, author = "V{\'\i}ctor Dom{\'\i}nguez and Francisco-Javier Sayas", title = "{Algorithm 884}: a Simple {Matlab} Implementation of the {Argyris} Element", journal = j-TOMS, volume = "35", number = "2", pages = "16:1--16:11", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377612.1377620", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:13:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this work we propose a new algorithm to evaluate the basis functions of the Argyris finite element and their derivatives. The main novelty here is an efficient way to calculate the matrix which gives the change of coordinates between the bases of the Argyris element for the reference and for an arbitrary triangle. This matrix is factored as the product of two rectangular matrices with a strong block structure which makes their computation very easy. We show and comment on an implementation of this algorithm in Matlab. Two numerical experiments, an interpolation of a smooth function on a triangle and the finite-element solution of the Dirichlet problem for the biLaplacian, are presented in the last section to check the performance of our implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Argyris element; finite elements; Matlab", } @Article{Jansson:2009:ADS, author = "Johan Jansson and Anders Logg", title = "Algorithms and Data Structures for Multi-Adaptive Time-Stepping", journal = j-TOMS, volume = "35", number = "3", pages = "17:1--17:24", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391990", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algorithms; C++; continuous Galerkin; discontinuous Galerkin; DOLFIN; implementation; individual time steps; local time steps; mcgq; mdgq; Multi-adaptivity; multirate; ODE", } @Article{Gordon:2009:CRR, author = "Dan Gordon and Rachel Gordon", title = "{CGMN} Revisited: Robust and Efficient Solution of Stiff Linear Systems Derived from Elliptic Partial Differential Equations", journal = j-TOMS, volume = "35", number = "3", pages = "18:1--18:27", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391991", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Given a linear system $A x = b$, one can construct a related ``normal equations'' system $A A^T y = b$, $x = A^T y$. Bj{\"o}rck and Elfving have shown that the SSOR algorithm, applied to the normal equations, can be accelerated by the conjugate gradient algorithm (CG). The resulting algorithm, called CGMN, is error-reducing and in theory it always converges even when the equation system is inconsistent and/or nonsquare. SSOR on the normal equations is equivalent to the Kaczmarz algorithm (KACZ), with a fixed relaxation parameter, run in a double (forward and backward) sweep on the original equations. CGMN was tested on nine well-known large and sparse linear systems obtained by central-difference discretization of elliptic convection-diffusion partial differential equations (PDEs). Eight of the PDEs were strongly convection-dominated, and these are known to produce very stiff systems with large off-diagonal elements. CGMN was compared with some of the foremost state-of-the art Krylov subspace methods: restarted GMRES, Bi-CGSTAB, and CGS. These methods were tested both with and without various preconditioners. CGMN converged in all the cases, while none of the preceding algorithm/preconditioner combinations achieved this level of robustness. Furthermore, on varying grid sizes, there was only a gradual increase in the number of iterations as the grid was refined. On the eight convection-dominated cases, the initial convergence rate of CGMN was better than all the other combinations of algorithms and preconditioners, and the residual decreased monotonically. The CGNR algorithm was also tested, and it was as robust as CGMN, but slower.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "CGMN; CGNR; conjugate-gradient; convection-dominated; elliptic equations; Kaczmarz; linear systems; normal equations; partial differential equations; row projections; SOR; sparse linear systems; SSOR; stiff equations", } @Article{Dumas:2009:DLA, author = "Jean-Guillaume Dumas and Pascal Giorgi and Cl{\'e}ment Pernet", title = "Dense Linear Algebra over Word-Size Prime Fields: the {FFLAS} and {FFPACK} Packages", journal = j-TOMS, volume = "35", number = "3", pages = "19:1--19:35", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391992", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known that modular techniques such as the Chinese remainder algorithm or the $p$-adic lifting allow very good practical performance, especially when word size arithmetic is used. Therefore, finite field arithmetic becomes an important core for efficient exact linear algebra libraries. In this article, we study high performance implementations of basic linear algebra routines over word size prime fields: especially matrix multiplication; our goal being to provide an exact alternate to the numerical BLAS library. We show that this is made possible by a careful combination of numerical computations and asymptotically faster algorithms. Our kernel has several symbolic linear algebra applications enabled by diverse matrix multiplication reductions: symbolic triangularization, system solving, determinant, and matrix inverse implementations are thus studied.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS level 1-2-3; determinant; inverse; linear algebra package; matrix factorization; s symbolic matrix multiplication; Winograd' Word size prime fields", } @Article{Linhart:2009:ACL, author = "Jean Marie Linhart", title = "{Algorithm 885}: Computing the Logarithm of the Normal Distribution", journal = j-TOMS, volume = "35", number = "3", pages = "20:1--20:10", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391993", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present and compare three C functions to compute the logarithm of the cumulative standard normal distribution. The first is a new algorithm derived from Algorithm 304's calculation of the standard normal distribution via a series or continued fraction approximation, and it is good to the accuracy of the machine. The second is based on Algorithm 715's calculation of the standard normal distribution via rational Chebyshev approximation. This is related to, and an improvement on, the algorithm for the logarithm of the normal distribution available in the software package R. The third is a new and simple algorithm that uses the compiler's implementation of the error function, and complement of the error function, to compute the log of the normal distribution.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "error function; logarithm of the standard normal distribution; Normal distribution; normal integral", } @Article{Caliari:2009:APL, author = "Marco Caliari and Stefanode Marchi and Marco Vianello", title = "{Algorithm 886}: {Padua$2$D} --- {Lagrange} Interpolation at {Padua} Points on Bivariate Domains", journal = j-TOMS, volume = "35", number = "3", pages = "21:1--21:11", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391994", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a stable and efficient Fortran implementation of polynomial interpolation at the Padua points on the square $[-1,1]^2$. These points are unisolvent and their Lebesgue constant has minimal order of growth (log square of the degree). The algorithm is based on the representation of the Lagrange interpolation formula in a suitable orthogonal basis, and takes advantage of a new matrix formulation together with the machine-specific optimized BLAS subroutine for the matrix-matrix product. Extension to interpolation on rectangles, triangles and ellipses is also described.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bivariate Chebyshev orthogonal basis; Bivariate Lagrange interpolation; Fortran 77; Padua points", } @Article{Chen:2009:ACS, author = "Yanqing Chen and Timothy A. Davis and William W. Hager and Sivasankaran Rajamanickam", title = "{Algorithm 887}: {CHOLMOD}, Supernodal Sparse {Cholesky} Factorization and Update\slash Downdate", journal = j-TOMS, volume = "35", number = "3", pages = "22:1--22:14", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1391995", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form $A$ or $AA^T$, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system $Lx = b$, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB$^{\sc TM}$ interfaces. It appears in MATLAB 7.2 as $x = A\backslash b$ when $A$ is sparse symmetric positive definite, as well as in several other sparse matrix functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Cholesky factorization; linear equations; sparse matrices", } @Article{Drake:2009:ASH, author = "John B. Drake and Pat Worley and Eduardo D'Azevedo", title = "{Algorithm 888}: Spherical Harmonic Transform Algorithms", journal = j-TOMS, volume = "35", number = "3", pages = "23:1--23:23", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1404581", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A collection of MATLAB classes for computing and using spherical harmonic transforms is presented. Methods of these classes compute differential operators on the sphere and are used to solve simple partial differential equations in a spherical geometry. The spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are presented in detail. A set of methods associated with a spectral\_field class provides spectral approximation to the differential operators $\nabla \cdot$, $\nabla \times$, $\nabla$, and $\nabla^2$ in spherical geometry. Laplace inversion and Helmholtz equation solvers are also methods for this class. The use of the class and methods in MATLAB is demonstrated by the solution of the barotropic vorticity equation on the sphere. A survey of alternative algorithms is given and implementations for parallel high performance computers are discussed in the context of global climate and weather models.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "fluid dynamics; geophysical flow; high performance computing; Spectral transform methods; spherical", } @Article{Cazals:2009:AJG, author = "Fr{\'e}d{\'e}ric Cazals and Marc Pouget", title = "{Algorithm 889}: {Jet\_fitting\_3}: --- a Generic {C++} Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting", journal = j-TOMS, volume = "35", number = "3", pages = "24:1--24:20", month = oct, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1391989.1404582", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 1 19:57:00 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Surfaces of $R^3$ are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in computer graphics, computer aided design, computational geometry, and computer vision. One strategy to perform such an estimation consists of resorting to polynomial fitting, either interpolation or approximation, but this route is difficult for several reasons: choice of the coordinate system, numerical handling of the fitting problem, and extraction of the differential properties.\par This article presents a generic C++ software package solving these problems. On the theoretical side and as established in a companion paper, the interpolation and approximation methods provided achieve the best asymptotic error bounds known to date. On the implementation side and following state-of-the-art coding rules in computational geometry, genericity of the package is achieved thanks to four template classes accounting for, (a) the type of the input points, (b) the internal geometric computations, (c) a conversion mechanism between these two geometries, and (d) the linear algebra operations. An instantiation within the Computational Geometry Algorithms Library (CGAL, version 3.3) and using LAPACK is also provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Approximation; C++ design; computational geometry; differential geometry; interpolation; numerical linear algebra; sampled surfaces", } @Article{Eijkhout:2009:SSN, author = "Victor Eijkhout and Erika Fuentes", title = "A Standard and Software for Numerical Metadata", journal = j-TOMS, volume = "35", number = "4", pages = "25:1--25:20", month = feb, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1462173.1462174", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 13 18:09:40 MST 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We propose a standard for generating, manipulating, and storing metadata describing numerical problems, in particular properties of matrices and linear systems. The standard comprises:\par --an API for metadata generating and querying software, and\par --an XML format for permanent storage of metadata.\par The API is open-ended, allowing for other parties to define additional metadata categories to be generated and stored within this framework. Furthermore, we present two software libraries, NMD and AnaMod, that implement this standard, and that contain a number of computational modules for numerical metadata. The libraries, more than simply illustrating the use of the standard, provide considerable utility to numerical researchers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Taylor:2009:CCT, author = "Alan Taylor and Desmond J. Higham", title = "{CONTEST}: a Controllable Test Matrix Toolbox for {MATLAB}", journal = j-TOMS, volume = "35", number = "4", pages = "26:1--26:17", month = feb, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1462173.1462175", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 13 18:09:40 MST 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "clustering; matrix computation; preferential attachment; random graph; rewiring; small-world; sparse matrix", } @Article{Davis:2009:DSS, author = "Timothy A. Davis and William W. Hager", title = "Dynamic Supernodes in Sparse {Cholesky} Update\slash Downdate and Triangular Solves", journal = j-TOMS, volume = "35", number = "4", pages = "27:1--27:23", month = feb, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1462173.1462176", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 13 18:09:40 MST 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The supernodal method for sparse Cholesky factorization represents the factor $L$ as a set of supernodes, each consisting of a contiguous set of columns of $L$ with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of $L$ does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to $A$ (an update\slash downdate, $\bar{A} = A \pm W W^T$). Supernodes merge and split apart during an update\slash downdate. Dynamic supernodes are introduced which allow a sparse Cholesky update\slash downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update\slash downdate package which forms the basis of {\tt $x = A \backslash b$} in MATLAB when {\tt A} is sparse and symmetric positive definite.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Cholesky factorization; linear equations; sparse matrices", } @Article{Demmel:2009:EPI, author = "James Demmel and Yozo Hida and E. Jason Riedy and Xiaoye S. Li", title = "Extra-Precise Iterative Refinement for Overdetermined Least Squares Problems", journal = j-TOMS, volume = "35", number = "4", pages = "28:1--28:32", month = feb, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1462173.1462177", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 13 18:09:40 MST 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/lawn.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the algorithm, error bounds, and numerical results for extra-precise iterative refinement applied to overdetermined linear least squares (LLS) problems. We apply our linear system refinement algorithm to Bj{\"o}rck's augmented linear system formulation of an LLS problem. Our algorithm reduces the forward normwise and componentwise errors to $ O(\epsilon_w) $, where $ \epsilon_w $ is the working precision, unless the system is too ill conditioned. In contrast to linear systems, we provide two separate error bounds for the solution $x$ and the residual $r$. The refinement algorithm requires only limited use of extra precision and adds only $ O(m n)$ work to the $ O(m n^2)$ cost of QR factorization for problems of size $ m \times n$. The extra precision calculation is facilitated by the new extended-precision BLAS standard in a portable way, and the refinement algorithm will be included in a future release of LAPACK and can be extended to the other types of least squares problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS; floating-point arithmetic; LAPACK; Linear algebra", remark = "Journal publication of LAWN 188 \cite{Demmel:2007:EPI}.", } @Article{vandenBerg:2009:AST, author = "Ewout van den Berg and Michael P. Friedlander and Gilles Hennenfent and Felix J. Herrmann and Rayan Saab and {\"O}zg{\"u}r Yilmaz", title = "{Algorithm 890}: {Sparco}: a Testing Framework for Sparse Reconstruction", journal = j-TOMS, volume = "35", number = "4", pages = "29:1--29:16", month = feb, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1462173.1462178", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Feb 13 18:09:40 MST 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Sparco is a framework for testing and benchmarking algorithms for sparse reconstruction. It includes a large collection of sparse reconstruction problems drawn from the imaging, compressed sensing, and geophysics literature. Sparco is also a framework for implementing new test problems and can be used as a tool for reproducible research. Sparco is implemented entirely in Matlab, and is released as open-source software under the GNU Public License.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Compressed sensing; linear operators; sparse recovery", } @Article{Mayer:2009:NEP, author = "Jan Mayer", title = "A numerical evaluation of preprocessing and {ILU}-type preconditioners for the solution of unsymmetric sparse linear systems using iterative methods", journal = j-TOMS, volume = "36", number = "1", pages = "1:1--1:26", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486526", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Recent advances in multilevel LU factorizations and novel preprocessing techniques have led to an extremely large number of possibilities for preconditioning sparse, unsymmetric linear systems for solving with iterative methods. However, not all combinations work well for all systems, so making the right choices is essential for obtaining an efficient solver. The numerical results for 256 matrices presented in this article give an indication of which approaches are suitable for which matrices (based on different criteria, such as total computation time or fill-in) and of the differences between the methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Incomplete LU factorization; iterative methods; preconditioning; sparse linear systems", } @Article{Lourakis:2009:SSP, author = "Manolis I. A. Lourakis and Antonis A. Argyros", title = "{SBA}: a software package for generic sparse bundle adjustment", journal = j-TOMS, volume = "36", number = "1", pages = "2:1--2:30", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486527", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Bundle adjustment constitutes a large, nonlinear least-squares problem that is often solved as the last step of feature-based structure and motion estimation computer vision algorithms to obtain optimal estimates. Due to the very large number of parameters involved, a general purpose least-squares algorithm incurs high computational and memory storage costs when applied to bundle adjustment. Fortunately, the lack of interaction among certain subgroups of parameters results in the corresponding Jacobian being sparse, a fact that can be exploited to achieve considerable computational savings. This article presents sba, a publicly available C/C++ software package for realizing generic bundle adjustment with high efficiency and flexibility regarding parameterization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "bundle adjustment; engineering applications; Levenberg--Marquardt; multiple-view geometry; nonlinear least squares; sparse Jacobian; structure and motion estimation; Unconstrained optimization", } @Article{DAlberto:2009:AWM, author = "Paolo D'Alberto and Alexandru Nicolau", title = "Adaptive {Winograd}'s matrix multiplications", journal = j-TOMS, volume = "36", number = "1", pages = "3:1--3:23", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486528", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Modern architectures have complex memory hierarchies and increasing parallelism (e.g., multicores). These features make achieving and maintaining good performance across rapidly changing architectures increasingly difficult. Performance has become a complex tradeoff, not just a simple matter of counting cost of simple CPU operations.\par We present a novel, hybrid, and adaptive recursive Strassen-Winograd's matrix multiplication (MM) that uses automatically tuned linear algebra software (ATLAS) or GotoBLAS. Our algorithm applies to any size and shape matrices stored in either row or column major layout (in double precision in this work) and thus is efficiently applicable to both C and FORTRAN implementations. In addition, our algorithm divides the computation into equivalent in-complexity sub-MMs and does not require any extra computation to combine the intermediary sub-MM results.\par We achieve up to 22\% execution-time reduction versus GotoBLAS/ATLAS alone for a single core system and up to 19\% for a two dual-core processor system. Most importantly, even for small matrices such as $1500 \times 1500$, our approach attains already 10\% execution-time reduction and, for MM of matrices larger than $3000 \times 3000$, it delivers performance that would correspond, for a classic $O(n^3)$ algorithm, to faster-than-processor peak performance (i.e., our algorithm delivers the equivalent of 5 GFLOPS performance on a system with 4.4 GFLOPS peak performance and where GotoBLAS achieves only 4 GFLOPS). This is a result of the savings in operations (and thus FLOPS). Therefore, our algorithm is faster than any {\em classic\/} MM algorithms could ever be for matrices of this size. Furthermore, we present experimental evidence based on established methodologies found in the literature that our algorithm is, for a family of matrices, as accurate as the classic algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "fast algorithms; Winograd's matrix multiplications", } @Article{Bangerth:2009:DSR, author = "W. Bangerth and O. Kayser-Herold", title = "Data structures and requirements for {\em hp\/} finite element software", journal = j-TOMS, volume = "36", number = "1", pages = "4:1--4:31", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486529", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Finite element methods approximate solutions of partial differential equations by restricting the problem to a finite dimensional function space. In {\em hp\/} adaptive finite element methods, one defines these discrete spaces by choosing different polynomial degrees for the shape functions defined on a locally refined mesh.\par Although this basic idea is quite simple, its implementation in algorithms and data structures is challenging. It has apparently not been documented in the literature in its most general form. Rather, most existing implementations appear to be for special combinations of finite elements, or for discontinuous Galerkin methods.\par In this article, we discuss generic data structures and algorithms used in the implementation of {\em hp\/} methods for arbitrary elements, and the complications and pitfalls one encounters. As a consequence, we list the information a description of a finite element has to provide to the generic algorithms for it to be used in an {\em hp\/} context. We support our claim that our reference implementation is efficient using numerical examples in two dimensions and three dimensions, and demonstrate that the {\em hp\/} -specific parts of the program do not dominate the total computing time. This reference implementation is also made available as part of the Open Source deal. II finite element library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "data structures; finite element software; hp finite element methods; Object orientation; software design", } @Article{Reid:2009:AFV, author = "John K. Reid and Jennifer A. Scott", title = "{Algorithm 891}: a {Fortran} virtual memory system", journal = j-TOMS, volume = "36", number = "1", pages = "5:1--5:12", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486530", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Fortran\_Virtual\_Memory is a Fortran 95 package that provides facilities for reading from and writing to direct-access files. A buffer is used to avoid actual input/output operations whenever possible. The data may be spread over many files and for very large data sets these may be held on more than one device. We describe the design of Fortran\_Virtual\_Memory and comment on its use within an out-of-core sparse direct solver.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "direct-access files; Fortran; out-of-core; Virtual memory", } @Article{Jonasson:2009:ADF, author = "Kristjan Jonasson", title = "{Algorithm 892}: {DISPMODULE}, a {Fortran 95} module for pretty-printing matrices", journal = j-TOMS, volume = "36", number = "1", pages = "6:1--6:7", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486531", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A standard Fortran 95 module for printing scalars, vectors, and matrices to external files is provided. The module can display variables of default kind of all intrinsic types (integer, real, complex, logical, and character), and add-on modules are provided for data of the nondefault kind. The main module is self-contained and incorporating it only requires that it be compiled and linked with a program containing a ``use dispmodule'' statement. A generic interface and optional parameters are used, so that the same subroutine name, DISP, is used to display items of different data type and rank, irrespective of display options. The subroutine is quite versatile, and hopefully can improve Fortran's competitiveness against other array programming languages. The module also contains a function TOSTRING to convert numerical scalars and vectors to strings.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "array programming language; Fortran 95; matrix pretty-printing; matrix printing; output utilities", } @Article{Renka:2009:ATT, author = "Robert J. Renka", title = "{Algorithm 893}: {TSPACK}: tension spline package for curve design and data fitting", journal = j-TOMS, volume = "36", number = "1", pages = "7:1--7:8", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1486525.1486532", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 17 17:22:09 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "TSPACK is a curve-fitting package based on exponential tension splines with automatic selection of tension factors. It serves both as a method for data fitting with preservation of shape properties or more general constraints, and as a means of computer aided geometric design of curves in two or three dimensions. The package is based on a translation of Algorithm 716 from Fortran 77 into MATLAB. The translation includes bug corrections, vectorization where possible, and extensions, including a B-spline representation, designed to facilitate curve design as opposed to data fitting. An interactive graphical user interface, not part of the algorithm, is available from the author.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Convexity preserving; cubic spline; exponential spline; interpolation; monotonicity preserving; parametric curve; piecewise polynomial; shape preserving; smoothing; spline under tension; tension factor", } @Article{Padula:2009:SFA, author = "Anthony D. Padula and Shannon D. Scott and William W. Symes", title = "A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms", journal = j-TOMS, volume = "36", number = "2", pages = "8:1--8:36", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499097", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Rice Vector Library is a collection of C++ classes expressing core concepts (vector, function,\ldots{}) of calculus in Hilbert space with minimal implementation dependence, and providing standardized interfaces behind which to hide application-dependent implementation details (data containers, function objects). A variety of coordinate-free algorithms from linear algebra and optimization, including Krylov subspace methods and various relatives of Newton's method for nonlinear equations and constrained and unconstrained optimization, may be expressed purely in terms of this system of classes. The resulting code may be used {\em without alteration\/} in a wide range of control, design, and parameter estimation applications, in serial and parallel computing environments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Abstract numerical algorithms; complex simulation; numerical optimization", } @Article{Reid:2009:CSC, author = "John K. Reid and Jennifer A. Scott", title = "An out-of-core sparse {Cholesky} solver", journal = j-TOMS, volume = "36", number = "2", pages = "9:1--9:33", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499098", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Direct methods for solving large sparse linear systems of equations are popular because of their generality and robustness. Their main weakness is that the memory they require usually increases rapidly with problem size. We discuss the design and development of the first release of a new symmetric direct solver that aims to circumvent this limitation by allowing the system matrix, intermediate data, and the matrix factors to be stored externally. The code, which is written in Fortran and called HSL\_MA77, implements a multifrontal algorithm. The first release is for positive-definite systems and performs a Cholesky factorization. Special attention is paid to the use of efficient dense linear algebra kernel codes that handle the full-matrix operations on the frontal matrix and to the input/output operations. The input/output operations are performed using a separate package that provides a virtual-memory system and allows the data to be spread over many files; for very large problems these may be held on more than one device.\par Numerical results are presented for a collection of 30 large real-world problems, all of which were solved successfully.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Cholesky; multifrontal; out-of-core solver; sparse symmetric linear systems", } @Article{Yang:2009:KMT, author = "Chao Yang and Juan C. Meza and Byounghak Lee and Lin-Wang Wang", title = "{KSSOLV} --- a {MATLAB} toolbox for solving the {Kohn--Sham} equations", journal = j-TOMS, volume = "36", number = "2", pages = "10:1--10:35", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499099", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe the design and implementation of KSSOLV, a MATLAB toolbox for solving a class of nonlinear eigenvalue problems known as the {\em Kohn--Sham equations}. These types of problems arise in electronic structure calculations, which are nowadays essential for studying the microscopic quantum mechanical properties of molecules, solids, and other nanoscale materials. KSSOLV is well suited for developing new algorithms for solving the Kohn--Sham equations and is designed to enable researchers in computational and applied mathematics to investigate the convergence properties of the existing algorithms. The toolbox makes use of the object-oriented programming features available in MATLAB so that the process of setting up a physical system is straightforward and the amount of coding effort required to prototype, test, and compare new algorithms is significantly reduced. All of these features should also make this package attractive to other computational scientists and students who wish to study small- to medium-size systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "density functional theory (DFT); direct constrained minimization (DCM); electronic structure calculation; Kohn--Sham equations; nonlinear eigenvalue problem; Planewave discretization; pseudopotential; self-consistent field iteration (SCF)", } @Article{Gustavson:2009:DSC, author = "Fred G. Gustavson and Lars Karlsson and Bo K{\aa}gstr{\"o}m", title = "Distributed {SBP Cholesky} factorization algorithms with near-optimal scheduling", journal = j-TOMS, volume = "36", number = "2", pages = "11:1--11:25", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499100", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The minimal block storage Distributed Square Block Packed (DSBP) format for distributed memory computing on symmetric and triangular matrices is presented. Three algorithm variants (Basic, Static, and Dynamic) of the blocked right-looking Cholesky factorization are designed for the DSBP format, implemented, and evaluated. On our target machine, all variants outperform standard full-storage implementations while saving almost half the storage. Communication overhead is shown to be virtually eliminated by the Static and Dynamic variants, both of which take advantage of hardware parallelism to hide communication costs. The Basic variant is shown to yield comparable or slightly better performance than the full-storage ScaLAPACK routine PDPOTRF while clearly outperformed by both Static and Dynamic. Models of execution assuming zero communication costs and overhead are developed. For medium- and larger-sized problems, the Static schedule is near optimal on our target machine based on comparisons with these models and measurements of synchronization overhead.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Cholesky factorization; distributed square block format; packed storage; parallel algorithms; parallel computing; positive definite matrices; Real symmetric matrices", } @Article{Koikari:2009:ABS, author = "Souji Koikari", title = "{Algorithm 894}: {On} a block {Schur--Parlett} algorithm for $\varphi$-functions based on the sep-inverse estimate", journal = j-TOMS, volume = "36", number = "2", pages = "12:1--12:20", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499101", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FORTRAN 95 software is provided for computing the matrix values of $\varphi$-functions required in exponential integrators. The subroutines in the library accept as their argument a full, diagonal, or upper quasitriangular matrix with real or complex entries in one of four precisions. Two different algorithms are implemented, one is the scaling and squaring method, and the other is a modified block Schur--Parlett algorithm. In the latter algorithm, a recursive three-by-three blocking is applied to the argument based on an estimate of the sep-inverse function. The estimation of the sep-inverse function is carried out by Hager--Higham estimator implemented as the subroutine xLACON in LAPACK. Our modifications to the block Schur--Parlett algorithm are described together with the results of numerical experiments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ϕ -functions; block Schur--Parlett algorithm; exponential integrators; matrix functions", } @Article{Baker:2009:ASN, author = "C. G. Baker and U. L. Hetmaniuk and R. B. Lehoucq and H. K. Thornquist", title = "{Anasazi} software for the numerical solution of large-scale eigenvalue problems", journal = j-TOMS, volume = "36", number = "3", pages = "13:1--13:23", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1527286.1527287", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 21 14:09:07 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Anasazi is a package within the Trilinos software project that provides a framework for the iterative, numerical solution of large-scale eigenvalue problems. Anasazi is written in ANSI C++ and exploits modern software paradigms to enable the research and development of eigensolver algorithms. Furthermore, Anasazi provides implementations for some of the most recent eigensolver methods. The purpose of our article is to describe the design and development of the Anasazi framework. A performance comparison of Anasazi and the popular FORTRAN 77 code ARPACK is given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Eigenvalue problems; generic programming; large-scale scientific computing; numerical algorithms; object-oriented programming", } @Article{Quintana-Orti:2009:PMA, author = "Gregorio Quintana-Ort{\'\i} and Enrique S. Quintana-Ort{\'\i} and Robert A. {Van De Geijn} and Field G. {Van Zee} and Ernie Chan", title = "Programming matrix algorithms-by-blocks for thread-level parallelism", journal = j-TOMS, volume = "36", number = "3", pages = "14:1--14:26", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1527286.1527288", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 21 14:09:07 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "With the emergence of thread-level parallelism as the primary means for continued performance improvement, the programmability issue has reemerged as an obstacle to the use of architectural advances. We argue that evolving legacy libraries for dense and banded linear algebra is not a viable solution due to constraints imposed by early design decisions. We propose a philosophy of abstraction and separation of concerns that provides a promising solution in this problem domain. The first abstraction, FLASH, allows algorithms to express computation with matrices consisting of contiguous blocks, facilitating algorithms-by-blocks. Operand descriptions are registered for a particular operation a priori by the library implementor. A runtime system, SuperMatrix, uses this information to identify data dependencies between suboperations, allowing them to be scheduled to threads out-of-order and executed in parallel. But not all classical algorithms in linear algebra lend themselves to conversion to algorithms-by-blocks. We show how our recently proposed LU factorization with incremental pivoting and a closely related algorithm-by-blocks for the QR factorization, both originally designed for out-of-core computation, overcome this difficulty. Anecdotal evidence regarding the development of routines with a core functionality demonstrates how the methodology supports high productivity while experimental results suggest that high performance is abundantly achievable.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "high-performance; libraries; Linear algebra; multithreaded architectures", } @Article{Backeljauw:2009:ACF, author = "Franky Backeljauw and Annie Cuyt", title = "{Algorithm 895}: a continued fractions package for special functions", journal = j-TOMS, volume = "36", number = "3", pages = "15:1--15:20", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1527286.1527289", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 21 14:09:07 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The continued fractions for special functions package (in the sequel abbreviated as CFSF package) complements a systematic study of continued fraction representations for special functions. It provides all the functionality to create continued fractions, in particular $k$-periodic or limit $k$-periodic fractions, to compute approximants, make use of continued fraction tails, perform equivalence transformations and contractions, and much more. The package, developed in Maple, includes a library of more than 200 representations of special functions, of which only 10\% can be found in the 1964 NBS {\em Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables\/} by M. Abramowitz and I. Stegun.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "CAS software; continued fractions; Maple; special functions", } @Article{Luksan:2009:ALA, author = "Ladislav Luk{\v{s}}an and Ctirad Matonoha and Jan Vl{\v{c}}ek", title = "{Algorithm 896}: {LSA}: {Algorithms} for large-scale optimization", journal = j-TOMS, volume = "36", number = "3", pages = "16:1--16:29", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1527286.1527290", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 21 14:09:07 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present 14 basic Fortran subroutines for large-scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations. Subroutines PLIS and PLIP, intended for dense general optimization problems, are based on limited-memory variable metric methods. Subroutine PNET, also intended for dense general optimization problems, is based on an inexact truncated Newton method. Subroutines PNED and PNEC, intended for sparse general optimization problems, are based on modifications of the discrete Newton method. Subroutines PSED and PSEC, intended for partially separable optimization problems, are based on partitioned variable metric updates. Subroutine PSEN, intended for nonsmooth partially separable optimization problems, is based on partitioned variable metric updates and on an aggregation of subgradients. Subroutines PGAD and PGAC, intended for sparse nonlinear least-squares problems, are based on modifications and corrections of the Gauss--Newton method. Subroutine PMAX, intended for minimization of a maximum value (minimax), is based on the primal line-search interior-point method. Subroutine PSUM, intended for minimization of a sum of absolute values, is based on the primal trust-region interior-point method. Subroutines PEQN and PEQL, intended for sparse systems of nonlinear equations, are based on the discrete Newton method and the inverse column-update quasi-Newton method, respectively. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of the proposed algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "discrete Newton methods; large-scale nonlinear least squares; large-scale nonlinear minimax; large-scale nonsmooth optimization; Large-scale optimization; large-scale systems of nonlinear equations; limited-memory methods; partially separable problems; primal interior-point methods; quasi-Newton methods; sparse problems", } @Article{He:2009:AVS, author = "Jian He and Layne T. Watson and Masha Sosonkina", title = "{Algorithm 897}: {VTDIRECT95}: {Serial} and parallel codes for the global optimization algorithm direct", journal = j-TOMS, volume = "36", number = "3", pages = "17:1--17:24", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1527286.1527291", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 21 14:09:07 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Sosonkina:2015:RAV}.", abstract = "VTDIRECT95 is a Fortran 95 implementation of D. R. Jones' deterministic global optimization algorithm called {\em DIRECT}, which is widely used in multidisciplinary engineering design, biological science, and physical science applications. The package includes both a serial code and a data-distributed massively parallel code for different problem scales and optimization (exploration vs. exploitation) goals. Dynamic data structures are used to organize local data, handle unpredictable memory requirements, reduce the memory usage, and share the data across multiple processors. The parallel code employs a multilevel functional and data parallelism to boost concurrency and mitigate the data dependency, thus improving the load balancing and scalability. In addition, checkpointing features are integrated into both versions to provide fault tolerance and hot restarts. Important algorithm modifications and design considerations are discussed regarding data structures, parallel schemes, error handling, and portability. Using several benchmark functions and real-world applications, the software is evaluated on different systems in terms of optimization effectiveness, data structure efficiency, parallel performance, and checkpointing overhead. The package organization and usage are also described in detail.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "checkpointing; data structures; DIRECT; global optimization; parallel schemes", } @Article{Ramachandran:2009:OOD, author = "Prabhu Ramachandran and M. Ramakrishna", title = "An Object-Oriented Design for Two-Dimensional Vortex Particle Methods", journal = j-TOMS, volume = "36", number = "4", pages = "18:1--18:28", month = aug, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1555386.1555387", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 31 15:04:00 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Vortex methods offer a grid-free alternative to simulating incompressible, viscous, fluid flows. They require the use of fairly sophisticated algorithms and can be complicated to implement for general flows. This article describes an object-oriented design used to implement a vortex particle based flow solver in two dimensions. We provide an overview of the various abstractions that arose as a result of this design. Several of the algorithms have common components that may be abstracted and reused. We demonstrate how the design allowed us to derive the traditional benefits of OOD. In addition, we show how the design directly suggested elegant generalizations of existing algorithms. Finally, we show the benefits of using software testing techniques and building a powerful scripting layer for the library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Keiner:2009:UNS, author = "Jens Keiner and Stefan Kunis and Daniel Potts", title = "Using {NFFT 3} --- a Software Library for Various Nonequispaced {Fast Fourier Transforms}", journal = j-TOMS, volume = "36", number = "4", pages = "19:1--19:30", month = aug, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1555386.1555388", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 31 15:04:00 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "NFFT 3 is a software library that implements the nonequispaced fast Fourier transform (NFFT) and a number of related algorithms, for example, nonequispaced fast Fourier transforms on the sphere and iterative schemes for inversion. This article provides a survey on the mathematical concepts behind the NFFT and its variants, as well as a general guideline for using the library. Numerical examples for a number of applications are given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Martins:2009:POO, author = "Joaquim R. R. A. Martins and Christopher Marriage and Nathan Tedford", title = "{pyMDO}: An Object-Oriented Framework for Multidisciplinary Design Optimization", journal = j-TOMS, volume = "36", number = "4", pages = "20:1--20:25", month = aug, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1555386.1555389", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 31 15:04:00 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present pyMDO, an object-oriented framework that facilitates the usage and development of algorithms for multidisciplinary optimization (MDO). The resulting implementation of the MDO methods is efficient and portable. The main advantage of the proposed framework is that it is flexible, with a strong emphasis on object-oriented classes and operator overloading, and it is therefore useful for the rapid development and evaluation of new MDO methods. The top layer interface is programmed in Python and it allows for the layers below the interface to be programmed in C, C++, Fortran, and other languages. We describe an implementation of pyMDO and demonstrate that we can take advantage of object-oriented programming to obtain intuitive, easy-to-read, and easy-to-develop codes that are at the same time efficient. This allows developers to focus on the new algorithms they are developing and testing, rather than on implementation details. Examples demonstrate the user interface and the corresponding results show that the various MDO methods yield the correct solutions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Garcia-Alonso:2009:ANI, author = "Fernando Garc{\'\i}a-Alonso and Jos{\'e} A. Reyes and Jos{\'e} M. Ferr{\'a}ndiz and Jes{\'u}s Vigo-Aguiar", title = "Accurate Numerical Integration of Perturbed Oscillatory Systems in Two Frequencies", journal = j-TOMS, volume = "36", number = "4", pages = "21:1--21:34", month = aug, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1555386.1555390", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 31 15:04:00 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Highly accurate long-term numerical integration of nearly oscillatory systems of ordinary differential equations (ODEs) is a common problem in astrodynamics. Scheifele's algorithm is one of the excellent integrators developed in the past years to take advantage of special transformations of variables such as the K-S set. It is based on using expansions in series of the so-called G-functions, and generalizes the Taylor series integrators but with the remarkable property of integrating without truncation error oscillations in one basic known frequency. A generalization of Scheifele's method capable of integrating exactly harmonic oscillations in two known frequencies is developed here, after introducing a two parametric family of analytical $\varphi$-functions. Moreover, the local error contains the perturbation parameter as a factor when the algorithm is applied to perturbed problems. The good behavior and the long-term accuracy of the new method are shown through several examples, including systems with low- and high-frequency constituents and a perturbed satellite orbit. The new methods provide significantly higher accuracy and efficiency than a selection of well-reputed general-purpose integrators and even recent symplectic or symmetric integrators, whose good behavior in the long-term integration of the Kepler problem and the other oscillatory systems is well stated in recent literature.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meerbergen:2009:CBE, author = "Karl Meerbergen and Kresimir Fresl and Toon Knapen", title = "{C++} Bindings to External Software Libraries with Examples from {BLAS}, {LAPACK}, {UMFPACK}, and {MUMPS}", journal = j-TOMS, volume = "36", number = "4", pages = "22:1--22:23", month = aug, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1555386.1555391", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 31 15:04:00 MDT 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FORTRAN and C software packages are often used in generic C++ software. Calling nongeneric functions in generic code is not straightforward. The bindings in this article help the C++ programmer using external software with a small effort. The bindings provide a mechanism to keep external software interfaces and specific vector and matrix containers orthogonal. We show examples using BLAS, LAPACK, UMFPACK, and MUMPS functions and subroutines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Vomel:2010:SMA, author = "Christof V{\"o}mel", title = "{ScaLAPACK}'s {MRRR} algorithm", journal = j-TOMS, volume = "37", number = "1", pages = "1:1--1:35", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644002", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The (sequential) algorithm of Multiple Relatively Robust Representations, MRRR, is a more efficient variant of inverse iteration that does not require reorthogonalization. It solves the eigenproblem of an unreduced symmetric tridiagonal matrix $T \in R^{n \times n}$ at $O(n^2)$ cost. The computed normalized eigenvectors are numerically orthogonal in the sense that the dot product between different vectors is $O(n \epsilon)$, where $\epsilon$ refers to the relative machine precision.\par This article describes the design of ScaLAPACK's parallel MRRR algorithm. One emphasis is on the critical role of the representation tree in achieving both adequate accuracy and parallel scalability. A second point concerns the favorable properties of this code: subset computation, the use of static memory, and scalability.\par Unlike ScaLAPACK's Divide \& Conquer and QR, MRRR can compute subsets of eigenpairs at reduced cost. And in contrast to inverse iterations which can fail, it is guaranteed to produce a satisfactory answer while maintaining memory scalability.\par ParEig, the parallel MRRR algorithm for PLAPACK, uses dynamic memory allocation. This is avoided by our code at marginal additional cost. We also use a different representation tree criterion that allows for more accurate computation of the eigenvectors but can make parallelization more difficult.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "design; implementation; Multiple relatively robust representations; numerical software; parallel computation; ScaLAPACK; symmetric eigenvalue problem", } @Article{Daumas:2010:CBE, author = "Marc Daumas and Guillaume Melquiond", title = "Certification of bounds on expressions involving rounded operators", journal = j-TOMS, volume = "37", number = "1", pages = "2:1--2:20", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644003", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Gappa is a tool designed to formally verify the correctness of numerical software and hardware. It uses interval arithmetic and forward error analysis to bound mathematical expressions that involve rounded as well as exact operators. It then generates a theorem and its proof for each verified enclosure. This proof can be automatically checked with a proof assistant, such as Coq or HOL Light. It relies on a large companion library of facts that we have developed. This Coq library provides theorems dealing with addition, multiplication, division, and square root, for both fixed- and floating-point arithmetics. Gappa uses multiple-precision dyadic fractions for the endpoints of intervals and performs forward error analysis on rounded operators when necessary. When asked, Gappa reports the best bounds it is able to reach for a given expression in a given context. This feature can be used to identify where the set of facts and automatic techniques implemented in Gappa becomes insufficient. Gappa handles seamlessly additional properties expressed as interval properties or rewriting rules in order to establish more intricate bounds. Recent work showed that Gappa is suited to discharge proof obligations generated for small pieces of software. They may be produced by third-party tools and the first applications of Gappa use proof obligations written by designers or obtained from traces of execution.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Coq; dyadic fraction; floating point; Forward error analysis; HOL Light; interval arithmetic; proof obligation; proof system; PVS", } @Article{Rouson:2010:DPM, author = "Damian W. I. Rouson and Helgi Adalsteinsson and Jim Xia", title = "Design patterns for multiphysics modeling in {Fortran 2003} and {C++}", journal = j-TOMS, volume = "37", number = "1", pages = "3:1--3:30", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644004", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present three new object-oriented software design patterns in Fortran 2003 and C++. These patterns integrate coupled differential equations, facilitating the flexible swapping of physical and numerical software abstractions at compile-time and runtime. The Semi-Discrete pattern supports the time advancement of a dynamical system encapsulated in a single abstract data type (ADT). The Puppeteer pattern combines ADTs into a multiphysics package, mediates interabstraction communications, and enables implicit marching even when nonlinear terms couple separate ADTs with private data. The Surrogate pattern emulates C++ forward references in Fortran 2003. After code demonstrations using the Lorenz equations, we provide architectural descriptions of our use of the new patterns in extending the Rouson et al. [2008a] Navier--Stokes solver to simulate multiphysics phenomena. We also describe the relationships between the new patterns and two previously developed architectural elements: the Strategy pattern of Gamma et al. [1995] and the template emulation technique of Akin [2003]. This report demonstrates how these patterns manage complexity by providing logical separation between individual physics models and the control logic that bridges between them. Additionally, it shows how language features such as operator overloading and automated memory management enable a clear mathematical notation for model bridging and system evolution.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Design patterns; Lorenz equations; multiphysics modeling", } @Article{Kornerup:2010:CCR, author = "Peter Kornerup and Christoph Lauter and Vincent Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller", title = "Computing correctly rounded integer powers in floating-point arithmetic", journal = j-TOMS, volume = "37", number = "1", pages = "4:1--4:23", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644005", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a {\em fused multiply-add\/} (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Correct rounding; floating-point arithmetic; integer power function", } @Article{Kirby:2010:SFE, author = "Robert C. Kirby", title = "Singularity-free evaluation of collapsed-coordinate orthogonal polynomials", journal = j-TOMS, volume = "37", number = "1", pages = "5:1--5:16", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644006", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The $L^2$ -orthogonal polynomials used in finite and spectral element methods on nonrectangular elements may be defined in terms of {\em collapsed\/} coordinates, wherein the shapes are mapped to a square or cube by means of a singular change of variables. The orthogonal basis is a product of specific Jacobi polynomials in these new coordinates. Implementations of these polynomials require special handling of the coordinate singularities. We derive new recurrence relations for these polynomials on triangles and tetrahedra that work directly in the original coordinates. These relations, also applicable to pyramids and prisms, do not require any special treatment of singular points. These recurrences are seen to speed up both symbolic and numerical computation of the orthogonal polynomials.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "nonrectangular domain; Orthogonal polynomial; recurrence relation", } @Article{Alnaes:2010:ESC, author = "Martin Sandve Aln{\ae}s and Kent-Andr{\'e} Mardal", title = "On the efficiency of symbolic computations combined with code generation for finite element methods", journal = j-TOMS, volume = "37", number = "1", pages = "6:1--6:26", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644007", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Efficient and easy implementation of variational forms for finite element discretization can be accomplished with metaprogramming. Using a high-level language like Python and symbolic mathematics makes an abstract problem definition possible, but the use of a low-level compiled language is vital for run-time efficiency. By generating low-level C++ code based on symbolic expressions for the discrete weak form, it is possible to accomplish a high degree of abstraction in the problem definition while surpassing the run-time efficiency of traditional hand written C++ codes. We provide several examples where we demonstrate orders of magnitude in speedup.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automation; code generation; compiler; finite element; metaprogramming; Variational forms", } @Article{Savage:2010:COA, author = "John E. Savage and Mohammad Zubair", title = "Cache-optimal algorithms for option pricing", journal = j-TOMS, volume = "37", number = "1", pages = "7:1--7:30", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644008", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Today computers have several levels of memory hierarchy. To obtain good performance on these processors it is necessary to design algorithms that minimize I/O traffic to slower memories in the hierarchy. In this article, we study the computation of option pricing using the binomial and trinomial models on processors with a multilevel memory hierarchy. We derive lower bounds on memory traffic between different levels of the hierarchy for these two models. We also develop algorithms for the binomial and trinomial models that have near-optimal memory traffic between levels. We have implemented these algorithms on an UltraSparc IIIi processor with a 4-level of memory hierarchy and demonstrated that our algorithms outperform algorithms without cache blocking by a factor of up to 5 and operate at 70\% of peak performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "cache blocking; Memory hierarchy", } @Article{Olgaard:2010:OQR, author = "Kristian B. {\O}lgaard and Garth N. Wells", title = "Optimizations for quadrature representations of finite element tensors through automated code generation", journal = j-TOMS, volume = "37", number = "1", pages = "8:1--8:23", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644009", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We examine aspects of the computation of finite element matrices and vectors that are made possible by automated code generation. Given a variational form in a syntax that resembles standard mathematical notation, the low-level computer code for building finite element tensors, typically matrices, vectors and scalars, can be generated automatically via a form compiler. In particular, the generation of code for computing finite element matrices using a quadrature approach is addressed. For quadrature representations, a number of optimization strategies which are made possible by automated code generation are presented. The relative performance of two different automatically generated representations of finite element matrices is examined, with a particular emphasis on complicated variational forms. It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run-time performance, the time required to generate the code or the size of the generated code. The approach and optimizations elaborated here are effective for a range of variational forms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "code generation; Finite element method", } @Article{Albrecht:2010:AEM, author = "Martin Albrecht and Gregory Bard and William Hart", title = "{Algorithm 898}: {Efficient} multiplication of dense matrices over {GF(2)}", journal = j-TOMS, volume = "37", number = "1", pages = "9:1--9:14", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644010", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (F$_2$). In particular we present our implementation --- in the M4RI library --- of Strassen--Winograd matrix multiplication and the ``Method of the Four Russians for Multiplication'' (M4RM) and compare it against other available implementations. Good performance is demonstrated on AMD's Opteron processor and particularly good performance on Intel's Core 2 duo processor. The open-source M4RI library is available as a stand-alone package as well as part of the Sage mathematics system.\par In machine terms, addition in F$_2$ is logical-XOR, and multiplication is logical-AND, thus a machine word of 64 bits allows one to operate on 64 elements of F$_2$ in parallel: at most one CPU cycle for 64 parallel additions or multiplications. As such, element-wise operations over F$_2$ are relatively cheap. In fact, in this paper, we conclude that the actual bottlenecks are memory reads and writes and issues of data locality. We present our empirical findings in relation to minimizing these and give an analysis thereof.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "GF(2); greasing; linear algebra; matrix; multiplication; Strassen", } @Article{Sarra:2010:AMP, author = "Scott A. Sarra", title = "{Algorithm 899}: {The Matlab} postprocessing toolkit", journal = j-TOMS, volume = "37", number = "1", pages = "10:1--10:15", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644011", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Global polynomial approximation methods applied to piecewise continuous functions exhibit the well-known Gibbs phenomenon. We summarize known methods to remove the Gibbs oscillations and present a collection of Matlab programs that implement the methods. The software features a Graphical User Interface that allows easy access to the postprocessing algorithms for benchmarking and educational purposes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Gibbs phenomenon; Matlab; postprocessing; Pseudospectral methods", } @Article{Torres:2010:ADT, author = "Germ{\'a}n A. Torres", title = "{Algorithm 900}: a discrete time {Kalman} filter package for large scale problems", journal = j-TOMS, volume = "37", number = "1", pages = "11:1--11:16", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644012", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Data assimilation is the process of feeding a partially unknown prediction model with available information from observations, with the objective of correcting and improving the modeled results. One of the most important mathematical tools to perform data assimilation is the Kalman filter. This is essentially a predictor-corrector algorithm that is optimal in the sense of minimizing the trace of the covariance matrix of the errors. Unfortunately, the computational cost of applying the filter to large scale problems is enormous, and the programming of the filter is highly dependent on the model and the format of the data involved. The first objective of this article is to present a set of Fortran 90 modules that implement the reduced rank square root versions of the Kalman filter, adapted for the assimilation of a very large number of variables. The second objective is to present a Kalman filter implementation whose code is independent of both the model and observations and is easy to use. A detailed description of the algorithms, structure, parallelization is given along with examples of using the package to solve practical problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "data assimilation; Kalman filter; Large scale problems", } @Article{Vlachos:2010:ALP, author = "D. S. Vlachos and T. E. Simos", title = "{Algorithm 901}: {LMEF} --- a program for the construction of linear multistep methods with exponential fitting for the numerical solution of ordinary differential equations", journal = j-TOMS, volume = "37", number = "1", pages = "12:1--12:10", month = jan, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1644001.1644013", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Mar 15 10:45:33 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "LMEF is a program written in MATLAB, to calculate the coefficients of a linear multi-step method (explicit, implicit or backward differentiation formulas) with algebraic and/or exponential fitting, for the numerical solution of first order ordinary differential equations. Moreover, LMEF calculates the local truncation error and in the case of exponential fitting, the Taylor expansions of the coefficients that are necessary for the implementation of the method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "backward differentiation formulas; exponential fitting; Linear multistep methods", } @Article{Rasch:2010:EIE, author = "Arno Rasch and H. Martin B{\"u}cker", title = "{EFCOSS}: an interactive environment facilitating optimal experimental design", journal = j-TOMS, volume = "37", number = "2", pages = "13:1--13:37", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731023", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An interactive software environment is proposed that combines numerical simulation codes with optimization software packages in an automated and modular way. It simplifies the experimentation with varying objective functions for common optimization problems such as parameter estimation and optimal experimental design that are frequently encountered in computational science and engineering. The design philosophy takes into consideration the need for derivatives of potentially large-scale simulation codes via automatic differentiation as well as distributed computing in a heterogeneous environment via CORBA.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "automatic differentiation; distributed computing; optimal experimental design; parameter estimation; Problem solving environments", } @Article{Chen:2010:ECF, author = "Wei Chen and Gabor T. Herman", title = "Efficient controls for finitely convergent sequential algorithms", journal = j-TOMS, volume = "37", number = "2", pages = "14:1--14:23", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731024", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Finding a feasible point that satisfies a set of constraints is a common task in scientific computing; examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems; an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice usually converges faster than ART3. In this article we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (1) finite convergence is retained, and (2) the speed of convergence is improved. The first of these properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Algebraic reconstruction technique; cyclic subgradient projections; feasibility problem; finite convergence; sequential algorithm", } @Article{Krogh:2010:SSO, author = "Fred T. Krogh", title = "Stepsize selection for ordinary differential equations", journal = j-TOMS, volume = "37", number = "2", pages = "15:1--15:21", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731025", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This note offers a new approach based on a least squares fit to past data in order to select the stepsize when solving an ordinary differential equation. The approach used may have applicability to other situations where one wants to repeatedly make short term predictions given somewhat noisy data. Additional ad hoc rules help significantly for reliability and efficiency. Comparisons with some Runge--Kutta codes, an Adams code, and an extrapolation code are also included.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "ODE; prediction; stepsize", } @Article{Rutten:2010:EFP, author = "Luc Rutten and Marko {Van Eekelen}", title = "Efficient and formally proven reduction of large integers by small moduli", journal = j-TOMS, volume = "37", number = "2", pages = "16:1--16:21", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731026", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "On $w$-bit processors which are much faster at multiplying two $w$-bit integers than at dividing $2w$-bit integers by $w$-bit integers, reductions of large integers by moduli $M$ smaller than $2^{w-1}$ are often implemented suboptimally, leading applications to take excessive processing time.\par We present a modular reduction algorithm implementing division by a modulus through multiplication by a reciprocal of that modulus, a well-known method for moduli larger than $2^{w-1}$. We show that application of this method to smaller moduli makes it possible to express certain modular sums and differences without having to compensate for word overflows.\par By embedding the algorithm in a loop and applying a few transformations to the loop, we obtain an algorithm for reduction of large integers by moduli up to $2^{w - 1}$. Implementations of this algorithm can run considerably faster than implementations of similar algorithms that allow for moduli up to $2^w$. This is substantiated by measurements on processors with relatively fast multiplication instructions.\par It is notoriously hard to specify efficient mathematical algorithms on the level of abstract machine instructions in an error-free manner. In order to eliminate the chance of errors as much as possible, we have created formal correctness proofs of our algorithms, checked by a mechanized proof assistant.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Computer arithmetic; machine-checked proofs; modular reduction; optimization", } @Article{Hogg:2010:FRM, author = "J. D. Hogg and J. A. Scott", title = "A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems", journal = j-TOMS, volume = "37", number = "2", pages = "17:1--17:24", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731027", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for using single precision for the solution of linear systems is a potential loss of accuracy in the computed solutions. For sparse linear systems, the use of mixed precision in which double-precision iterative methods are preconditioned by a single-precision factorization can enable the recovery of high-precision solutions more quickly and use less memory than a sparse direct solver run using double-precision arithmetic.\par In this article, we consider the use of single precision within direct solvers for sparse symmetric linear systems, exploiting both the reduction in memory requirements and the performance gains. We develop a practical algorithm to apply a mixed-precision approach and suggest parameters and techniques to minimize the number of solves required by the iterative recovery process. These experiments provide the basis for our new code HSL\_MA79 --- a fast, robust, mixed-precision sparse symmetric solver that is included in the mathematical software library HSL.\par Numerical results for a wide range of problems from practical applications are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "FGMRES; Fortran 95; Gaussian elimination; iterative refinement; mixed precision; multifrontal method; sparse symmetric linear systems", } @Article{Gustavson:2010:RFP, author = "Fred G. Gustavson and Jerzy Wa{\'s}niewski and Jack J. Dongarra and Julien Langou", title = "Rectangular full packed format for {Cholesky}'s algorithm: factorization, solution, and inversion", journal = j-TOMS, volume = "37", number = "2", pages = "18:1--18:21", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731028", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a new data format for storing triangular, symmetric, and Hermitian matrices called {\em Rectangular Full Packed Format\/} (RFPF). The standard two-dimensional arrays of Fortran and C (also known as {\em full format\/}) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full-format representation. Also, RFPF requires exactly the same minimal storage as the packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full-format routine and two calls to Level 3 BLAS routines. This means {\em no\/} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution, and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using the standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "BLAS; Cholesky factorization and solution; complex Hermitian matrices; LAPACK; linear algebra libraries; novel packed matrix data structures; positive definite matrices; Real symmetric matrices; Rectangular Full Packed Format; recursive algorithms", } @Article{Scott:2010:SPC, author = "Jennifer A. Scott", title = "Scaling and pivoting in an out-of-core sparse direct solver", journal = j-TOMS, volume = "37", number = "2", pages = "19:1--19:23", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731029", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Out-of-core sparse direct solvers reduce the amount of main memory needed to factorize and solve large sparse linear systems of equations by holding the matrix data, the computed factors, and some of the work arrays in files on disk. The efficiency of the factorization and solution phases is dependent upon the number of entries in the factors. For a given pivot sequence, the level of fill in the factors beyond that predicted on the basis of the sparsity pattern alone depends on the number of pivots that are delayed (i.e., the number of pivots that are used later than expected because of numerical stability considerations). Our aim is to limit the number of delayed pivots, while maintaining robustness and accuracy. In this article, we consider a new out-of-core multifrontal solver HSL\_MA78 from the HSL mathematical software library that is designed to solve the unsymmetric sparse linear systems that arise from finite element applications. We consider how equilibration can be built into the solver without requiring the system matrix to be held in main memory. We also examine the effects of different pivoting strategies, including threshold partial pivoting, threshold rook pivoting, and static pivoting. Numerical experiments on problems arising from a range of practical applications illustrate the importance of scaling and show that, in some cases, rook pivoting can be more efficient than partial pivoting in terms of both the factorization time and the sparsity of the computed factors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "element problems; Large sparse unsymmetric linear systems; multifrontal; out-of-core solver; partial pivoting; rook pivoting; scaling", } @Article{Logg:2010:DAF, author = "Anders Logg and Garth N. Wells", title = "{DOLFIN}: {Automated} finite element computing", journal = j-TOMS, volume = "37", number = "2", pages = "20:1--20:28", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731030", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled, and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This article discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "code generation; DOLFIN; FEniCS project; form compiler", } @Article{Stathopoulos:2010:PPI, author = "Andreas Stathopoulos and James R. McCombs", title = "{PRIMME}: preconditioned iterative multimethod eigensolver --- methods and software description", journal = j-TOMS, volume = "37", number = "2", pages = "21:1--21:30", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731031", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes the PRIMME software package for solving large, sparse Hermitian standard eigenvalue problems. The difficulty and importance of these problems have increased over the years, necessitating the use of preconditioning and near optimally converging iterative methods. However, the complexity of tuning or even using such methods has kept them outside the reach of many users. Responding to this problem, we have developed PRIMME, a comprehensive package that brings state-of-the-art methods from ``bleeding edge'' to production, with the best possible robustness, efficiency, and a flexible, yet highly usable interface that requires minimal or no tuning. We describe (1) the PRIMME multimethod framework that implements a variety of algorithms, including the near optimal methods GD+$k$ and JDQMR; (2) a host of algorithmic innovations and implementation techniques that endow the software with its robustness and efficiency; (3) a multilayer interface that captures our experience and addresses the needs of both expert and end users.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "block; conjugate gradient; Davidson; eigenvalues; eigenvectors; Hermitian; iterative; Jacobi--Davidson; Lanczos; locking; preconditioning; software package", } @Article{Rao:2010:AGM, author = "Anil V. Rao and David A. Benson and Christopher Darby and Michael A. Patterson and Camila Francolin and Ilyssa Sanders and Geoffrey T. Huntington", title = "{Algorithm 902}: {GPOPS}, a {MATLAB} software [sic] for solving multiple-phase optimal control problems using the {Gauss} pseudospectral method", journal = j-TOMS, volume = "37", number = "2", pages = "22:1--22:39", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731032", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrigendum \cite{Rao:2011:CAG}.", abstract = "An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the {\em Gauss pseudospectral method}. The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differential-algebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A large-scale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called {\em GPOPS}, is applied to three classical optimal control problems to demonstrate its utility. The algorithm described in this article will provide researchers and engineers a useful software tool and a reference when it is desired to implement the Gauss pseudospectral method in other programming languages.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "computational methods; Dynamic optimization; nonlinear optimization; nonlinear programming; optimal control; phases", } @Article{Celledoni:2010:AFF, author = "Elena Celledoni and Antonella Zanna", title = "{Algorithm 903}: {FRB} --- {Fortran} routines for the exact computation of free rigid body motions", journal = j-TOMS, volume = "37", number = "2", pages = "23:1--23:24", month = apr, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1731022.1731033", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 21 11:39:57 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part $m$ by Jacobi elliptic functions, and suitably chosen frames for the attitude matrix\slash quaternion $ Q / q $, respectively. The frame transformation requires the computation of elliptic integrals of the third kind. Implementation and usage of the routines are described, and some examples of drivers are included. Accuracy and performance are also tested to provide reliable numerical results.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "attitude rotation; Jacobi elliptic integrals; numerical methods; Rigid body; splitting methods", } @Article{Haggard:2010:CTP, author = "Gary Haggard and David J. Pearce and Gordon Royle", title = "Computing {Tutte} Polynomials", journal = j-TOMS, volume = "37", number = "3", pages = "24:1--24:17", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824802", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Tutte polynomial of a graph, also known as the partition function of the $q$-state Potts model is a 2-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial as partial evaluations, and various numerical invariants such as the number of spanning trees as complete evaluations. However despite its ubiquity, there are no widely available effective computational tools able to compute the Tutte polynomial of a general graph of reasonable size. In this article we describe the implementation of a program that exploits isomorphisms in the computation tree to extend the range of graphs for which it is feasible to compute their Tutte polynomials, and we demonstrate the utility of the program by finding counterexamples to a conjecture of Welsh on the location of the real flow roots of a graph.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Chromatic polynomial; flow polynomial; graph polynomial; graph theory; Tutte polynomial", } @Article{Gonzalez-Pinto:2010:CBT, author = "Severiano Gonz{\'a}lez-Pinto and Rogel Rojas-Bello", title = "A Code Based on the Two-Stage {Runge--Kutta Gauss} Formula for Second-Order Initial Value Problems", journal = j-TOMS, volume = "37", number = "3", pages = "25:1--25:30", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824803", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A code based on the two-stage Gauss formula (order four) for second-order initial value problems of a special type is developed. This code can be used to obtain a low- to medium-precision integration for a wide range of problems in the class of oscillatory type, Hamiltonian problems, and time-dependent partial differential equations discretized in space by finite differences or finite elements. The iteration process used in solving for the stage values of the Gauss formula, the selection of the initial step size, and the choice of an appropriate local error estimator for determining the step size change according to a particular tolerance specified by the user are studied. Moreover, a global error estimate and a dense output at equidistant points in the integration interval are supplied with the code. Numerical experiments and some comparisons with certain standard codes on relevant test problems are also given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "implicit Runge--Kutta Nystr{\"o} initial step size; local error estimators; m methods; predictors; Second-order problems; stage values", } @Article{Gonnet:2010:IRA, author = "Pedro Gonnet", title = "Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants", journal = j-TOMS, volume = "37", number = "3", pages = "26:1--26:32", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824804", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat nonnumerical values of the integrand, how they deal with improper divergent integrals, and how they estimate the integration error. The main focus of these improvements is to increase the {\em reliability\/} of the algorithms without significantly impacting their {\em efficiency}. Both algorithms are implemented in MATLAB and tested using both the ``families'' suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Adaptive quadrature; error estimation; interpolation; orthogonal polynomials", } @Article{Yamazaki:2010:APS, author = "Ichitaro Yamazaki and Zhaojun Bai and Horst Simon and Lin-Wang Wang and Kesheng Wu", title = "Adaptive Projection Subspace Dimension for the Thick-Restart {Lanczos} Method", journal = j-TOMS, volume = "37", number = "3", pages = "27:1--27:18", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824805", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package $a$-TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots, $a$-TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Adaptive subspace dimension; electronic structure calculation; Lanczos; thick-restart", } @Article{Anand:2010:UTE, author = "Christopher Kumar Anand and Anuroop Sharma", title = "Unified Tables for Exponential and Logarithm Families", journal = j-TOMS, volume = "37", number = "3", pages = "28:1--28:23", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824806", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Accurate table methods allow for very accurate and efficient evaluation of elementary functions. We present new single-table approaches to logarithm and exponential evaluation, by which we mean that a single table of values works for both $\log(x)$ and $log(1 + x)$, and a single table for $e^x$ and $e^x - 1$. This approach eliminates special cases normally required to evaluate $\log(1 + x)$ and $e^x - 1$ accurately near zero, which will significantly improve performance on architectures which use SIMD parallelism, or on which data-dependent branching is expensive.\par We have implemented it on the Cell/B.E. SPU (SIMD compute engine) and found the resulting functions to be up to twice as fast as the conventional implementations distributed in the IBM Mathematical Acceleration Subsystem (MASS). We include the literate code used to generate all the variants of exponential and log functions in the article, and discuss relevant language and hardware features.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Accurate tables method; Cell/B.E; IEEE arithmetic; SIMD; vector library", } @Article{Ollivier-Gooch:2010:IDS, author = "Carl Ollivier-Gooch and Lori Diachin and Mark S. Shephard and Timothy Tautges and Jason Kraftcheck and Vitus Leung and Xiaojuan Luo and Mark Miller", title = "An Interoperable, Data-Structure-Neutral Component for Mesh Query and Manipulation", journal = j-TOMS, volume = "37", number = "3", pages = "29:1--29:28", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1864430", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Much of the effort required to create a new simulation code goes into developing infrastructure for mesh data manipulation, adaptive refinement, design optimization, and so forth. This infrastructure is an obvious target for code reuse, except that implementations of these functionalities are typically tied to specific data structures. In this article, we describe a software component---an abstract data model and programming interface---designed to provide low-level mesh query and manipulation support for meshing and solution algorithms. The component's data model provides a data abstraction, completely hiding all details of how mesh data is stored, while its interface defines how applications can interact with that data. Because the component has been carefully designed to be general purpose and efficient, it provides a practical platform for implementing high-level mesh operations independently of the underlying mesh data structures. After describing the data model and interface, we provide several usage examples, each of which has been used successfully with multiple implementations of the interface functionality. The overhead due to accessing mesh data through the interface rather than directly accessing the underlying mesh data is shown to be acceptably small.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Data structure independence; mesh modification; mesh-based simulations; software components", } @Article{DAmbra:2010:MPP, author = "Pasqua D'Ambra and Daniela {Di Serafino} and Salvatore Filippone", title = "{MLD2P4}: a Package of Parallel Algebraic Multilevel Domain Decomposition Preconditioners in {Fortran 95}", journal = j-TOMS, volume = "37", number = "3", pages = "30:1--30:23", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824808", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Domain decomposition ideas have long been an essential tool for the solution of PDEs on parallel computers. In recent years many research efforts have been focused on recursively employing domain decomposition methods to obtain multilevel preconditioners to be used with Krylov solvers. In this context, we developed MLD2P4 (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS), a package of parallel multilevel preconditioners that combines additive Schwarz domain decomposition methods with a smoothed aggregation technique to build a hierarchy of coarse-level corrections in an algebraic way. The design of MLD2P4 was guided by objectives such as extensibility, flexibility, performance, portability, and ease of use. They were achieved by following an object-based approach while using the Fortran 95 language, as well as by employing the PSBLAS library as a basic framework. In this article, we present MLD2P4 focusing on its design principles, software architecture, and use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "algebraic multilevel; domain decomposition; Mathematics of computing; object-based design; parallel preconditioners", } @Article{Wendykier:2010:PCH, author = "Piotr Wendykier and James G. Nagy", title = "{Parallel Colt}: a High-Performance {Java} Library for Scientific Computing and Image Processing", journal = j-TOMS, volume = "37", number = "3", pages = "31:1--31:22", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824809", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Major breakthroughs in chip and software design have been observed for the last nine years. In October 2001, IBM released the world's first multicore processor: POWER4. Six years later, in February 2007, NVIDIA made a public release of CUDA SDK, a set of development tools to write algorithms for execution on Graphic Processing Units (GPUs). Although software vendors have started working on parallelizing their products, the vast majority of existing code is still sequential and does not effectively utilize modern multicore CPUs and manycore GPUs.\par This article describes Parallel Colt, a multithreaded Java library for scientific computing and image processing. In addition to describing the design and functionality of Parallel Colt, a comparison to MATLAB is presented. Two ImageJ plugins for iterative image deblurring and motion correction of PET brain images are described as typical applications of this library. Performance comparisons with MATLAB, including GPU computations via AccelerEyes' Jacket toolbox are also given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Deconvolution; FFT; inverse problems; iterative methods; motion correction; multithreading; PET; regularization", } @Article{Granat:2010:PSS, author = "Robert Granat and Bo Kagstrom", title = "Parallel Solvers for {Sylvester}-Type Matrix Equations with Applications in Condition Estimation, {Part I}: Theory and Algorithms", journal = j-TOMS, volume = "37", number = "3", pages = "32:1--32:32", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824810", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Parallel ScaLAPACK-style algorithms for solving eight common standard and generalized Sylvester-type matrix equations and various sign and transposed variants are presented. All algorithms are blocked variants based on the Bartels--Stewart method and involve four major steps: reduction to triangular form, updating the right-hand side with respect to the reduction, computing the solution to the reduced triangular problem, and transforming the solution back to the original coordinate system. Novel parallel algorithms for solving reduced triangular matrix equations based on wavefront-like traversal of the right-hand side matrices are presented together with a generic scalability analysis. These algorithms are used in condition estimation and new robust parallel sep$^{ - 1}$ -estimators are developed. Experimental results from three parallel platforms, including results from a mixed OpenMP/MPI platform, are presented and analyzed using several performance and accuracy metrics. The analysis includes results regarding general and triangular parallel solvers as well as parallel condition estimators.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "condition estimation; Eigenvalue problems; library software; Sylvester matrix equations", } @Article{Granat:2010:ASL, author = "Robert Granat and Bo K{\aa}gstr{\"o}m", title = "{Algorithm 904}: {The SCASY Library} -- Parallel Solvers for {Sylvester}-Type Matrix Equations with Applications in Condition Estimation, {Part II}", journal = j-TOMS, volume = "37", number = "3", pages = "33:1--33:4", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824811", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We continue our presentation of parallel ScaLAPACK-style algorithms for solving Sylvester-type matrix equations. In Part II, we present SCASY (SCAlable SYlvester solvers), a state-of-the-art HPC software library for solving 44 sign and transpose variants of eight common standard and generalized Sylvester-type matrix equations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "condition estimation; Eigenvalue problems; parallel algorithms; Parallel computing; Sylvester matrix equations", } @Article{Thacker:2010:AMS, author = "William I. Thacker and Jingwei Zhang and Laynet Watson and Jeffrey B. Birch and Manjula A. Iyer and Michael W. Berry", title = "{Algorithm 905}: Modified {Shepard} Algorithm for Interpolation of Scattered Multivariate Data", journal = j-TOMS, volume = "37", number = "3", pages = "34:1--34:20", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824812", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Scattered data interpolation problems arise in many applications. Shepard's method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension $m$. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard's algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "M-estimation; RIPPLE; Shepard's algorithm", } @Article{Li:2010:AET, author = "Tiancheng Li and Ian Robinson", title = "{Algorithm 906}: {{\em elrint3d}} --- a Three-Dimensional Nonadaptive Automatic Cubature Routine Using a Sequence of Embedded Lattice Rules", journal = j-TOMS, volume = "37", number = "3", pages = "35:1--35:17", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824813", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A three-dimensional automatic cubature routine, called {\em elrint3d}, is described and numerical results are presented that demonstrate its applicability across a wide range of domains and integrand types. The underlying algorithm is based on a $2 s$-copy lattice augmentation sequence, the seed lattice for which has been determined by exhaustive search based on optimization of index of merit and trigonometric degree of precision.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "2s-copy lattice augmentation sequence; Automatic cubature routine; index of merit; seed lattice; trigonometric degree of precision", } @Article{Davis:2010:AKD, author = "Timothy A. Davis and Ekanathan Palamadai Natarajan", title = "{Algorithm 907}: {KLU}, a Direct Sparse Solver for Circuit Simulation Problems", journal = j-TOMS, volume = "37", number = "3", pages = "36:1--36:17", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824814", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "KLU is a software package for solving sparse unsymmetric linear systems of equations that arise in circuit simulation applications. It relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree and nested dissection), and Gilbert/Peierls' sparse left-looking LU factorization algorithm to factorize each block. The package is written in C and includes a MATLAB interface. Performance results comparing KLU with SuperLU, Sparse 1.3, and UMFPACK on circuit simulation matrices are presented. KLU is the default sparse direct solver in the Xyce$^{TM}$ circuit simulation package developed by Sandia National Laboratories.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "circuit simulation; LU factorization; sparse matrices", } @Article{Zhu:2010:AOE, author = "Yong-Kang Zhu and Wayne B. Hayes", title = "{Algorithm 908}: Online Exact Summation of Floating-Point Streams", journal = j-TOMS, volume = "37", number = "3", pages = "37:1--37:13", month = sep, year = "2010", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1824801.1824815", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 27 10:15:50 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a novel, online algorithm for exact summation of a stream of floating-point numbers. By ``online'' we mean that the algorithm needs to see only one input at a time, and can take an arbitrary length input stream of such inputs while requiring only constant memory. By ``exact'' we mean that the sum of the internal array of our algorithm is exactly equal to the sum of all the inputs, and the returned result is the correctly-rounded sum. The proof of correctness is valid for all inputs (including nonnormalized numbers but modulo intermediate overflow), and is independent of the number of summands or the condition number of the sum. The algorithm asymptotically needs only 5 FLOPs per summand, and due to instruction-level parallelism runs only about 2--3 times slower than the obvious, fast-but-dumb ``ordinary recursive summation'' loop when the number of summands is greater than 10,000. Thus, to our knowledge, it is the fastest, most accurate, and most memory efficient among known algorithms. Indeed, it is difficult to see how a faster algorithm or one requiring significantly fewer FLOPs could exist without hardware improvements. An application for a large number of summands is provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "Floating-point summation; rounding error", } @Article{Rozloznik:2011:PTT, author = "Miroslav Rozlo{\v{z}}n{\'\i}k and Gil Shklarski and Sivan Toledo", title = "Partitioned Triangular Tridiagonalization", journal = j-TOMS, volume = "37", number = "4", pages = "38:1--38:16", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916462", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a partitioned algorithm for reducing a symmetric matrix to a tridiagonal form, with partial pivoting. That is, the algorithm computes a factorization $P A P^T = L T L^T$, where, $P$ is a permutation matrix, $L$ is lower triangular with a unit diagonal and entries' magnitudes bounded by 1, and $T$ is symmetric and tridiagonal. The algorithm is based on the basic (nonpartitioned) methods of Parlett and Reid and of Aasen. We show that our factorization algorithm is componentwise backward stable (provided that the growth factor is not too large), with a similar behavior to that of Aasen's basic algorithm. Our implementation also computes the QR factorization of $T$ and solves linear systems of equations using the computed factorization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cook:2011:SVS, author = "William Cook and Daniel E. Steffy", title = "Solving Very Sparse Rational Systems of Equations", journal = j-TOMS, volume = "37", number = "4", pages = "39:1--39:21", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916463", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Efficient methods for solving linear-programming problems in exact precision rely on the solution of sparse systems of linear equations over the rational numbers. We consider a test set of instances arising from exact-precision linear programming and use this test set to compare the performance of several techniques designed for symbolic sparse linear-system solving. We compare a direct exact solver based on LU factorization, Wiedemann's method for black-box linear algebra, Dixon's p-adic-lifting algorithm, and the use of iterative numerical methods and rational reconstruction as developed by Wan.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lin:2011:SAS, author = "Lin Lin and Chao Yang and Juan C. Meza and Jianfeng Lu and Lexing Ying and Weinan E", title = "{SelInv}---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix", journal = j-TOMS, volume = "37", number = "4", pages = "40:1--40:19", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916464", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe an efficient implementation of an algorithm for computing selected elements of a general sparse symmetric matrix $A$ that can be decomposed as $A = L D L^T$, where $L$ is lower triangular and $D$ is diagonal. Our implementation, which is called SelInv, is built on top of an efficient supernodal left-looking $L D L^T$ factorization of $A$. We discuss how computational efficiency can be gained by making use of a relative index array to handle indirect addressing. We report the performance of SelInv on a collection of sparse matrices of various sizes and nonzero structures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "40", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Taylor:2011:CAS, author = "Ken Taylor and Scott Rickard and Konstantinos Drakakis", title = "{Costas} Arrays: Survey, Standardization, and {MATLAB} Toolbox", journal = j-TOMS, volume = "37", number = "4", pages = "41:1--41:31", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916465", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A Costas array is an arrangement of N dots on an N-by-N grid, one per row, one per column, such that no two dots share the same displacement vector with any other pair. Costas arrays have applications in SONAR\slash RADAR systems, communication systems, cryptography, and other areas. We present a standardization of notation and language which can be used to discuss Costas array generation techniques and array manipulations. Using this standardization we can concisely and clearly state various theorems about Costas arrays, including several new theorems about the symmetries of Costas arrays. We also define labels for each array (generated, emergent, and sporadic), which describe whether the array is generated using a known technique, generated using a semiempirical variation of a known technique, or of unexplained origin.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "41", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Silvester:2011:OIS, author = "David J. Silvester and Valeria Simoncini", title = "An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation", journal = j-TOMS, volume = "37", number = "4", pages = "42:1--42:22", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural ``energy'' norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a ``proof of concept'' MATLAB implementation of this algorithm, which we call EST\_MINRES, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package (cf. ACM Transactions on Mathematical Software 33, Article 14, 2007).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "42", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2011:SAI, author = "Xiaoye S. Li and Meiyue Shao", title = "A Supernodal Approach to Incomplete {LU} Factorization with Partial Pivoting", journal = j-TOMS, volume = "37", number = "4", pages = "43:1--43:20", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a new supernode-based incomplete LU factorization method to construct a preconditioner for solving sparse linear systems with iterative methods. The new algorithm is primarily based on the ILUTP approach by Saad, and we incorporate a number of techniques to improve the robustness and performance of the traditional ILUTP method. These include new dropping strategies that accommodate the use of supernodal structures in the factored matrix and an area-based fill control heuristic for the secondary dropping strategy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "43", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{LeDigabel:2011:ANN, author = "S{\'e}bastien {Le Digabel}", title = "{Algorithm 909}: {NOMAD}: Nonlinear Optimization with the {MADS} Algorithm", journal = j-TOMS, volume = "37", number = "4", pages = "44:1--44:15", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916468", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "NOMAD is software that implements the Mesh Adaptive Direct Search (MADS) algorithm for blackbox optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and aims for the best possible solution with a small number of evaluations. The objective of this article is to describe the underlying algorithm, the software's functionalities, and its implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "44", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kormanyos:2011:APC, author = "Christopher Kormanyos", title = "{Algorithm 910}: a Portable {C++} Multiple-Precision System for Special-Function Calculations", journal = j-TOMS, volume = "37", number = "4", pages = "45:1--45:27", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916469", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents a portable C++ system for multiple precision calculations of special functions called {\tt e\_float}. It has an extendable architecture with a uniform C++ layer which can be used with any suitably prepared MP type. The system implements many high-precision special functions and extends some of these to very large parameter ranges. It supports calculations with 30 \ldots{} 300 decimal digits of precision. Interoperabilities with Microsoft's CLR, Python, and Mathematica{\reg} are supported. The {\tt e\_float} system and its usage are described in detail. Implementation notes, testing results, and performance measurements are provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "45", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Smith:2011:AMP, author = "David M. Smith", title = "{Algorithm 911}: Multiple-Precision Exponential Integral and Related Functions", journal = j-TOMS, volume = "37", number = "4", pages = "46:1--46:16", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916470", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes a collection of Fortran-95 routines for evaluating the exponential integral function, error function, sine and cosine integrals, Fresnel integrals, Bessel functions, and related mathematical special functions using the FM multiple-precision arithmetic package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "46", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kodama:2011:AMC, author = "Masao Kodama", title = "{Algorithm 912}: a Module for Calculating Cylindrical Functions of Complex Order and Complex Argument", journal = j-TOMS, volume = "37", number = "4", pages = "47:1--47:25", month = feb, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1916461.1916471", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 16:05:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The present algorithm provides a module for calculating the cylindrical functions $ J_\nu (z) $, $ Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z) $, where the order $ \nu $ is complex and the complex argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The algorithm is written in Fortran 90 and calculates the functions using real and complex numbers of any intrinsic data type whose kind type parameter the user's Fortran system accepts. The methods of calculating the functions are based on two kinds of series expansions and numerical integration. Wronskian tests examine the functional values computed by this algorithm with double precision at 4,100,625 pseudorandom test points in the region $ | \Re \nu | \leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300 $, $ | \Im z| \leq 300 $.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "47", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2011:UFS, author = "Timothy A. Davis and Yifan Hu", title = "The {University of Florida} sparse matrix collection", journal = j-TOMS, volume = "38", number = "1", pages = "1:1--1:25", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049663", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dalberto:2011:EPM, author = "Paolo D'alberto and Marco Bodrato and Alexandru Nicolau", title = "Exploiting parallelism in matrix-computation kernels for symmetric multiprocessor systems: Matrix-multiplication and matrix-addition algorithm optimizations by software pipelining and threads allocation", journal = j-TOMS, volume = "38", number = "1", pages = "2:1--2:30", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049664", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a simple and efficient methodology for the development, tuning, and installation of matrix algorithms such as the hybrid Strassen's and Winograd's fast matrix multiply or their combination with the 3M algorithm for complex matrices (i.e., hybrid: a recursive algorithm as Strassen's until a highly tuned BLAS matrix multiplication allows performance advantages). We investigate how modern Symmetric Multiprocessor (SMP) architectures present old and new challenges that can be addressed by the combination of an algorithm design with careful and natural parallelism exploitation at the function level (optimizations) such as function-call parallelism, function percolation, and function software pipelining. We have three contributions: first, we present a performance overview for double- and double-complex-precision matrices for state-of-the-art SMP systems; second, we introduce new algorithm implementations: a variant of the 3M algorithm and two new different schedules of Winograd's matrix multiplication (achieving up to 20\% speedup with respect to regular matrix multiplication).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cazals:2011:CVU, author = "Frederic Cazals and Harshad Kanhere and S{\'e}bastien Loriot", title = "Computing the volume of a union of balls: a certified algorithm", journal = j-TOMS, volume = "38", number = "1", pages = "3:1--3:20", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049665", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Balls and spheres are amongst the simplest 3D modeling primitives, and computing the volume of a union of balls is an elementary problem. Although a number of strategies addressing this problem have been investigated in several communities, we are not aware of any robust algorithm, and present the first such algorithm. Our calculation relies on the decomposition of the volume of the union into convex regions, namely the restrictions of the balls to their regions in the power diagram. Theoretically, we establish a formula for the volume of a restriction, based on Gauss' divergence theorem. The proof being constructive, we develop the associated algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanDeGeijn:2011:HPD, author = "Robert A. {Van De Geijn} and Field G. {Van Zee}", title = "High-performance up-and-downdating via {Householder}-like transformations", journal = j-TOMS, volume = "38", number = "1", pages = "4:1--4:17", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049666", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present high-performance algorithms for up-and-downdating a Cholesky factor or QR factorization. The method uses Householder-like transformations, sometimes called hyperbolic Householder transformations, that are accumulated so that most computation can be cast in terms of high-performance matrix-matrix operations. The resulting algorithms can then be used as building blocks for an algorithm-by-blocks that allows computation to be conveniently scheduled to multithreaded architectures like multicore processors. Performance is shown to be similar to that achieved by a blocked QR factorization via Householder transformations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanGijzen:2011:AEI, author = "Martin B. {Van Gijzen} and Peter Sonneveld", title = "{Algorithm 913}: an elegant {IDR($s$)} variant that efficiently exploits biorthogonality properties", journal = j-TOMS, volume = "38", number = "1", pages = "5:1--5:19", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049667", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The IDR(s) method that is proposed in Sonneveld and van Gijzen [2008] is a very efficient limited memory method for solving large nonsymmetric systems of linear equations. IDR(s) is based on the induced dimension reduction theorem, that provides a way to construct subsequent residuals that lie in a sequence of shrinking subspaces. The IDR(s) algorithm that is given in Sonneveld and van Gijzen [2008] is a direct translation of the theorem into an algorithm. This translation is not unique. This article derives a new IDR(s) variant, that imposes (one-sided) biorthogonalization conditions on the iteration vectors. The resulting method has lower overhead in vector operations than the original IDR(s) algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2011:APC, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 914}: {Parabolic} cylinder function {$ W(a, x) $} and its derivative", journal = j-TOMS, volume = "38", number = "1", pages = "6:1--6:5", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049668", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A Fortran 90 program for the computation of the real parabolic cylinder functions $W(a, \pm x)$, $x \geq 0$ and their derivatives is presented. The code also computes scaled functions for $a > 50$. The functions $W(a, \pm x)$ are a numerically satisfactory pair of solutions of the parabolic cylinder equation $y^\prime + (x^2/4 - a)y = 0$, $x \geq 0$. Using Wronskian tests, we claim a relative accuracy better than $5 \times 10^{-13}$ in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than $5 \times 10^{-14}$. This code, together with the algorithm and related software described in Gil et al.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Morales:2011:RAB, author = "Jos{\'e} Luis Morales and Jorge Nocedal", title = "Remark on {``Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization''}", journal = j-TOMS, volume = "38", number = "1", pages = "7:1--7:4", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049669", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Zhu:1997:ALF}.", abstract = "This remark describes an improvement and a correction to Algorithm 778. It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase. The correction concerns an error caused by the use of routine dpmeps to estimate machine precision.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2011:ASM, author = "Timothy A. Davis", title = "{Algorithm 915}, {SuiteSparseQR}: {Multifrontal} multithreaded rank-revealing sparse {QR} factorization", journal = j-TOMS, volume = "38", number = "1", pages = "8:1--8:22", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049670", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel's Threading Building Blocks library. The symbolic analysis and ordering phase pre-eliminates singletons by permuting the input matrix A into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill-reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of ATA. Approximate rank-detection is performed within each frontal matrix using Heath's method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rao:2011:CAG, author = "Anil V. Rao and David A. Benson and Christopher Darby and Michael A. Patterson and Camila Francolin and Ilyssa Sanders and Geoffrey T. Huntington", title = "Corrigendum: {Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss pseudospectral method}", journal = j-TOMS, volume = "38", number = "1", pages = "9:1--9:2", month = nov, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049662.2049671", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 15 08:59:34 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Rao:2010:AGM}.", abstract = "An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differential-algebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A large-scale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called GPOPS, is applied to three classical optimal control problems to demonstrate its utility.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reid:2011:PFD, author = "John K. Reid and Jennifer A. Scott", title = "Partial factorization of a dense symmetric indefinite matrix", journal = j-TOMS, volume = "38", number = "2", pages = "10:1--10:19", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049674", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "At the heart of a frontal or multifrontal solver for the solution of sparse symmetric sets of linear equations, there is the need to partially factorize dense matrices (the frontal matrices) and to be able to use their factorizations in subsequent forward and backward substitutions. For a large problem, packing (holding only the lower or upper triangular part) is important to save memory. It has long been recognized that blocking is the key to efficiency and this has become particularly relevant on modern hardware. For stability in the indefinite case, the use of interchanges and $2 \times 2$ pivots as well as $1 \times 1$ pivots is equally well established.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Colman:2011:VCC, author = "Michel Colman and Annie Cuyt and Joris {Van Deun}", title = "Validated computation of certain hypergeometric functions", journal = j-TOMS, volume = "38", number = "2", pages = "11:1--11:20", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049675", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Beattie:2011:NSH, author = "Christopher Beattie and Zlatko Drmav{\v{c}} and Serkan Gugercin", title = "A note on shifted {Hessenberg} systems and frequency response computation", journal = j-TOMS, volume = "38", number = "2", pages = "12:1--12:16", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049676", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article, we propose a numerical algorithm for efficient and robust solution of a sequence of shifted Hessenberg linear systems. In particular, we show how the frequency response ${\cal G}(\sigma) = d - C(A - \sigma \mathbb{I})^{-1} b$ in the single input case can be computed more efficiently than with other state-of-the-art methods. We also provide a backward stability analysis of the proposed algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Duff:2011:DIA, author = "Iain S. Duff and Kamer Kaya and Bora U{\c{c}}car", title = "Design, implementation, and analysis of maximum transversal algorithms", journal = j-TOMS, volume = "38", number = "2", pages = "13:1--13:31", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049677", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F50 (05C70 05C85)", MRnumber = "2893028", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We report on careful implementations of seven algorithms for solving the problem of finding a maximum transversal of a sparse matrix. We analyze the algorithms and discuss the design choices. To the best of our knowledge, this is the most comprehensive comparison of maximum transversal algorithms based on augmenting paths. Previous papers with the same objective either do not have all the algorithms discussed in this article or they used nonuniform implementations from different researchers. We use a common base to implement all of the algorithms and compare their relative performance on a wide range of graphs and matrices. We systematize, develop, and use several ideas for enhancing performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bangerth:2011:ADS, author = "Wolfgang Bangerth and Carsten Burstedde and Timo Heister and Martin Kronbichler", title = "Algorithms and data structures for massively parallel generic adaptive finite element codes", journal = j-TOMS, volume = "38", number = "2", pages = "14:1--14:28", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049678", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an ``oracle'' that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zaghloul:2011:ACF, author = "Mofreh R. Zaghloul and Ahmed N. Ali", title = "{Algorithm 916}: Computing the {Faddeyeva} and {Voigt} functions", journal = j-TOMS, volume = "38", number = "2", pages = "15:1--15:22", month = dec, year = "2011", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2049673.2049679", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 30 17:43:07 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Zaghloul:2016:RAC}.", abstract = "We present a MATLAB function for the numerical evaluation of the Faddeyeva function $w(z)$. The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs efficiency trade-off through a controlling parameter that may be used to reduce accuracy and computational time and vice versa. Verification of the flexibility, reliability, and superior accuracy of the algorithm is provided through comparison with standard algorithms available in other libraries and software packages.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lantoine:2012:UMV, author = "Gregory Lantoine and Ryan P. Russell and Thierry Dargent", title = "Using Multicomplex Variables for Automatic Computation of High-Order Derivatives", journal = j-TOMS, volume = "38", number = "3", pages = "16:1--16:21", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The computations of the high-order partial derivatives in a given problem are often cumbersome or not accurate. To combat such shortcomings, a new method for calculating exact high-order sensitivities using multicomplex numbers is presented. Inspired by the recent complex step method that is only valid for first-order sensitivities, the new multicomplex approach is valid to arbitrary order. The mathematical theory behind this approach is revealed, and an efficient procedure for the automatic implementation of the method is described. Several applications are presented to validate and demonstrate the accuracy and efficiency of the algorithm. The results are compared to conventional approaches such as finite differencing, the complex step method, and two separate automatic differentiation tools. The multicomplex method performs favorably in the preliminary comparisons and is therefore expected to be useful for a variety of algorithms that exploit higher order derivatives.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gustavson:2012:PCE, author = "Fred Gustavson and Lars Karlsson and Bo K{\aa}gstr{\"o}m", title = "Parallel and Cache-Efficient In-Place Matrix Storage Format Conversion", journal = j-TOMS, volume = "38", number = "3", pages = "17:1--17:32", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168775", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Techniques and algorithms for efficient in-place conversion to and from standard and blocked matrix storage formats are described. Such functionality is required by numerical libraries that use different data layouts internally. Parallel algorithms and a software package for in-place matrix storage format conversion based on in-place matrix transposition are presented and evaluated. A new algorithm for in-place transposition which efficiently determines the structure of the transposition permutation a priori is one of the key ingredients. It enables effective load balancing in a parallel environment.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DeWitte:2012:IIC, author = "Virginie {De Witte} and Willy Govaerts and Yuri A. Kuznetsov and Mark Friedman", title = "Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in {MATLAB}", journal = j-TOMS, volume = "38", number = "3", pages = "18:1--18:34", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168776", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "{\tt matcont} is a MATLAB continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits in {\tt matcont}. The implementation is done using the continuation of invariant subspaces, with the Riccati equations included in the defining system. A key feature is the possibility to initiate both types of homoclinic orbits interactively, starting from an equilibrium point and using a homotopy method. All known codimension-two homoclinic bifurcations are tested for during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way. Heteroclinic orbits can now also be continued and an analogous homotopy method can be used for the initialization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{More:2012:EDN, author = "Jorge J. Mor{\'e} and Stefan M. Wild", title = "Estimating Derivatives of Noisy Simulations", journal = j-TOMS, volume = "38", number = "3", pages = "19:1--19:21", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168777", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We employ recent work on computational noise to obtain near-optimal difference estimates of the derivative of a noisy function. Our analysis relies on a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily computable difference parameter that is provably near-optimal. Numerical results closely resemble the theory and show that we obtain accurate derivative estimates even when the noisy function is deterministic.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lawrence:2012:ACD, author = "Piers W. Lawrence and Robert M. Corless and David J. Jeffrey", title = "{Algorithm 917}: Complex Double-Precision Evaluation of the {Wright} $\omega$ Function", journal = j-TOMS, volume = "38", number = "3", pages = "20:1--20:17", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168779", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes an efficient and robust algorithm and implementation for the evaluation of the Wright $\omega$ function in IEEE double precision arithmetic over the complex plane.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sadkane:2012:ASM, author = "Miloud Sadkane and Ahmed Touhami", title = "{Algorithm 918}: {{\tt specdicho}}: a {MATLAB} Program for the Spectral Dichotomy of Regular Matrix Pencils", journal = j-TOMS, volume = "38", number = "3", pages = "21:1--21:13", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168780", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Given a regular matrix pencil $ \lambda B - A $ and a positively oriented contour \gamma in the complex plane, the spectral dichotomy methods applied to $ \lambda B - A $ and \gamma consist in determining whether $ \lambda B - A $ possesses eigenvalues on or in a neighborhood of $ \gamma $. When no such eigenvalues exist, these methods compute iteratively the spectral projector P onto the right deflating subspace of $ \lambda B - A $ associated with the eigenvalues inside/outside $ \gamma $. The computation of the projector is accompanied by the spectral norm $ ||H|| $ of a Hermitian positive definite matrix $H$ called the dichotomy condition number, which indicates the numerical quality of the spectral projector P. The smaller $ ||H|| $ is, the better this quality. This article presents a MATLAB program ({\tt specdicho}) implementing the main types of spectral dichotomy where $ \gamma $ is a circle, an ellipse, the imaginary axis or a parabola.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Niesen:2012:AKS, author = "Jitse Niesen and Will M. Wright", title = "{Algorithm 919}: a {Krylov} Subspace Algorithm for Evaluating the $\varphi$-Functions Appearing in Exponential Integrators", journal = j-TOMS, volume = "38", number = "3", pages = "22:1--22:19", month = apr, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2168773.2168781", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu May 3 16:27:26 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing the initial condition. The matrix function is a linear combination of the matrix exponential and other functions related to the exponential (the so-called $\varphi$-functions). Such computations are the major computational burden in the implementation of exponential integrators, which can solve general ODEs. Our approach is to compute the action of the matrix function by constructing a Krylov subspace using Arnoldi or Lanczos iteration and projecting the function on this subspace. This is combined with time-stepping to prevent the Krylov subspace from growing too large. The algorithm is fully adaptive: it varies both the size of the time steps and the dimension of the Krylov subspace to reach the required accuracy. We implement this algorithm in the Matlab function {\tt phipm} and we give instructions on how to obtain and use this function. Various numerical experiments show that the {\tt phipm} function is often significantly more efficient than the state-of-the-art.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Filippone:2012:OOT, author = "Salvatore Filippone and Alfredo Buttari", title = "Object-Oriented Techniques for Sparse Matrix Computations in {Fortran 2003}", journal = j-TOMS, volume = "38", number = "4", pages = "23:1--23:20", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331131", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The efficiency of a sparse linear algebra operation heavily relies on the ability of the sparse matrix storage format to exploit the computing power of the underlying hardware. Since no format is universally better than the others across all possible kinds of operations and computers, sparse linear algebra software packages should provide facilities to easily implement and integrate new storage formats within a sparse linear algebra application without the need to modify it; it should also allow to dynamically change a storage format at run-time depending on the specific operations to be performed. Aiming at these important features, we present an Object Oriented design model for a sparse linear algebra package which relies on Design Patterns. We show that an implementation of our model can be efficiently achieved through some of the unique features of the Fortran 2003 language. Experimental results show that the proposed software infrastructure improves the modularity and ease of use of the code at no performance loss.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{George:2012:EAP, author = "Thomas George and Anshul Gupta and Vivek Sarin", title = "An Empirical Analysis of the Performance of Preconditioners for {SPD} Systems", journal = j-TOMS, volume = "38", number = "4", pages = "24:1--24:30", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331132", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Quintana-Orti:2012:RSP, author = "Gregorio Quintana-Ort{\'\i} and Francisco D. Igual and Mercedes Marqu{\'e}s and Enrique S. Quintana-Ort{\'\i} and Robert A. van de Geijn", title = "A Runtime System for Programming Out-of-Core Matrix Algorithms-by-Tiles on Multithreaded Architectures", journal = j-TOMS, volume = "38", number = "4", pages = "25:1--25:25", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331133", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Out-of-core implementations of algorithms for dense matrix computations have traditionally focused on optimal use of memory so as to minimize I/O, often trading programmability for performance. In this article we show how the current state of hardware and software allows the programmability problem to be addressed without sacrificing performance. This comes from the realizations that memory is cheap and large, making it less necessary to optimally orchestrate I/O, and that new algorithms view matrices as collections of submatrices and computation as operations with those submatrices. This enables libraries to be coded at a high level of abstraction, leaving the tasks of scheduling the computations and data movement in the hands of a runtime system. This is in sharp contrast to more traditional approaches that leverage optimal use of in-core memory and, at the expense of introducing considerable programming complexity, explicit overlap of I/O with computation. Performance is demonstrated for this approach on multicore architectures as well as platforms equipped with hardware accelerators.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Birkisson:2012:AFD, author = "Asgeir Birkisson and Tobin A. Driscoll", title = "Automatic {Fr{\'e}chet} Differentiation for the Numerical Solution of Boundary-Value Problems", journal = j-TOMS, volume = "38", number = "4", pages = "26:1--26:29", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331134", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new solver for nonlinear boundary-value problems (BVPs) in Matlab is presented, based on the Chebfun software system for representing functions and operators automatically as numerical objects. The solver implements Newton's method in function space, where instead of the usual Jacobian matrices, the derivatives involved are Fr{\'e}chet derivatives. A major novelty of this approach is the application of automatic differentiation (AD) techniques to compute the operator-valued Fr{\'e}chet derivatives in the continuous context. Other novelties include the use of anonymous functions and numbering of each variable to enable a recursive, delayed evaluation of derivatives with forward mode AD. The AD techniques are applied within a new Chebfun class called which allows users to set up and solve nonlinear BVPs, both scalar and systems of coupled equations, in a few lines of code, using the ``nonlinear backslash'' operator ($\backslash$). This framework enables one to study the behaviour of Newton's method in function space.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kim:2012:ASS, author = "Sunyoung Kim and Masakazu Kojima and Hayato Waki and Makato Yamashita", title = "{Algorithm 920}: {SFSDP}: a Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems", journal = j-TOMS, volume = "38", number = "4", pages = "27:1--27:19", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331135", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SFSDP is a Matlab package for solving sensor network localization (SNL) problems. These types of problems arise in monitoring and controlling applications using wireless sensor networks. SFSDP implements the semidefinite programming (SDP) relaxation proposed in Kim et al. [2009] for sensor network localization problems, as a sparse version of the full semidefinite programming relaxation (FSDP) by Biswas and Ye [2004]. To improve the efficiency of FSDP, SFSDP exploits the aggregated and correlative sparsity of a sensor network localization problem. As a result, SFSDP can handle much larger problems than other software as well as three-dimensional anchor-free problems. SFSDP analyzes the input data of a sensor network localization problem, solves the problem, and displays the computed locations of sensors. SFSDP also includes the features of generating test problems for numerical experiments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hauenstein:2012:AAC, author = "Jonathan D. Hauenstein and Frank Sottile", title = "{Algorithm 921}: {alphaCertified}: Certifying Solutions to Polynomial Systems", journal = j-TOMS, volume = "38", number = "4", pages = "28:1--28:20", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331136", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Smale's $\alpha$-theory uses estimates related to the convergence of Newton's method to certify that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements algorithms based on $\alpha$-theory to certify solutions of polynomial systems using both exact rational arithmetic and arbitrary precision floating point arithmetic. It also implements algorithms that certify whether a given point corresponds to a real solution, and algorithms to heuristically validate solutions to overdetermined systems. Examples are presented to demonstrate the algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ji:2012:AMF, author = "Xia Ji and Jiguang Sun and Tiara Turner", title = "{Algorithm 922}: a Mixed Finite Element Method for {Helmholtz} Transmission Eigenvalues", journal = j-TOMS, volume = "38", number = "4", pages = "29:1--29:8", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331137", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: (1) the formulation leads to a generalized eigenvalue problem naturally without the need to invert a related linear system, and (2) the nonphysical zero transmission eigenvalue, which has an infinitely dimensional eigenspace, is eliminated. To solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method is proposed. To make the computation efficient, the search interval is decided using a Faber--Krahn type inequality for transmission eigenvalues and the interval is updated at each iteration. The algorithm is implemented using Matlab. The code can be easily used in the qualitative methods in inverse scattering and modified to compute transmission eigenvalues for other models such as elasticity problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wimmer:2012:AEN, author = "M. Wimmer", title = "{Algorithm 923}: Efficient Numerical Computation of the {Pfaffian} for Dense and Banded Skew-Symmetric Matrices", journal = j-TOMS, volume = "38", number = "4", pages = "30:1--30:17", month = aug, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2331130.2331138", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Aug 30 18:55:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathematica.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form. We develop efficient numerical methods for computing this tridiagonal form based on Gaussian elimination, using a skew-symmetric, blocked form of the Parlett-Reid algorithm, or based on unitary transformations, using block Householder transformations and Givens rotations, that are applicable to dense and banded matrices, respectively. We also give a complete and fully optimized implementation of these algorithms in Fortran (including a C interface), and also provide Python, Matlab and Mathematica implementations for convenience. Finally, we apply these methods to compute the topological charge of a class D nanowire, and show numerically the equivalence of definitions based on the Hamiltonian and the scattering matrix.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Notz:2012:GBS, author = "Patrick K. Notz and Roger P. Pawlowski and James C. Sutherland", title = "Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics {PDE} Software", journal = j-TOMS, volume = "39", number = "1", pages = "1:1--1:21", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382586", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Multiphysics simulation software is plagued by complexity stemming from nonlinearly coupled systems of Partial Differential Equations (PDEs). Such software typically supports many models, which may require different transport equations, constitutive laws, and equations of state. Strong coupling and a multiplicity of models leads to complex algorithms (i.e., the properly ordered sequence of steps to assemble a discretized set of coupled PDEs) and rigid software. This work presents a design strategy that shifts focus away from high-level algorithmic concerns to low-level data dependencies. Mathematical expressions are represented as software objects that directly expose data dependencies. The entire system of expressions forms a directed acyclic graph and the high-level assembly algorithm is generated automatically through standard graph algorithms. This approach makes problems with complex dependencies entirely tractable, and removes virtually all logic from the algorithm itself. Changes are highly localized, allowing developers to implement models without detailed understanding of any algorithms (i.e., the overall assembly process). Furthermore, this approach complements existing MPI-based frameworks and can be implemented within them easily. Finally, this approach enables algorithmic parallelization via threads. By exposing dependencies in the algorithm explicitly, thread-based parallelism is implemented through algorithm decomposition, providing a basis for exploiting parallelism independent from domain decomposition approaches.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanZee:2012:FAR, author = "Field G. {Van Zee} and Robert A. van de Geijn and Gregorio Quintana-Ort{\'\i} and G. Joseph Elizondo", title = "Families of Algorithms for Reducing a Matrix to Condensed Form", journal = j-TOMS, volume = "39", number = "1", pages = "2:1--2:32", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382587", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In a recent paper it was shown how memory traffic can be diminished by reformulating the classic algorithm for reducing a matrix to bidiagonal form, a preprocess when computing the singular values of a dense matrix. The key is a reordering of the computation so that the most memory-intensive operations can be ``fused.'' In this article, we show that other operations that reduce matrices to condensed form (reduction to upper Hessenberg form and reduction to tridiagonal form) can be similarly reorganized, yielding different sets of operations that can be fused. By developing the algorithms with a common framework and notation, we facilitate the comparing and contrasting of the different algorithms and opportunities for optimization on sequential architectures. We discuss the algorithms, develop a simple model to estimate the speedup potential from fusing, and showcase performance improvements consistent with the what the model predicts.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bell:2012:PSA, author = "Nathan Bell and Anil N. Hirani", title = "{PyDEC}: Software and Algorithms for Discretization of Exterior Calculus", journal = j-TOMS, volume = "39", number = "1", pages = "3:1--3:41", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382588", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes. We describe efficient algorithms for constructing the operators and objects that arise in discrete exterior calculus, lowest-order finite element exterior calculus, and in related topological problems. Our algorithms are formulated in terms of high-level matrix operations which extend to arbitrary dimension. As a result, our implementations map well to the facilities of numerical libraries such as NumPy and SciPy. The availability of such libraries makes Python suitable for prototyping numerical methods. We demonstrate how PyDEC is used to solve physical and topological problems through several concise examples.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Burton:2012:CCN, author = "Benjamin A. Burton and Melih Ozlen", title = "Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces", journal = j-TOMS, volume = "39", number = "1", pages = "4:1--4:18", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382589", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The crosscap number of a knot is an invariant describing the nonorientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We present three methods for computing crosscap number that offer varying trade-offs between precision and speed: (i) an algorithm based on Hilbert basis enumeration and (ii) an algorithm based on exact integer programming, both of which either compute the solution precisely or reduce it to two possible values, and (iii) a fast but limited precision integer programming algorithm that bounds the solution from above. The first two algorithms advance the theoretical state-of-the-art, but remain intractable for practical use. The third algorithm is fast and effective, which we show in a practical setting by making significant improvements to the current knowledge of crosscap numbers in knot tables. Our integer programming framework is general, with the potential for further applications in computational geometry and topology.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Abad:2012:ATT, author = "Alberto Abad and Roberto Barrio and Fernando Blesa and Marcos Rodr{\'\i}guez", title = "{Algorithm 924}: {TIDES}, a {Taylor Series Integrator for Differential EquationS}", journal = j-TOMS, volume = "39", number = "1", pages = "5:1--5:28", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382590", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article introduces the software package TIDES and revisits the use of the Taylor series method for the numerical integration of ODEs. The package TIDES provides an easy-to-use interface for standard double precision integrations, but also for quadruple precision and multiple precision integrations. The motivation for the development of this package is that more and more scientific disciplines need very high precision solution of ODEs, and a standard ODE method is not able to reach these precision levels. The TIDES package combines a preprocessor step in M athematica that generates Fortran or C programs with a library in C. Another capability of TIDES is the direct solution of sensitivities of the solution of ODE systems, which means that we can compute the solution of variational equations up to any order without formulating them explicitly. Different options of the software are discussed, and finally it is compared with other well-known available methods, as well as with different options of TIDES. From the numerical tests, TIDES is competitive, both in speed and accuracy, with standard methods, but it also provides new capabilities.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Yamashita:2012:APS, author = "Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhide Nakata and Maho Nakata", title = "{Algorithm 925}: Parallel Solver for Semidefinite Programming Problem having Sparse {Schur} Complement Matrix", journal = j-TOMS, volume = "39", number = "1", pages = "6:1--6:22", month = nov, year = "2012", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2382585.2382591", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Dec 6 07:36:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical optimization. SDP provides an effective computation framework for many research fields. Some applications, however, require solving a large-scale SDP whose size exceeds the capacity of a single processor both in terms of computation time and available memory. SDPARA (SemiDefinite Programming Algorithm paRAllel package) [Yamashita et al. 2003b] was designed to solve such large-scale SDPs. Its parallel performance is outstanding for general SDPs in most cases. However, the parallel implementation is less successful for some sparse SDPs obtained from applications such as Polynomial Optimization Problems (POPs) or Sensor Network Localization (SNL) problems, since this version of SDPARA cannot directly handle sparse Schur Complement Matrices (SCMs). In this article we improve SDPARA by focusing on the sparsity of the SCM and we propose a new parallel implementation using the formula-cost-based distribution along with a replacement of the dense Cholesky factorization. We verify numerically that these features are key to solving SDPs with sparse SCMs more quickly on parallel computing systems. The performance is further enhanced by multithreading and the new SDPARA attains considerable scalability in general. It also finds solutions for extremely large-scale SDPs arising from POPs which cannot be obtained by other solvers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Betcke:2013:NCN, author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann and Christian Schr{\"o}der and Fran{\c{c}}oise Tisseur", title = "{NLEVP}: a Collection of Nonlinear Eigenvalue Problems", journal = j-TOMS, volume = "39", number = "2", pages = "7:1--7:28", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427024", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on these and other properties can be used to extract particular types of problems from the collection. A brief description of each problem is given. NLEVP serves both to illustrate the tremendous variety of applications of nonlinear eigenvalue problems and to provide representative problems for testing, tuning, and benchmarking of algorithms and codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Baboulin:2013:ALS, author = "Marc Baboulin and Jack Dongarra and Julien Herrmann and Stanimire Tomov", title = "Accelerating Linear System Solutions Using Randomization Techniques", journal = j-TOMS, volume = "39", number = "2", pages = "8:1--8:13", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427025", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system $A x = b$. We study a random transformation of $A$ that enables us to avoid pivoting and then to reduce the amount of communication. Numerical experiments show that this randomization can be performed at a very affordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random Butterfly Transformation (PRBT) is optimized in terms of data storage and flops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the current hybrid multicore\slash GPU machines and we compare its Gflop/s performance with a solver implemented in a current parallel library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gustavson:2013:LCF, author = "Fred G. Gustavson and Jerzy Wa{\'s}niewski and Jack J. Dongarra and Jos{\'e} R. Herrero and Julien Langou", title = "Level-3 {Cholesky} Factorization Routines Improve Performance of Many {Cholesky} Algorithms", journal = j-TOMS, volume = "39", number = "2", pages = "9:1--9:10", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427026", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F05 (65Y15)", MRnumber = "3031628", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Four routines called DPOTF3i, $ i = a, b, c, d $, are presented. DPOTF3i are a novel type of level-3 BLAS for use by BPF (Blocked Packed Format) Cholesky factorization and LAPACK routine DPOTRF. Performance of routines DPOTF3i are still increasing when the performance of Level-2 routine DPOTF2 of LAPACK starts decreasing. This is our main result and it implies, due to the use of larger block size $ n_b $, that DGEMM, DSYRK, and DTRSM performance also increases! The four DPOTF3i routines use simple register blocking. Different platforms have different numbers of registers. Thus, our four routines have different register blocking sizes. BPF is introduced. LAPACK routines for POTRF and PPTRF using BPF instead of full and packed format are shown to be trivial modifications of LAPACK POTRF source codes. We call these codes BPTRF. There are two variants of BPF: lower and upper. Upper BPF is ``identical'' to Square Block Packed Format (SBPF). ``LAPACK'' implementations on multicore processors use SBPF. Lower BPF is less efficient than upper BPF. Vector inplace transposition converts lower BPF to upper BPF very efficiently. Corroborating performance results for DPOTF3i versus DPOTF2 on a variety of common platforms are given for $ n \approx n_b $ as well as results for large $ n $ comparing DBPTRF versus DPOTRF.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Knepley:2013:FEI, author = "Matthew G. Knepley and Andy R. Terrel", title = "Finite Element Integration on {GPUs}", journal = j-TOMS, volume = "39", number = "2", pages = "10:1--10:13", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427027", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a novel finite element integration method for low-order elements on GPUs. We achieve more than 100GF for element integration on first order discretizations of both the Laplacian and Elasticity operators on an NVIDIA GTX285, which has a nominal single precision peak flop rate of 1 TF/s and bandwidth of 159 GB/s, corresponding to a bandwidth limited peak of 40 GF/s.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boisvert:2013:RKB, author = "Jason J. Boisvert and Paul H. Muir and Raymond J. Spiteri", title = "A {Runge--Kutta} {BVODE} Solver with Global Error and Defect Control", journal = j-TOMS, volume = "39", number = "2", pages = "11:1--11:22", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427028", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Boundary value ordinary differential equations (BVODEs) are systems of ODEs with boundary conditions imposed at two or more distinct points. The global error (GE) of a numerical solution to a BVODE is the amount by which the numerical solution differs from the exact solution. The defect is the amount by which the numerical solution fails to satisfy the ODEs and boundary conditions. Although GE control is often familiar to users, the defect controlled numerical solution can be interpreted as the exact solution to a perturbation of the original BVODE. Software packages based on GE control and on defect control are in wide use. The defect control solver, BVP\_SOLVER, can provide an a posteriori estimate of the GE using Richardson extrapolation. In this article, we consider three more strategies for GE estimation based on (i) the direct use of a higher-order discretization formula (HO), (ii) the use of a higher-order discretization formula within a deferred correction (DC) framework, and (iii) the product of an estimate of the maximum defect and an estimate of the BVODE conditioning constant, and demonstrate that the HO and DC approaches have superior performance. We also modify BVP\_SOLVER to introduce GE control.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Saito:2013:VMT, author = "Mutsuo Saito and Makoto Matsumoto", title = "Variants of {Mersenne Twister} Suitable for Graphic Processors", journal = j-TOMS, volume = "39", number = "2", pages = "12:1--12:20", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427029", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article proposes a type of pseudorandom number generator, Mersenne Twister for Graphic Processor (MTGP), for efficient generation on graphic processing units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the high parallelism of GPUs in computing many steps of the recursion in parallel. The second proposal is a parameter-set generator for MTGP, named MTGP Dynamic Creator (MTGPDC). MTGPDC creates up to $2^{32}$ distinct parameter sets which generate sequences with high-dimensional uniformity. This facility is suitable for a large grid of GPUs where each GPU requires separate random number streams. MTGP is based on linear recursion over the two-element field, and has better high-dimensional equidistribution than the Mersenne Twister pseudorandom number generator.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Poulson:2013:ENF, author = "Jack Poulson and Bryan Marker and Robert A. van de Geijn and Jeff R. Hammond and Nichols A. Romero", title = "{Elemental}: a New Framework for Distributed Memory Dense Matrix Computations", journal = j-TOMS, volume = "39", number = "2", pages = "13:1--13:24", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427030", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Parallelizing dense matrix computations to distributed memory architectures is a well-studied subject and generally considered to be among the best understood domains of parallel computing. Two packages, developed in the mid 1990s, still enjoy regular use: ScaLAPACK and PLAPACK. With the advent of many-core architectures, which may very well take the shape of distributed memory architectures within a single processor, these packages must be revisited since the traditional MPI-based approaches will likely need to be extended. Thus, this is a good time to review lessons learned since the introduction of these two packages and to propose a simple yet effective alternative. Preliminary performance results show the new solution achieves competitive, if not superior, performance on large clusters.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Thompson:2013:AIG, author = "Ian Thompson", title = "{Algorithm 926}: Incomplete {Gamma} Functions with Negative Arguments", journal = j-TOMS, volume = "39", number = "2", pages = "14:1--14:9", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427031", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An algorithm for accurately computing the lower incomplete gamma function $ \gamma (a, t) $ in the case where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of $n$, and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precomputations carried out in Maple.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cash:2013:AMC, author = "J. R. Cash and D. Hollevoet and F. Mazzia and A. M. Nagy", title = "{Algorithm 927}: The {MATLAB} Code {{\tt bvptwp.m}} for the Numerical Solution of Two Point Boundary Value Problems", journal = j-TOMS, volume = "39", number = "2", pages = "15:1--15:12", month = feb, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2427023.2427032", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 20 16:46:13 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we describe the code bvptwp.m, a MATLAB code for the solution of two point boundary value problems. This code is based on the well-known Fortran codes, twpbvp.f, twpbvpl.f and acdc.f, that employ a mesh selection strategy based on the estimation of the local error, and on revisions of these codes, called twpbvpc.f, twpbvplc.f and acdcc.f, that employ a mesh selection strategy based on the estimation of the local error and the estimation of two parameters which characterize the conditioning of the problem. The codes twpbvp.f/tpbvpc.f use a deferred correction scheme based on Mono-Implicit Runge--Kutta methods (MIRK); the other codes use a deferred correction scheme based on Lobatto formulas. The acdc.f/acdcc.f codes implement an automatic continuation strategy. The performance and features of the new solver are checked by performing some numerical tests to show that the new code is robust and able to solve very difficult singularly perturbed problems. The results obtained show that bvptwp.m is often able to solve problems requiring stringent accuracies and problems with very sharp changes in the solution. This code, coupled with the existing boundary value codes such as bvp4c.m, makes the MATLAB BVP section an extremely powerful one for a very wide range of problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ltaief:2013:HPB, author = "Hatem Ltaief and Piotr Luszczek and Jack Dongarra", title = "High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures", journal = j-TOMS, volume = "39", number = "3", pages = "16:1--16:22", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450154", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents a new high-performance bidiagonal reduction (BRD) for homogeneous multicore architectures. This article is an extension of the high-performance tridiagonal reduction implemented by the same authors [Luszczek et al., IPDPS 2011] to the BRD case. The BRD is the first step toward computing the singular value decomposition of a matrix, which is one of the most important algorithms in numerical linear algebra due to its broad impact in computational science. The high performance of the BRD described in this article comes from the combination of four important features: (1) tile algorithms with tile data layout, which provide an efficient data representation in main memory; (2) a two-stage reduction approach that allows to cast most of the computation during the first stage (reduction to band form) into calls to Level 3 BLAS and reduces the memory traffic during the second stage (reduction from band to bidiagonal form) by using high-performance kernels optimized for cache reuse; (3) a data dependence translation layer that maps the general algorithm with column-major data layout into the tile data layout; and (4) a dynamic runtime system that efficiently schedules the newly implemented kernels across the processing units and ensures that the data dependencies are not violated. A detailed analysis is provided to understand the critical impact of the tile size on the total execution time, which also corresponds to the matrix bandwidth size after the reduction of the first stage. The performance results show a significant improvement over currently established alternatives. The new high-performance BRD achieves up to a 30-fold speedup on a 16-core Intel Xeon machine with a 12000$ \times $ 12000 matrix size against the state-of-the-art open source and commercial numerical software packages, namely LAPACK, compiled with optimized and multithreaded BLAS from MKL as well as Intel MKL version 10.2.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Patterson:2013:EOM, author = "Michael A. Patterson and Matthew Weinstein and Anil V. Rao", title = "An efficient overloaded method for computing derivatives of mathematical functions in {MATLAB}", journal = j-TOMS, volume = "39", number = "3", pages = "17:1--17:36", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450155", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An object-oriented method is presented that computes without truncation the error derivatives of functions defined by MATLAB computer codes. The method implements forward-mode automatic differentiation via operator overloading in a manner that produces a new MATLAB code that computes the derivatives of the outputs of the original function with respect to the differentiation variables. Because the derivative code has the same input as the original function code, the method can be used recursively to generate derivatives of any order desired. In addition, the approach developed in this article has the feature that the derivatives are generated by simply evaluating the function on an instance of the class, thus making the method straightforward to use while simultaneously enabling differentiation of highly complex functions. A detailed description of the method is presented and the approach is illustrated and shown to be efficient on four examples.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hammarling:2013:ACS, author = "Sven Hammarling and Christopher J. Munro and Fran{\c{c}}oise Tisseur", title = "An algorithm for the complete solution of quadratic eigenvalue problems", journal = j-TOMS, volume = "39", number = "3", pages = "18:1--18:19", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450156", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable conditioning and backward stability properties, and a preprocessing step that reveals and deflates the zero and infinite eigenvalues contributed by singular leading and trailing matrix coefficients. The algorithm is backward-stable for quadratics that are not too heavily damped. Numerical experiments show that our MATLAB implementation of the algorithm, quadeig, outperforms the MATLAB function polyeig in terms of both stability and efficiency.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bosner:2013:EGH, author = "Nela Bosner and Zvonimir Bujanovi{\'c} and Zlatko Drma{\v{c}}", title = "Efficient generalized {Hessenberg} form and applications", journal = j-TOMS, volume = "39", number = "3", pages = "19:1--19:19", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450157", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article proposes an efficient algorithm for reducing matrices to generalized Hessenberg form by unitary similarity, and recommends using it as a preprocessor in a variety of applications. To illustrate its usefulness, two cases from control theory are analyzed in detail: a solution procedure for a sequence of shifted linear systems with multiple right hand sides (e.g. evaluating the transfer function of a MIMO LTI dynamical system at many points) and computation of the staircase form. The proposed algorithm for the generalized Hessenberg reduction uses two levels of aggregation of Householder reflectors, thus allowing efficient BLAS 3-based computation. Another level of aggregation is introduced when solving many shifted systems by processing the shifts in batches. Numerical experiments confirm that the proposed methods have superior efficiency.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hascoet:2013:TAD, author = "Laurent Hascoet and Val{\'e}rie Pascual", title = "The {Tapenade} automatic differentiation tool: Principles, model, and specification", journal = j-TOMS, volume = "39", number = "3", pages = "20:1--20:43", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450158", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Tapenade is an Automatic Differentiation (AD) tool which, given a Fortran or C code that computes a function, creates a new code that computes its tangent or adjoint derivatives. Tapenade puts particular emphasis on adjoint differentiation, which computes gradients at a remarkably low cost. This article describes the principles of Tapenade, a subset of the general principles of AD. We motivate and illustrate with examples the AD model of Tapenade, that is, the structure of differentiated codes and the strategies used to make them more efficient. Along with this informal description, we formally specify this model by means of data-flow equations and rules of Operational Semantics, making this the reference specification of the tangent and adjoint modes of Tapenade. One benefit we expect from this formal specification is the capacity to formally study the AD model itself, especially for the adjoint mode and its sophisticated strategies. This article also describes the architectural choices of the implementation of Tapenade. We describe the current performance of Tapenade on a set of codes that include industrial-size applications. We present the extensions of the tool that are planned in a foreseeable future, deriving from our ongoing research on AD.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rios:2013:AGP, author = "Joseph Rios", title = "{Algorithm 928}: a general, parallel implementation of {Dantzig--Wolfe} decomposition", journal = j-TOMS, volume = "39", number = "3", pages = "21:1--21:10", month = apr, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2450153.2450159", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 30 18:50:55 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Dantzig--Wolfe Decomposition is recognized as a powerful, algorithmic tool for solving linear programs of block-angular form. While use of the approach has been reported in a wide variety of domains, there has not been a general implementation of Dantzig--Wolfe decomposition available. This article describes an open-source implementation of the algorithm. It is general in the sense that any properly decomposed linear program can be provided to the software for solving. While the original description of the algorithm was motivated by its reduced memory usage, modern computers can also take advantage of the algorithm's inherent parallelism. This implementation is parallel and built upon the POSIX threads (pthreads) library. Some computational results are provided to motivate use of such parallel solvers, as this implementation outperforms state-of-the-art commercial solvers in terms of wall-clock runtime by an order of magnitude or more on several problem instances.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Castaldo:2013:SLP, author = "Anthony M. Castaldo and R. Clint Whaley and Siju Samuel", title = "Scaling {LAPACK} panel operations using parallel cache assignment", journal = j-TOMS, volume = "39", number = "4", pages = "22:1--22:30", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491492", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In LAPACK many matrix operations are cast as block algorithms which iteratively process a panel using an unblocked algorithm and then update a remainder matrix using the high performance Level 3 BLAS. The Level 3 BLAS have excellent scaling, but panel processing tends to be bus bound, and thus scales with bus speed rather than the number of processors ( p ). Amdahl's law therefore ensures that as p grows, the panel computation will become the dominant cost of these LAPACK routines. Our contribution is a novel parallel cache assignment approach to the panel factorization which we show scales well with p. We apply this general approach to the QR, QL, RQ, LQ and LU panel factorizations. We show results for two commodity platforms: an 8-core Intel platform and a 32-core AMD platform. For both platforms and all twenty implementations (five factorizations each of which is available in 4 types), we present results that demonstrate that our approach yields significant speedup over the existing state of the art.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Khan:2013:EEC, author = "Kamil A. Khan and Paul I. Barton", title = "Evaluating an element of the {Clarke} generalized {Jacobian} of a composite piecewise differentiable function", journal = j-TOMS, volume = "39", number = "4", pages = "23:1--23:28", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491493", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Bundle methods for nonsmooth optimization and semismooth Newton methods for nonsmooth equation solving both require computation of elements of the (Clarke) generalized Jacobian, which provides slope information for locally Lipschitz continuous functions. Since the generalized Jacobian does not obey sharp calculus rules, this computation can be difficult. In this article, methods are developed for evaluating generalized Jacobian elements for a nonsmooth function that is expressed as a finite composition of known elemental piecewise differentiable functions. In principle, these elemental functions can include any piecewise differentiable function whose analytical directional derivatives are known. The methods are fully automatable, and are shown to be computationally tractable relative to the cost of a function evaluation. An implementation developed in C++ is discussed, and the methods are applied to several example problems for illustration.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dingle:2013:RIT, author = "Nicholas J. Dingle and Nicholas J. Higham", title = "Reducing the influence of tiny normwise relative errors on performance profiles", journal = j-TOMS, volume = "39", number = "4", pages = "24:1--24:11", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491494", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "It is a widespread but little-noticed phenomenon that the normwise relative error $ || x - y || / || x || $ of vectors $x$ and $y$ of floating point numbers of the same precision, where $y$ is an approximation to x, can be many orders of magnitude smaller than the unit roundoff. We analyze this phenomenon and show that in the $ \infty $-norm it happens precisely when $x$ has components of widely varying magnitude and every component of $x$ of largest magnitude agrees with the corresponding component of $y$. Performance profiles are a popular way to compare competing algorithms according to particular measures of performance. We show that performance profiles based on normwise relative errors can give a misleading impression due to the influence of zero or tiny normwise relative errors. We propose a transformation that reduces the influence of these extreme errors in a controlled manner, while preserving the monotonicity of the underlying data and leaving the performance profile unchanged at its left end-point. Numerical examples with both artificial and genuine data illustrate the benefits of the transformation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{deDinechin:2013:ZRT, author = "Florent de Dinechin and Christoph Lauter and Jean-Michel Muller and Serge Torres", title = "On {Ziv}'s rounding test", journal = j-TOMS, volume = "39", number = "4", pages = "25:1--25:19", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491495", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A very simple test, introduced by Ziv, allows one to determine if an approximation to the value $ f(x) $ of an elementary function at a given point x suffices to return the floating-point number nearest $ f(x) $. The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a ``magic constant'' $e$. We show how to choose that constant $e$ to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of $ f(x)$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Russell:2013:OCG, author = "Francis P. Russell and Paul H. J. Kelly", title = "Optimized code generation for finite element local assembly using symbolic manipulation", journal = j-TOMS, volume = "39", number = "4", pages = "26:1--26:29", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491496", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Automated code generators for finite element local assembly have facilitated exploration of alternative implementation strategies within generated code. However, even for a theoretical performance indicator such as operation count, an optimal strategy for local assembly is unknown. We explore a code generation strategy based on symbolic integration and polynomial common subexpression elimination (CSE). We present our implementation of a local assembly code generator using these techniques. We systematically evaluate the approach, measuring operation count, execution time and numerical error using a benchmark suite of synthetic variational forms, comparing against the FEniCS Form Compiler (FFC). Our benchmark forms span complexities chosen to expose the performance characteristics of different code generation approaches. We show that it is possible with additional computational cost, to consistently achieve much of, and sometimes substantially exceed, the performance of alternative approaches without compromising precision. Although the approach of using symbolic integration and CSE for optimizing local assembly is not new, we distinguish our work through our strategies for maintaining numerical precision and detecting common subexpressions. We discuss the benefits of the symbolic approach for inferring numerical relationships, and analyze the relationship to other proposed techniques which also have greater computational complexity than those of FFC.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mehra:2013:ASW, author = "Mani Mehra and Kavita Goyal", title = "{Algorithm 929}: a suite on wavelet differentiation algorithms", journal = j-TOMS, volume = "39", number = "4", pages = "27:1--27:28", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491497", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A collection of the Matlab routines that compute the values of the scaling and wavelet functions ($ \phi (x) $ and $ \psi (x) $ respectively) and the derivative of an arbitrary function (periodic or non periodic) using wavelet bases is presented. Initially, the case of Daubechies wavelets is taken and the procedure is explained for both collocation and Galerkin approaches. For each case a Matlab routine is provided to compute the differentiation matrix and the derivative of the function {$ f^{(d)} = D^{(d)} f $}. Moreover, the convergence of the derivative is shown graphically as a function of different parameters (the wavelet genus, {$D$} and the scale, {$J$}) for two test functions. We then consider the use of spline wavelets.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2013:AFO, author = "Timothy A. Davis", title = "{Algorithm 930}: {FACTORIZE}: an object-oriented linear system solver for {MATLAB}", journal = j-TOMS, volume = "39", number = "4", pages = "28:1--28:18", month = jul, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2491491.2491498", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 19 17:20:56 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The MATLAB backslash ({\tt x = A \backslash b}) is an elegant and powerful interface to a suite of high-performance factorization methods for the direct solution of the linear system {$ A x = b $} and the least-squares problem {$ \min_x || b - A x || $}. It is a meta-algorithm that selects the best factorization method for a particular matrix, whether sparse or dense. However, the simplicity and elegance of its single-character interface prohibits the reuse of its factorization for subsequent systems. Requiring MATLAB users to find the best factorization method on their own can lead to suboptimal choices; even MATLAB experts can make the wrong choice. Furthermore, naive MATLAB users have a tendency to translate mathematical expressions from linear algebra directly into MATLAB, so that {$ x = A^{-1} b $} becomes the inferior yet all-too-prevalent {\tt x = inv(A) * b}. To address these issues, an object-oriented FACTORIZE method is presented. Via simple-to-use operator overloading, solving two linear systems can be written as {\tt F = factorize(A); \tt x = F \backslash b; y= F \backslash c}, where {$A$} is factorized only once. The selection of the best factorization method (LU, Cholesky, {$ L D L^T $}, QR, or a complete orthogonal decomposition for rank-deficient matrices) is hidden from the user. The mathematical expression {$ x = A^{-1} b $} directly translates into the MATLAB expression {\tt x = inverse(A) * b}, which does not compute the inverse at all, but does the right thing by factorizing {$A$} and solving the corresponding triangular systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gebremedhin:2013:CSG, author = "Assefaw H. Gebremedhin and Duc Nguyen and Md. Mostofa Ali Patwary and Alex Pothen", title = "{ColPack}: Software for graph coloring and related problems in scientific computing", journal = j-TOMS, volume = "40", number = "1", pages = "1:1--1:31", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513110", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a suite of fast and effective algorithms, encapsulated in a software package called ColPack, for a variety of graph coloring and related problems. Many of the coloring problems model partitioning needs arising in compression-based computation of Jacobian and Hessian matrices using Algorithmic Differentiation. Several of the coloring problems also find important applications in many areas outside derivative computation, including frequency assignment in wireless networks, scheduling, facility location, and concurrency discovery and data movement operations in parallel and distributed computing. The presentation in this article includes a high-level description of the various coloring algorithms within a common design framework, a detailed treatment of the theory and efficient implementation of known as well as new vertex ordering techniques upon which the coloring algorithms rely, a discussion of the package's software design, and an illustration of its usage. The article also includes an extensive experimental study of the major algorithms in the package using real-world as well as synthetically generated graphs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Poppe:2013:CMO, author = "Koen Poppe and Ronald Cools", title = "{CHEBINT}: a {MATLAB\slash Octave} toolbox for fast multivariate integration and interpolation based on {Chebyshev} approximations over hypercubes", journal = j-TOMS, volume = "40", number = "1", pages = "2:1--2:13", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513111", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the fast approximation of multivariate functions based on Chebyshev series for two types of Chebyshev lattices and show how a fast Fourier transform (FFT) based discrete cosine transform (DCT) can be used to reduce the complexity of this operation. Approximating multivariate functions using rank-1 Chebyshev lattices can be seen as a one-dimensional DCT while a full-rank Chebyshev lattice leads to a multivariate DCT. We also present a MATLAB/Octave toolbox which uses this fast algorithms to approximate functions on a axis aligned hyper-rectangle. Given a certain accuracy of this approximation, interpolation of the original function can be achieved by evaluating the approximation while the definite integral over the domain can be estimated based on this Chebyshev approximation. We conclude with an example for both operations and actual timings of the two methods presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gao:2013:GGA, author = "Mingcen Gao and Thanh-Tung Cao and Ashwin Nanjappa and Tiow-Seng Tan and Zhiyong Huang", title = "{gHull}: a {GPU} algorithm for {$3$D} convex hull", journal = j-TOMS, volume = "40", number = "1", pages = "3:1--3:19", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513112", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A novel algorithm is presented to compute the convex hull of a point set in R$^3$ using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the approximation of the convex hull from the former. The other extreme vertices of the convex hull are then found by using a two-round checking in the digital and the continuous space successively. The algorithm does not need explicit locking or any other concurrency control mechanism, thus it can maximize the parallelism available on the modern GPU. The implementation using the CUDA programming model on NVIDIA GPUs is exact and efficient. The experiments show that it is up to an order of magnitude faster than other sequential convex hull implementations running on the CPU for inputs of millions of points. The works demonstrate that the GPU can be used to solve nontrivial computational geometry problems with significant performance benefit.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hogg:2013:PST, author = "Jonathan D. Hogg and Jennifer A. Scott", title = "Pivoting strategies for tough sparse indefinite systems", journal = j-TOMS, volume = "40", number = "1", pages = "4:1--4:19", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513113", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen before the factorization begins. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to ensure numerical stability. These modifications can have serious consequences in terms of time as well as the memory and flops required for the factorization and subsequent solves. This study focuses on hard-to-solve sparse symmetric indefinite problems for which standard threshold partial pivoting leads to significant modifications. We perform a detailed review of pivoting strategies that are aimed at reducing the modifications without compromising numerical stability. Extensive numerical experiments are performed on a set of tough problems arising from practical applications. Based on our findings, we make recommendations on which strategy to use and, in particular, a matching-based approach is recommended for numerically challenging problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hao:2013:AAS, author = "Wenrui Hao and Andrew J. Sommese and Zhonggang Zeng", title = "{Algorithm 931}: an algorithm and software for computing multiplicity structures at zeros of nonlinear systems", journal = j-TOMS, volume = "40", number = "1", pages = "5:1--5:16", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513114", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A Matlab implementation, multiplicity, of a numerical algorithm for computing the multiplicity structure of a nonlinear system at an isolated zero is presented. The software incorporates a newly developed equation-by-equation strategy that significantly improves the efficiency of the closedness subspace algorithm and substantially reduces the storage requirement. The equation-by-equation strategy is actually based on a variable-by-variable closedness subspace approach. As a result, the algorithm and software can handle much larger nonlinear systems and higher multiplicities than their predecessors, as shown in computational experiments on the included test suite of benchmark problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gander:2013:APS, author = "Martin J. Gander and Caroline Japhet", title = "{Algorithm 932}: {PANG}: Software for nonmatching grid projections in {$2$D} and {$3$D} with linear complexity", journal = j-TOMS, volume = "40", number = "1", pages = "6:1--6:25", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513115", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We design and analyze an algorithm with linear complexity to perform projections between 2D and 3D nonmatching grids. This algorithm, named the PANG algorithm, is based on an advancing front technique and neighboring information. Its implementation is surprisingly short, and we give the entire Matlab code. For computing the intersections, we use a direct and numerically robust approach. We show numerical experiments both for 2D and 3D grids, which illustrate the optimal complexity and negligible overhead of the algorithm. An outline of this algorithm has already been presented in a short proceedings paper of the 18th International Conference on Domain Decomposition Methods (see Gander and Japhet [2008]).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Foster:2013:ARC, author = "Leslie V. Foster and Timothy A. Davis", title = "{Algorithm 933}: Reliable calculation of numerical rank, null space bases, pseudoinverse solutions, and basic solutions using {suitesparseQR}", journal = j-TOMS, volume = "40", number = "1", pages = "7:1--7:23", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513116", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The SPQR\_RANK package contains routines that calculate the numerical rank of large, sparse, numerically rank-deficient matrices. The routines can also calculate orthonormal bases for numerical null spaces, approximate pseudoinverse solutions to least squares problems involving rank-deficient matrices, and basic solutions to these problems. The algorithms are based on SPQR from SuiteSparseQR (ACM Transactions on Mathematical Software 38, Article 8, 2011). SPQR is a high-performance routine for forming QR factorizations of large, sparse matrices. It returns an estimate for the numerical rank that is usually, but not always, correct. The new routines improve the accuracy of the numerical rank calculated by SPQR and reliably determine the numerical rank in the sense that, based on extensive testing with matrices from applications, the numerical rank is almost always accurately determined when our methods report that the numerical rank should be correct. Reliable determination of numerical rank is critical to the other calculations in the package. The routines work well for matrices with either small or large null space dimensions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Erricolo:2013:AFS, author = "Danilo Erricolo and Giuseppe Carluccio", title = "{Algorithm 934}: {Fortran 90} subroutines to compute {Mathieu} functions for complex values of the parameter", journal = j-TOMS, volume = "40", number = "1", pages = "8:1--8:19", month = sep, year = "2013", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2513109.2513117", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Sep 30 16:05:58 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real. After an introduction on the notation and the definitions of Mathieu functions and their related properties, Fortran 90 subroutines to compute them are described and validated with some comparisons. A sample application is also provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alnaes:2014:UFL, author = "Martin S. Aln{\ae}s and Anders Logg and Kristian B. {\O}lgaard and Marie E. Rognes and Garth N. Wells", title = "{Unified Form Language}: a domain-specific language for weak formulations of partial differential equations", journal = j-TOMS, volume = "40", number = "2", pages = "9:1--9:37", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2566630", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gower:2014:CSP, author = "Robert Mansel Gower and Margarida Pinheiro Mello", title = "Computing the sparsity pattern of {Hessians} using automatic differentiation", journal = j-TOMS, volume = "40", number = "2", pages = "10:1--10:15", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2490254", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We compare two methods that calculate the sparsity pattern of Hessian matrices using the computational framework of automatic differentiation. The first method is a forward-mode algorithm by Andrea Walther in 2008 which has been implemented as the driver called hess\_pat in the automatic differentiation package ADOL-C. The second is edge\_push\_sp, a new reverse mode algorithm descended from the edge\_pushing algorithm for calculating Hessians by Gower and Mello in 2012. We present complexity analysis and perform numerical tests for both algorithms. The results show that the new reverse algorithm is very promising.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Goualard:2014:HDY, author = "Fr{\'e}d{\'e}ric Goualard", title = "How do you compute the midpoint of an interval?", journal = j-TOMS, volume = "40", number = "2", pages = "11:1--11:25", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2493882", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The algorithm that computes the midpoint of an interval with floating-point bounds requires some careful devising to handle all possible inputs correctly. We review several implementations from prominent C/C++ interval arithmetic packages and analyze their potential failure to deliver the expected results. We then show how to amend them to avoid common pitfalls. The results presented are also relevant to noninterval arithmetic computation such as the implementation of bisection methods. Enough background on IEEE 754 floating-point arithmetic is provided for this article to serve as a practical introduction to the analysis of floating-point computation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Karlsson:2014:OPC, author = "Lars Karlsson and Daniel Kressner and Bruno Lang", title = "Optimally packed chains of bulges in multishift {$QR$} algorithms", journal = j-TOMS, volume = "40", number = "2", pages = "12:1--12:15", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2559986", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A. After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom right corner along the subdiagonal of A. To increase data locality and create potential for parallelism, modern variants of the QR algorithm perform several iterations simultaneously, which amounts to chasing a chain of several bulges instead of a single bulge. To make effective use of level 3 BLAS, it is important to pack these bulges as tightly as possible within the chain. In this work, we show that the tightness of the packing in existing approaches is not optimal and can be increased. This directly translates into a reduced chain length by 33\% compared to the state-of-the-art LAPACK implementation of the QR algorithm. To demonstrate the impact of our idea, we have modified the LAPACK implementation to make use of the optimal packing. Numerical experiments reveal a uniform reduction of the execution time, without affecting stability or robustness.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Romero:2014:PID, author = "Eloy Romero and Jose E. Roman", title = "A parallel implementation of {Davidson} methods for large-scale eigenvalue problems in {SLEPc}", journal = j-TOMS, volume = "40", number = "2", pages = "13:1--13:29", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2543696", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi--Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is prohibitive or highly inefficient. However, these types of methods are not generally available in the form of high-quality parallel implementations, especially for the case of non-Hermitian eigenproblems. We present our implementation of various Davidson-type methods in SLEPc, the Scalable Library for Eigenvalue Problem Computations. The solvers incorporate many algorithmic variants for subspace expansion and extraction, and cover a wide range of eigenproblems including standard and generalized, Hermitian and non-Hermitian, with either real or complex arithmetic. We provide performance results on a large battery of test problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ratnanather:2014:ATI, author = "J. Tilak Ratnanather and Jung H. Kim and Sirong Zhang and Anthony M. J. Davis and Stephen K. Lucas", title = "{Algorithm 935}: {{\tt IIPBF}}, a {{\tt MATLAB}} toolbox for infinite integral of products of two {Bessel} functions", journal = j-TOMS, volume = "40", number = "2", pages = "14:1--14:12", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2508435", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A {\tt MATLAB} toolbox, {\tt IIPBF}, for calculating infinite integrals involving a product of two Bessel functions $ J_a(\rho x) J_b(\tau x) $, $ J_a(\rho x) Y_b(\tau x) $, and $ Y_a(\rho x) Y_b(\tau x) $, for non-negative integers $a$, $b$, and a well-behaved function $ f(x) $, is described. Based on the Lucas algorithm previously developed for $ J_a(\rho x) J_b(\tau x) $ only, {\tt IIPBF} recasts each product as the sum of two functions whose oscillatory behavior is exploited in the three-step procedure of adaptive integration, summation, and extrapolation. The toolbox uses customised {\tt QUADPACK} and {\tt IMSL} functions from a {\tt MATLAB} conversion of the {\tt SLATEC} library. In addition, {\tt MATLAB}'s own {\tt quadgk} function for adaptive Gauss--Kronrod quadrature results in a significant speed up compared with the original algorithm. Usage of {\tt IIPBF} is described and eighteen test cases illustrate the robustness of the toolbox; five additional ones are used to compare {\tt IIPBF} with the {\tt BESSELINT} code for rational and exponential forms of $ f(x) $ with $ J_a(\rho x) J_b(\tau x) $. Reliability for a broad range of values of $ \rho $ and $ \tau $ for the three different product types as well as different orders in one case is demonstrated. An electronic appendix provides a novel derivation of formulae for five cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:2014:AFM, author = "Fred T. Krogh", title = "{Algorithm 936}: a {Fortran} message processor", journal = j-TOMS, volume = "40", number = "2", pages = "15:1--15:4", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2559993", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Krogh:2017:RAF}.", abstract = "A code is presented which offers a simple clean way to get output that is very easy to read. Special support is given for the output of error messages which are a part of an application package or subprogram library. The code uses many of the features in Fortran 2003, and the ``NEWUNIT='' in an open statement from Fortran 2008. The latter can easily be replaced with ``UNIT=99''. One goal here is to illustrate some of the nice features in recent incarnations of Fortran.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Choi:2014:AMQ, author = "Sou-Cheng T. Choi and Michael A. Saunders", title = "{Algorithm 937}: {MINRES-QLP} for symmetric and {Hermitian} linear equations and least-squares problems", journal = j-TOMS, volume = "40", number = "2", pages = "16:1--16:12", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2527267", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite preconditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gunther:2014:ACC, author = "John C. Gunther", title = "{Algorithm 938}: Compressing circular buffers", journal = j-TOMS, volume = "40", number = "2", pages = "17:1--17:12", month = feb, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2559995", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 14 06:30:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/java2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Data sequences generated by on-line sensors can become arbitrarily large and must, therefore, be pared down to fit into available memory. For situations where only the most recent data is of interest, this problem can be solved with optimal efficiency by a simple circular buffer: it fills each memory location with useful data, and requires just one write to memory per update. The algorithm presented here provides essentially the same efficiency, but while maintaining a continuously updated, fixed-size, compressed representation of the entire data sequence. Each value in these compressed sequences represents a statistic (an average, maximum, random sample, etc.) computed over a contiguous chunk of the original sequence. Compressing circular buffers gain their efficiency by using an alternative indexing sequence, based on well-known principles of elementary number theory, to ensure that each newly written value gets stored in the unoccupied location created when the two oldest sequential over-sampled values are compressed into one. The associated Java implementation supports a variety of aggregating statistics and is used to compare the algorithm's performance with a more obvious approach (doubling).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zee:2014:RTB, author = "Field G. {Van Zee} and Robert A. van de Geijn and Gregorio Quintana-Ort{\'\i}", title = "Restructuring the Tridiagonal and Bidiagonal {QR} Algorithms for Performance", journal = j-TOMS, volume = "40", number = "3", pages = "18:1--18:34", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2535371", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We show how both the tridiagonal and bidiagonal QR algorithms can be restructured so that they become rich in operations that can achieve near-peak performance on a modern processor. The key is a novel, cache-friendly algorithm for applying multiple sets of Givens rotations to the eigenvector/singular vector matrix. This algorithm is then implemented with optimizations that: (1) leverage vector instruction units to increase floating-point throughput, and (2) fuse multiple rotations to decrease the total number of memory operations. We demonstrate the merits of these new QR algorithms for computing the Hermitian eigenvalue decomposition (EVD) and singular value decomposition (SVD) of dense matrices when all eigenvectors/singular vectors are computed. The approach yields vastly improved performance relative to traditional QR algorithms for these problems and is competitive with two commonly used alternatives---Cuppen's Divide-and-Conquer algorithm and the method of Multiple Relatively Robust Representations---while inheriting the more modest O ( n ) workspace requirements of the original QR algorithms. Since the computations performed by the restructured algorithms remain essentially identical to those performed by the original methods, robust numerical properties are preserved.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Awile:2014:PWF, author = "Omar Awile and Ivo F. Sbalzarini", title = "A {Pthreads} Wrapper for {Fortran 2003}", journal = j-TOMS, volume = "40", number = "3", pages = "19:1--19:15", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2558889", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "With the advent of multicore processors, numerical and mathematical software relies on parallelism in order to benefit from hardware performance increases. We present the design and use of a Fortran 2003 wrapper for POSIX threads, called forthreads. Forthreads is complete in the sense that is provides native Fortran 2003 interfaces to all pthreads routines where possible. We demonstrate the use and efficiency of forthreads for SIMD parallelism and task parallelism. We present forthreads/MPI implementations that enable hybrid shared-/distributed-memory parallelism in Fortran 2003. Our benchmarks show that forthreads offers performance comparable to that of OpenMP, but better thread control and more freedom. We demonstrate the latter by presenting a multithreaded Fortran 2003 library for POSIX Internet sockets, enabling interactive numerical simulations with runtime control.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2014:ACM, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 939}: Computation of the {Marcum} {$Q$}-Function", journal = j-TOMS, volume = "40", number = "3", pages = "20:1--20:21", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2591004", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Methods and an algorithm for computing the generalized Marcum $Q$-function $ (Q_\mu (x, y))$ and the complementary function $ (P_\mu (x, y))$ are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics, and probability theory, where they are called the noncentral chi-square or the noncentral gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $ 10^{-12}$ can be obtained in the parameter region $ (x, y, \mu) \in [0, A] \times [0, A] \times [1, A]$, $ A = 200$, while for larger parameters the accuracy decreases (close to $ 10^{-11}$ for $ A = 1000$ and close to $ 5 \times 10^{-11}$ for $ A = 10000$).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Nelson:2014:AOA, author = "Blake Nelson and Robert M. Kirby and Steven Parker", title = "{Algorithm 940}: Optimal Accumulator-Based Expression Evaluation through the Use of Expression Templates", journal = j-TOMS, volume = "40", number = "3", pages = "21:1--21:21", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2591005", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we present a compile-time algorithm, implemented using C++ template metaprogramming techniques, that minimizes the use of temporary storage when evaluating expressions. We present the basic building blocks of our algorithm---transformations that act locally on nodes of the expression parse tree---and demonstrate that the application of these local transformations generates a (nonunique) expression that requires a minimum number of temporary storage objects to evaluate. We discuss a C++ implementation of our algorithm using expression templates, and give results demonstrating the effectiveness of our approach.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kressner:2014:AHM, author = "Daniel Kressner and Christine Tobler", title = "{Algorithm 941}: {{\tt htucker}} --- A {Matlab} Toolbox for Tensors in Hierarchical {Tucker} Format", journal = j-TOMS, volume = "40", number = "3", pages = "22:1--22:22", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2538688", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a Matlab toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work with this format. The toolbox not only allows for the efficient storage and manipulation of tensors in hierarchical Tucker format but also offers a set of tools for the development of higher-level algorithms. Several examples for the use of the toolbox are given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{delaCruz:2014:ASS, author = "Ra{\'u}l de la Cruz and Mauricio Araya-Polo", title = "{Algorithm 942}: Semi-Stencil", journal = j-TOMS, volume = "40", number = "3", pages = "23:1--23:39", month = apr, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2591006", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Apr 21 17:42:14 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Finite Difference (FD) is a widely used method to solve Partial Differential Equations (PDE). PDEs are the core of many simulations in different scientific fields, such as geophysics, astrophysics, etc. The typical FD solver performs stencil computations for the entire computational domain, thus solving the differential operators. In general terms, the stencil computation consists of a weighted accumulation of the contribution of neighbor points along the cartesian axis. Therefore, optimizing stencil computations is crucial in reducing the application execution time. Stencil computation performance is bounded by two main factors: the memory access pattern and the inefficient reuse of the accessed data. We propose a novel algorithm, named Semi-stencil, that tackles these two problems. The main idea behind this algorithm is to change the way in which the stencil computation progresses within the computational domain. Instead of accessing all required neighbors and adding all their contributions at once, the Semi-stencil algorithm divides the computation into several updates. Then, each update gathers half of the axis neighbors, partially computing at the same time the stencil in a set of closely located points. As Semi-stencil progresses through the domain, the stencil computations are completed on precomputed points. This computation strategy improves the memory access pattern and efficiently reuses the accessed data. Our initial target architecture was the Cell/B.E., where the Semi-stencil in a SPE was 44\% faster than the naive stencil implementation. Since then, we have continued our research on emerging multicore architectures in order to assess and extend this work on homogeneous architectures. The experiments presented combine the Semi-stencil strategy with space- and time-blocking algorithms used in hierarchical memory architectures. Two x86 (Intel Nehalem and AMD Opteron) and two POWER (IBM POWER6 and IBM BG/P) platforms are used as testbeds, where the best improvements for a 25-point stencil range from 1.27 to 1.76$ \times $ faster. The results show that this novel strategy is a feasible optimization method which may be integrated into auto-tuning frameworks. Also, since all current architectures are multicore based, we have introduced a brief section where scalability results on IBM POWER7-, Intel Xeon-, and MIC-based systems are presented. In a nutshell, the algorithm scales as well as or better than other stencil techniques. For instance, the scalability of Semi-stencil on MIC for a certain testcase reached 93.8 $ \times $ over 244 threads.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2014:HER, author = "Jennifer Scott and Miroslav Tuma", title = "{HSL\_MI28}: an Efficient and Robust Limited-Memory Incomplete {Cholesky} Factorization Code", journal = j-TOMS, volume = "40", number = "4", pages = "24:1--24:19", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2617555", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article focuses on the design and development of a new robust and efficient general-purpose incomplete Cholesky factorization package HSL\_MI28, which is available within the HSL mathematical software library. It implements a limited memory approach that exploits ideas from the positive semidefinite Tismenetsky-Kaporin modification scheme and, through the incorporation of intermediate memory, is a generalization of the widely used ICFS algorithm of Lin and Mor{\'e}. Both the density of the incomplete factor and the amount of memory used in its computation are under the user's control. The performance of HSL\_MI28 is demonstrated using extensive numerical experiments involving a large set of test problems arising from a wide range of real-world applications. The numerical experiments are used to isolate the effects of scaling, ordering, and dropping strategies so as to assess their usefulness in the development of robust algebraic incomplete factorization preconditioners and to select default settings for HSL\_MI28. They also illustrate the significant advantage of employing a modest amount of intermediate memory. Furthermore, the results demonstrate that, with limited memory, high-quality yet sparse general-purpose preconditioners are obtained. Comparisons are made with ICFS, with a level-based incomplete factorization code and, finally, with a state-of-the-art direct solver.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2014:HPE, author = "Robert C. Kirby", title = "High-Performance Evaluation of Finite Element Variational Forms via Commuting Diagrams and Duality", journal = j-TOMS, volume = "40", number = "4", pages = "25:1--25:24", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2559983", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We revisit the question of optimizing the construction and application of finite element matrices. By using commuting properties of the reference mappings and duality, we reorganize stiffness matrix construction and matrix-free application so that the bulk of the work can be done by optimized matrix multiplication libraries. We provide examples, including numerical experiments, with the Laplace and curl-curl operators as well as develop a general framework. Our techniques are applicable in general geometry and are not restricted to constant coefficient operators.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hogan:2014:FRM, author = "Robin J. Hogan", title = "Fast Reverse-Mode Automatic Differentiation using Expression Templates in {C++}", journal = j-TOMS, volume = "40", number = "4", pages = "26:1--26:16", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2560359", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Gradient-based optimization problems are encountered in many fields, but the associated task of differentiating large computer algorithms can be formidable. The operator-overloading approach to performing reverse-mode automatic differentiation is the most convenient for the user but current implementations are typically 10--35 times slower than the original algorithm. In this paper a fast new operator-overloading method is presented that uses the expression template programming technique in C++ to provide a compile-time representation of each mathematical expression as a computational graph that can be efficiently traversed in either direction. Benchmarking with four different numerical algorithms shows this approach to be 2.6--9 times faster than current operator-overloading libraries, and 1.3--7.7 times more efficient in memory usage. It is typically less than 4 times the computational cost of the original algorithm, although poorer performance is found for all libraries in the case of simple loops containing no mathematical functions. An implementation is freely available in the Adept C++ software library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fabregat-Traver:2014:CPT, author = "Diego Fabregat-Traver and Paolo Bientinesi", title = "Computing Petaflops over Terabytes of Data: The Case of Genome-Wide Association Studies", journal = j-TOMS, volume = "40", number = "4", pages = "27:1--27:22", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2560421", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In many scientific and engineering applications, one has to solve not one but multiple instances of the same problem. Often times, these problems are linked in a way that allows intermediate results to be reused. A characteristic example for this class of applications is given by the Genome-Wide Association Studies (GWAS), a widely spread tool in computational biology. GWAS entails the solution of up to trillions (10$^{12}$ ) of correlated generalized least-squares problems, posing a daunting challenge: the performance of petaflops (10$^{15}$ floating-point operations) over terabytes (10$^{12}$ bytes) of data. In this article, we design an algorithm for performing GWAS on multicore architectures. This is accomplished in three steps. First, we show how to exploit the relation among successive problems, thus reducing the overall computational complexity. Then, through an analysis of the required data transfers, we identify how to eliminate any overhead due to input/output operations. Finally, we study how to decompose computation into tasks to be distributed among the available cores, to attain high performance and scalability. With our algorithm, a GWAS that currently requires the use of a supercomputer may now be performed in matter of hours on a single multicore node. The discussion centers around the methodology to develop the algorithm rather than the specific application. We believe this article contributes valuable guidelines of general applicability for computational scientists on how to develop and optimize numerical algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Erway:2014:AMM, author = "Jennifer B. Erway and Roummel F. Marcia", title = "Algorithm 943: {MSS}: {MATLAB} Software for {L-BFGS} Trust-Region Subproblems for Large-Scale Optimization", journal = j-TOMS, volume = "40", number = "4", pages = "28:1--28:12", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2616588", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A MATLAB implementation of the Mor{\'e}--Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the Mor{\'e}--Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations [Erway and Marcia 2012; Erway et al. 2012] and is able to compute solutions to any user-defined accuracy. This MATLAB implementation is a matrix-free iterative method for large-scale optimization. Numerical experiments on the CUTEr [Bongartz et al. 1995; Gould et al. 2003] suggest that using the MSS method as a trust-region subproblem solver can require significantly fewer function and gradient evaluations needed by a trust-region method as compared with the Steihaug-Toint method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Antonelli:2014:ATS, author = "Laura Antonelli and Stefania Corsaro and Zelda Marino and Mariarosaria Rizzardi", title = "Algorithm 944: {Talbot} Suite: Parallel Implementations of {Talbot}'s Method for the Numerical Inversion of {Laplace} Transforms", journal = j-TOMS, volume = "40", number = "4", pages = "29:1--29:18", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2616909", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present Talbot Suite, a C parallel software collection for the numerical inversion of Laplace Transforms, based on Talbot's method. It is designed to fit both single and multiple Laplace inversion problems, which arise in several application and research fields. In our software, we achieve high accuracy and efficiency, making full use of modern architectures and introducing two different levels of parallelism: coarse and fine grained parallelism. They offer a reasonable tradeoff between accuracy, the main aspect for a few inversions, and efficiency, the main aspect for multiple inversions. To take into account modern high-performance computing architectures, Talbot Suite provides different software versions: an OpenMP-based version for shared memory machines and a MPI-based version for distributed memory machines. Moreover, oriented to hybrid architectures, a combined MPI/OpenMP-based implementation is provided too. We describe our parallel algorithms and the software organization. We also report some performance results. Our software includes sample programs to call the Talbot Suite functions from C and from MATLAB.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Belson:2014:AMP, author = "Brandt A. Belson and Jonathan H. Tu and Clarence W. Rowley", title = "Algorithm 945: {{\tt modred}} --- A Parallelized Model Reduction Library", journal = j-TOMS, volume = "40", number = "4", pages = "30:1--30:23", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2616912", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We describe a new parallelized Python library for model reduction, modal analysis, and system identification of large systems and datasets. Our library, called modred, handles a wide range of problems and any data format. The modred library contains implementations of the Proper Orthogonal Decomposition (POD), balanced POD (BPOD) Petrov--Galerkin projection, and a more efficient variant of the Dynamic Mode Decomposition (DMD). The library contains two implementations of these algorithms, each with its own advantages. One is for smaller and simpler datasets, requires minimal knowledge to use, and follows a common matrix-based formulation. The second, for larger and more complicated datasets, preserves the abstraction of vectors as elements of a vector space and, as a result, allows the library to work with arbitrary data formats and eases distributed memory parallelization. We also include implementations of the Eigensystem Realization Algorithm (ERA), and Observer/Kalman Filter Identification (OKID). These methods are typically not computationally demanding and are not parallelized. The library is designed to be easy to use, with an object-oriented design, and includes comprehensive automated tests. In almost all cases, parallelization is done internally so that scripts that use the parallelized classes can be run in serial or in parallel without any modifications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DAmore:2014:ARC, author = "Luisa D'Amore and Rosanna Campagna and Valeria Mele and Almerico Murli", title = "Algorithm 946: {ReLIADiff} ---A {C++} Software Package for Real {Laplace} Transform Inversion based on Algorithmic Differentiation", journal = j-TOMS, volume = "40", number = "4", pages = "31:1--31:20", month = jun, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2616971", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 2 18:28:58 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used for calculating function values of the inverse Laplace transform. The software requires transform values at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article, we present ReLIADiff focusing on its design principles, performance, and use.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Patterson:2014:GIM, author = "Michael A. Patterson and Anil V. Rao", title = "{GPOPS-II}: a {MATLAB} Software for Solving Multiple-Phase Optimal Control Problems Using $ h p$-Adaptive {Gaussian} Quadrature Collocation Methods and Sparse Nonlinear Programming", journal = j-TOMS, volume = "41", number = "1", pages = "1:1--1:37", month = oct, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2558904", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 27 16:37:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A general-purpose MATLAB software program called GPOPS--II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre--Gauss--Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mitchell:2014:CAS, author = "William F. Mitchell and Marjorie A. McClain", title = "A Comparison of $ h p$-Adaptive Strategies for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "41", number = "1", pages = "2:1--2:39", month = oct, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629459", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 27 16:37:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The $ h p $ version of the finite element method ($ h p $ -FEM) combined with adaptive mesh refinement is a particularly efficient method for solving PDEs because it can achieve an exponential convergence rate in the number of degrees of freedom. $ h p$-FEM allows for refinement in both the element size, $h$, and the polynomial degree, $p$. Like adaptive refinement for the $h$ version of the finite element method, a posteriori error estimates can be used to determine where the mesh needs to be refined, but a single error estimate cannot simultaneously determine whether it is better to do the refinement by $h$ or $p$. Several strategies for making this determination have been proposed over the years. These strategies are summarized, and the results of a numerical experiment to study the performance of these strategies is presented. It was found that the reference-solution-based methods are very effective, but also considerably more expensive, in terms of computation time, than other approaches. The method based on a priori knowledge is very effective when there are known point singularities. The method based on the decay rate of the expansion coefficients appears to be the best choice as a general strategy across all categories of problems, whereas many of the other strategies perform well in particular situations and are reasonable in general.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kim:2014:PSD, author = "Kyungjoo Kim and Victor Eijkhout", title = "A Parallel Sparse Direct Solver via Hierarchical {DAG} Scheduling", journal = j-TOMS, volume = "41", number = "1", pages = "3:1--3:27", month = oct, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629641", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 27 16:37:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a parallel sparse direct solver for multicore architectures based on Directed Acyclic Graph (DAG) scheduling. Recently, DAG scheduling has become popular in advanced Dense Linear Algebra libraries due to its efficient asynchronous parallel execution of tasks. However, its application to sparse matrix problems is more challenging as it has to deal with an enormous number of highly irregular tasks. This typically results in substantial scheduling overhead both in time and space, which causes overall parallel performance to be suboptimal. We describe a parallel solver based on two-level task parallelism: tasks are first generated from a parallel tree traversal on the assembly tree; next, those tasks are further refined by using algorithms-by-blocks to gain fine-grained parallelism. The resulting fine-grained tasks are asynchronously executed after their dependencies are analyzed. Our approach is distinct from others in that we adopt two-level task scheduling to mirror the two-level parallelism. As a result, we reduce scheduling overhead, and increase efficiency and flexibility. The proposed parallel sparse direct solver is evaluated for the particular problems arising from the $ h p$-Finite Element Method where conventional sparse direct solvers do not scale well.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Seibold:2014:SSO, author = "Benjamin Seibold and Martin Frank", title = "{StaRMAP} --- a Second Order Staggered {Grid} Method for Spherical Harmonics Moment Equations of Radiative Transfer", journal = j-TOMS, volume = "41", number = "1", pages = "4:1--4:28", month = oct, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2590808", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 27 16:37:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a simple method to solve spherical harmonics moment systems, such as the time-dependent PN and SPN equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the PN equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Langr:2014:APP, author = "Daniel Langr and Pavel Tvrd{\'\i}k and Tom{\'a}s Dytrych and Jerry P. Draayer", title = "{Algorithm 947}: {Paraperm} --- Parallel Generation of Random Permutations with {MPI}", journal = j-TOMS, volume = "41", number = "1", pages = "5:1--5:26", month = oct, year = "2014", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2669372", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 27 16:37:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "An algorithm for parallel generation of a random permutation of a large set of distinct integers is presented. This algorithm is designed for massively parallel systems with distributed memory architectures and the MPI-based runtime environments. Scalability of the algorithm is analyzed according to the memory and communication requirements. An implementation of the algorithm in a form of a software library based on the C++ programming language and the MPI application programming interface is further provided. Finally, performed experiments are described and their results discussed. The biggest of these experiments resulted in a generation of a random permutation of $ 2^{41} $ integers in slightly more than four minutes using 131072 CPU cores.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Smigaj:2015:SBI, author = "Wojciech {\'S}migaj and Timo Betcke and Simon Arridge and Joel Phillips and Martin Schweiger", title = "Solving Boundary Integral Problems with {BEM++}", journal = j-TOMS, volume = "41", number = "2", pages = "6:1--6:40", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2590830", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the boundary of the domain of interest. In order to solve such problems, the boundary element method (BEM) can be applied. The advantage compared to domain-discretisation-based methods such as finite element methods is that only a discretisation of the boundary is necessary, which significantly reduces the number of unknowns. Yet, BEM formulations are much more difficult to implement than finite element methods. In this article, we present BEM++, a novel open-source library for the solution of boundary integral equations for Laplace, Helmholtz and Maxwell problems in three space dimensions. BEM++ is a C++ library with Python bindings for all important features, making it possible to integrate the library into other C++ projects or to use it directly via Python scripts. The internal structure and design decisions for BEM++ are discussed. Several examples are presented to demonstrate the performance of the library for larger problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Muller:2015:ECC, author = "Jean-Michel Muller", title = "On the Error of Computing $ a b + c d $ using {Cornea}, {Harrison} and {Tang}'s Method", journal = j-TOMS, volume = "41", number = "2", pages = "7:1--7:8", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629615", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In their book, \booktitle{Scientific Computing on the Itanium}, Cornea et al. [2002] introduce an accurate algorithm for evaluating expressions of the form $ a b + c d $ in binary floating-point arithmetic, assuming an FMA instruction is available. They show that if $p$ is the precision of the floating-point format and if $ u = 2^{-p} $, the relative error of the result is of order $u$. We improve their proof to show that the relative error is bounded by $ 2 u + 7 u^2 + 6 u^3 $. Furthermore, by building an example for which the relative error is asymptotically (as $ p \to \infty $ or, equivalently, as $ u \to 0 $) equivalent to $ 2 u $, we show that our error bound is asymptotically optimal.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", remark = "This article compares two algorithms (Kahan's and Cornea / Harrison / Tang's) for computing $ a b + c d $. It shows that the worst-case error with FMA and round-to-nearest arithmetic is $ 2 u $ for the first, and $ 2 u + 7 u^2 + 6 u^3 $ for the second, suggesting that Kahan's is preferred. However, the second guarantees that $ a b + c d = = c d + a b $, whereas the first does not, so it may be preferred for applications like complex multiplication and division, in order to guarantee commutative arithmetic", } @Article{Lorenz:2015:SBP, author = "Dirk A. Lorenz and Marc E. Pfetsch and Andreas M. Tillmann", title = "Solving Basis Pursuit: Heuristic Optimality Check and Solver Comparison", journal = j-TOMS, volume = "41", number = "2", pages = "8:1--8:29", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2689662", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The problem of finding a minimum $ l_1 $ -norm solution to an underdetermined linear system is an important problem in compressed sensing, where it is also known as basis pursuit. We propose a heuristic optimality check as a general tool for $ l_1 $ -minimization, which often allows for early termination by ``guessing'' a primal-dual optimal pair based on an approximate support. Moreover, we provide an extensive numerical comparison of various state-of-the-art $ l_1 $ -solvers that have been proposed during the last decade, on a large test set with a variety of explicitly given matrices and several right-hand sides per matrix reflecting different levels of solution difficulty. The results, as well as improvements by the proposed heuristic optimality check, are analyzed in detail to provide an answer to the question which algorithm is the best.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pryce:2015:DMT, author = "John D. Pryce and Nedialko S. Nedialkov and Guangning Tan", title = "{DAESA} --- a {Matlab} Tool for Structural Analysis of Differential-Algebraic Equations: Theory", journal = j-TOMS, volume = "41", number = "2", pages = "9:1--9:20", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2689664", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "DAESA, \underline{D}ifferential-\underline{A}lgebraic \underline{E}quations \underline{S}tructural \underline{A}nalyzer, is a Matlab tool for structural analysis of differential-algebraic equations (DAEs). It allows convenient translation of a DAE system into Matlab and provides a small set of easy-to-use functions. daesa can analyze systems that are fully nonlinear, high-index, and of any order. It determines structural index, number of degrees of freedom, constraints, variables to be initialized, and suggests a solution scheme. The structure of a DAE can be readily visualized by this tool. It also can construct a block-triangular form of the DAE, which can be exploited to solve it efficiently in a block-wise manner. This article describes the theory and algorithms underlying the code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Janna:2015:FSP, author = "Carlo Janna and Massimiliano Ferronato and Flavio Sartoretto and Giuseppe Gambolati", title = "{FSAIPACK}: a Software Package for High-Performance Factored Sparse Approximate Inverse Preconditioning", journal = j-TOMS, volume = "41", number = "2", pages = "10:1--10:26", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629475", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Factorized Sparse Approximate Inverse (FSAI) is an efficient technique for preconditioning parallel solvers of symmetric positive definite sparse linear systems. The key factor controlling FSAI efficiency is the identification of an appropriate nonzero pattern. Currently, several strategies have been proposed for building such a nonzero pattern, using both static and dynamic techniques. This article describes a fresh software package, called FSAIPACK, which we developed for shared memory parallel machines. It collects all available algorithms for computing FSAI preconditioners. FSAIPACK allows for combining different techniques according to any specified strategy, hence enabling the user to thoroughly exploit the potential of each preconditioner, in solving any peculiar problem. FSAIPACK is freely available as a compiled library at http://www.dmsa.unipd.it/~janna/software.html, together with an open-source command language interpreter. By writing a command ASCII file, one can easily perform and test any given strategy for building an FSAI preconditioner. Numerical experiments are discussed in order to highlight the FSAIPACK features and evaluate its computational performance.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Si:2015:TDB, author = "Hang Si", title = "{TetGen}, a {Delaunay}-Based Quality Tetrahedral Mesh Generator", journal = j-TOMS, volume = "41", number = "2", pages = "11:1--11:36", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629697", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available. This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other software are presented.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Nedialkov:2015:ADM, author = "Nedialko S. Nedialkov and John D. Pryce and Guangning Tan", title = "Algorithm 948: {DAESA} --- a {Matlab} Tool for Structural Analysis of Differential-Algebraic Equations: Software", journal = j-TOMS, volume = "41", number = "2", pages = "12:1--12:14", month = jan, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2700586", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Feb 4 17:49:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "daesa, \underline{D}ifferential-\underline{A}lgebraic \underline{E}quations \underline{S}tructural \underline{A}nalyzer, is a Matlab tool for structural analysis of differential-algebraic equations (DAEs). It allows convenient translation of a DAE system into Matlab and provides a small set of easy-to-use functions. daesa can analyze systems that are fully nonlinear, high-index, and of any order. It determines structural index, number of degrees of freedom, constraints, variables to be initialized, and suggests a solution scheme. The structure of a DAE can be readily visualized by this tool. It can also construct a block-triangular form of the DAE, which can be exploited to solve it efficiently in a block-wise manner.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Heroux:2015:EAT, author = "Michael A. Heroux", title = "Editorial: {ACM TOMS Replicated Computational Results Initiative}", journal = j-TOMS, volume = "41", number = "3", pages = "13:1--13:5", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2743015", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The scientific community relies on the peer review process for assuring the quality of published material, the goal of which is to build a body of work we can trust. Computational journals such as the ACM Transactions on Mathematical Software (TOMS) use this process for rigorously promoting the clarity and completeness of content, and citation of prior work. At the same time, it is unusual to independently confirm computational results. ACM TOMS has established a Replicated Computational Results (RCR) review process as part of the manuscript peer review process. The purpose is to provide independent confirmation that results contained in a manuscript are replicable. Successful completion of the RCR process awards a manuscript with the Replicated Computational Results Designation. This issue of ACM TOMS contains the first [Van Zee and van de Geijn 2015] of what we anticipate to be a growing number of articles to receive the RCR designation, and the related RCR reviewer report [Willenbring 2015]. We hope that the TOMS RCR process will serve as a model for other publications and increase the confidence in and value of computational results in TOMS articles.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanZee:2015:RCR, author = "Field G. {Van Zee} and Robert A. van de Geijn", title = "Replicated Computational Results Certified {BLIS}: a Framework for Rapidly Instantiating {BLAS} Functionality", journal = j-TOMS, volume = "41", number = "3", pages = "14:1--14:33", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2764454", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See result replication \cite{Willenbring:2015:RCR}.", abstract = "The BLAS-like Library Instantiation Software (BLIS) framework is a new infrastructure for rapidly instantiating Basic Linear Algebra Subprograms (BLAS) functionality. Its fundamental innovation is that virtually all computation within level-2 (matrix--vector) and level-3 (matrix--matrix) BLAS operations can be expressed and optimized in terms of very simple kernels. While others have had similar insights, BLIS reduces the necessary kernels to what we believe is the simplest set that still supports the high performance that the computational science community demands. Higher-level framework code is generalized and implemented in ISO C99 so that it can be reused and/or reparameterized for different operations (and different architectures) with little to no modification. Inserting high-performance kernels into the framework facilitates the immediate optimization of any BLAS-like operations which are cast in terms of these kernels, and thus the framework acts as a productivity multiplier. Users of BLAS-dependent applications are given a choice of using the traditional Fortran-77 BLAS interface, a generalized C interface, or any other higher level interface that builds upon this latter API. Preliminary performance of level-2 and level-3 operations is observed to be competitive with two mature open source libraries (OpenBLAS and ATLAS) as well as an established commercial product (Intel MKL).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Willenbring:2015:RCR, author = "James M. Willenbring", title = "Replicated Computational Results {(RCR)} Report for {``BLIS: a Framework for Rapidly Instantiating BLAS Functionality''}", journal = j-TOMS, volume = "41", number = "3", pages = "15:1--15:4", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2738033", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{VanZee:2015:RCR}.", abstract = "``BLIS: A Framework for Rapidly Instantiating BLAS Functionality'' includes single-platform BLIS performance results for both level-2 and level-3 operations that is competitive with OpenBLAS, ATLAS, and Intel MKL. A detailed description of the configuration used to generate the performance results was provided to the reviewer by the authors. All the software components used in the comparison were reinstalled and new performance results were generated and compared to the original results. After completing this process, the published results are deemed replicable by the reviewer.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pandis:2015:NID, author = "Vassilis Pandis", title = "Numerical Integration of Discontinuous Functions in Many Dimensions", journal = j-TOMS, volume = "41", number = "3", pages = "16:1--16:7", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629476", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on which the integrand is smooth, generalising the standard practice of dividing the interval used in one-dimensional problems. Our procedure is combined with existing adaptive cubature algorithms to significantly reduce the necessary number of function evaluations and memory requirements of the integrator. The method is embarrassingly parallel and can be trivially scaled across many cores with virtually no overhead. Our method is particularly pertinent to the integration of Green's functions, a problem directly related to the perturbation theory of impurity models. In three spatial dimensions, we observe a speed-up of order 100 which increases with increasing dimensionality.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kroshko:2015:OPN, author = "Andrew Kroshko and Raymond J. Spiteri", title = "{odeToJava}: a {PSE} for the Numerical Solution of {IVPs}", journal = j-TOMS, volume = "41", number = "3", pages = "17:1--17:33", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2641563", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/java2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Problem-solving environments (PSEs) offer a powerful yet flexible and convenient means for general experimentation with computational methods, algorithm prototyping, and visualization and manipulation of data. Consequently, PSEs have become the modus operandi of many computational scientists and engineers. However, despite these positive aspects, PSEs typically do not offer the level of granularity required by the specialist or algorithm designer to conveniently modify the details. In other words, the level at which PSEs are black boxes is often still too high for someone interested in modifying an algorithm as opposed to trying an alternative. In this article, we describe odeToJava, a Java-based PSE for initial-value problems in ordinary differential equations. odeToJava implements explicit and linearly implicit implicit-explicit Runge--Kutta methods with error and stepsize control and intra-step interpolation (dense output), giving the user control and flexibility over the implementational aspects of these methods. We illustrate the usage and functionality of odeToJava by means of computational case studies of initial-value problems (IVPs).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Nelson:2015:RGH, author = "Thomas Nelson and Geoffrey Belter and Jeremy G. Siek and Elizabeth Jessup and Boyana Norris", title = "Reliable Generation of High-Performance Matrix Algebra", journal = j-TOMS, volume = "41", number = "3", pages = "18:1--18:27", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2629698", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls do not achieve optimal performance. The entire sequence needs to be optimized in concert. Instead of vendor-tuned BLAS, a programmer could start with source code in Fortran or C (e.g., based on the Netlib BLAS) and use a state-of-the-art optimizing compiler. However, our experiments show that optimizing compilers often attain only one-quarter of the performance of hand-optimized code. In this article, we present a domain-specific compiler for matrix kernels, the Build to Order BLAS (BTO), that reliably achieves high performance using a scalable search algorithm for choosing the best combination of loop fusion, array contraction, and multithreading for data parallelism. The BTO compiler generates code that is between 16\% slower and 39\% faster than hand-optimized code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kowalczyk:2015:CRF, author = "Piotr Kowalczyk", title = "Complex Root Finding Algorithm Based on {Delaunay} Triangulation", journal = j-TOMS, volume = "41", number = "3", pages = "19:1--19:13", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699457", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points is created, where the signs of the real and imaginary parts of the function change simultaneously. To verify and refine the results, an iterative algorithm is applied. The validity of the presented technique is supported by the results obtained in numerical tests involving three different types of functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fu:2015:AMT, author = "Zhixing Fu and Luis F. Gatica and Francisco-javier Sayas", title = "Algorithm 949: {MATLAB} Tools for {HDG} in Three Dimensions", journal = j-TOMS, volume = "41", number = "3", pages = "20:1--20:21", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2658992", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article, we provide some MATLAB tools for efficient vectorized implementation of the Hybridizable Discontinuous Galerkin for linear variable coefficient reaction-diffusion problems in polyhedral domains. The resulting tools are modular and include enhanced structures to deal with convection-diffusion problems, plus several projection operators and the postprocessing implementation that is necessary to realize the superconvergence property of the method. Loops over the elements are exclusively local and, as such, have been parallelized.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wittek:2015:ANS, author = "Peter Wittek", title = "Algorithm 950: {Ncpol2sdpa} --- Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables", journal = j-TOMS, volume = "41", number = "3", pages = "21:1--21:12", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699464", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting variables that creates the relaxation to be solved by SDPA --- a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in Python. The tool helps solve such as finding the ground state energy or testing quantum correlations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sosonkina:2015:RAV, author = "Masha Sosonkina and Layne T. Watson and Jian He", title = "Remark on Algorithm 897: {VTDIRECT95}: Serial and Parallel Codes for the Global Optimization Algorithm {DIRECT}", journal = j-TOMS, volume = "41", number = "3", pages = "22:1--22:2", month = jun, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699459", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jun 3 17:59:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{He:2009:AVS}.", abstract = "The Fortran95 code VTDIRECT95, based on the original MPI, has been modified to use MPI-2. An option for VTDIRECT95 is to divide the feasible box into subdomains, and concurrently apply the global direct search algorithm DIRECT within each subdomain. When the number of subdomains is greater than one, a bug causes VTDIRECT95 to occasionally sample outside the given feasible box, which is serious if the objective function is not defined outside the given box. This bug has been fixed, and the sample output files have been updated to reflect the correction. For completeness, the package VTDIRECT95 now contains both the MPI-1 (with the multiple subdomain bug fixed) and the MPI-2 versions of the code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jamin:2015:CGF, author = "Cl{\'e}ment Jamin and Pierre Alliez and Mariette Yvinec and Jean-Daniel Boissonnat", title = "{CGALmesh}: a Generic Framework for {Delaunay} Mesh Generation", journal = j-TOMS, volume = "41", number = "4", pages = "23:1--23:24", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699463", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes---surface triangular meshes or volume tetrahedral meshes---from input surfaces, 3D domains, and 3D multidomains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality and on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Graillat:2015:ECF, author = "Stef Graillat and Christoph Lauter and Ping Tak Peter Tang and Naoya Yamanaka and Shin'ichi Oishi", title = "Efficient Calculations of Faithfully Rounded $ l_2$-Norms of $n$-Vectors", journal = j-TOMS, volume = "41", number = "4", pages = "24:1--24:20", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699469", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article, we present an efficient algorithm to compute the faithful rounding of the $ l_2 $-norm of a floating-point vector. This means that the result is accurate to within 1 bit of the underlying floating-point type. This algorithm does not generate overflows or underflows spuriously, but does so when the final result calls for such a numerical exception to be raised. Moreover, the algorithm is well suited for parallel implementation and vectorization. The implementation runs up to 3 times faster than the netlib version on current processors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dalton:2015:OSM, author = "Steven Dalton and Luke Olson and Nathan Bell", title = "Optimizing Sparse Matrix--Matrix Multiplication for the {GPU}", journal = j-TOMS, volume = "41", number = "4", pages = "25:1--25:20", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699470", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Sparse matrix--matrix multiplication (SpGEMM) is a key operation in numerous areas from information to the physical sciences. Implementing SpGEMM efficiently on throughput-oriented processors, such as the graphics processing unit (GPU), requires the programmer to expose substantial fine-grained parallelism while conserving the limited off-chip memory bandwidth. Balancing these concerns, we decompose the SpGEMM operation into three highly parallel phases: expansion, sorting, and contraction, and introduce a set of complementary bandwidth-saving performance optimizations. Our implementation is fully general and our optimization strategy adaptively processes the SpGEMM workload row-wise to substantially improve performance by decreasing the work complexity and utilizing the memory hierarchy more effectively.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Naumann:2015:ADN, author = "Uwe Naumann and Johannes Lotz and Klaus Leppkes and Markus Towara", title = "Algorithmic Differentiation of Numerical Methods: Tangent and Adjoint Solvers for Parameterized Systems of Nonlinear Equations", journal = j-TOMS, volume = "41", number = "4", pages = "26:1--26:21", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2700820", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We discuss software tool support for the algorithmic differentiation (AD), also known as automatic differentiation, of numerical simulation programs that contain calls to solvers for parameterized systems of n nonlinear equations. The local computational overhead and the additional memory requirement for the computation of directional derivatives or adjoints of the solution of the nonlinear system with respect to the parameters can quickly become prohibitive for large values of n. Both are reduced drastically by analytical (and symbolic) approaches to differentiation of the underlying numerical methods. Following the discussion of the proposed terminology, we develop the algorithmic formalism building on prior work by other colleagues and present an implementation based on the AD software dco/c++. A representative case study supports the theoretically obtained computational complexity results with practical runtime measurements.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wang:2015:ACA, author = "Menghan Wang and Meera Sitharam", title = "Algorithm 951: {Cayley} Analysis of Mechanism Configuration Spaces using {CayMos}: Software Functionalities and Architecture", journal = j-TOMS, volume = "41", number = "4", pages = "27:1--27:8", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699462", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "For a common class of two-dimensional (2D) mechanisms called 1-dof tree-decomposable linkages, we present a software package, CayMos, which uses new theoretical results from Sitharam and Wang [2014] and Sitharam et al. [2011a, 2011b] to implement efficient algorithmic solutions for (a) meaningfully representing and visualizing the connected components in the Euclidean realization space; (b) finding a path of continuous motion between two realizations in the same connected component, with or without restricting the realization type (sometimes called orientation type); and (c) finding two ``closest'' realizations in different connected components.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dong:2015:APL, author = "Bohan Dong and Rida T. Farouki", title = "Algorithm 952: {PHquintic}: a Library of Basic Functions for the Construction and Analysis of Planar Quintic {Pythagorean}-Hodograph Curves", journal = j-TOMS, volume = "41", number = "4", pages = "28:1--28:20", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699467", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The implementation of a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph (PH) curves is presented using the complex representation. The special algebraic structure of PH curves permits exact algorithms for the computation of key properties, such as arc length, elastic bending energy, and offset (parallel) curves. Single planar PH quintic segments are constructed as interpolants to first-order Hermite data (end points and derivatives), and this construction is then extended to open or closed C$^2$ PH quintic spline curves interpolating a sequence of points in the plane. The nonlinear nature of PH curves incurs a multiplicity of formal solutions to such interpolation problems, and a key aspect of the algorithms is to efficiently single out the unique ``good'' interpolant among them.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Granat:2015:APL, author = "Robert Granat and Bo K{\aa}gstr{\"o}m and Daniel Kressner and Meiyue Shao", title = "Algorithm 953: Parallel Library Software for the Multishift {$ Q R $} Algorithm with Aggressive Early Deflation", journal = j-TOMS, volume = "41", number = "4", pages = "29:1--29:23", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699471", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel multishift QR algorithm [Granat et al., SIAM J. Sci. Comput. 32(4), 2010], we describe a number of algorithmic and implementation improvements. These include communication avoiding algorithms via data redistribution and a refined strategy for balancing between multishift QR sweeps and AED. Guidelines concerning several important tunable algorithmic parameters are provided. As a result of these improvements, a computational bottleneck within AED has been removed in the parallel multishift QR algorithm. A performance model is established to explain the scalability behavior of the new parallel multishift QR algorithm. Numerous computational experiments confirm that our new implementation significantly outperforms previous parallel implementations of the QR algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Flocke:2015:AAE, author = "N. Flocke", title = "{Algorithm 954}: an Accurate and Efficient Cubic and Quartic Equation Solver for Physical Applications", journal = j-TOMS, volume = "41", number = "4", pages = "30:1--30:24", month = oct, year = "2015", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699468", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 26 17:31:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We report on an accurate and efficient algorithm for obtaining all roots of general real cubic and quartic polynomials. Both the cubic and quartic solvers give highly accurate roots and place no restrictions on the magnitude of the polynomial coefficients. The key to the algorithm is a proper rescaling of both polynomials. This puts upper bounds on the magnitude of the roots and is very useful in stabilizing the root finding process. The cubic solver is based on dividing the cubic polynomial into six classes. By analyzing the root surface for each class, a fast convergent Newton--Raphson starting point for a real root is obtained at a cost no higher than three additions and four multiplications. The quartic solver uses the cubic solver in getting information about stationary points and, when the quartic has real roots, stable Newton--Raphson iterations give one of the extreme real roots. The remaining roots follow by composite deflation to a cubic. If the quartic has only complex roots, the present article shows that a stable Newton--Raphson iteration on a derived symmetric sixth degree polynomial can be formulated for the real parts of the complex roots. The imaginary parts follow by solving suitable quadratics.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hogg:2016:SSI, author = "Jonathan D. Hogg and Evgueni Ovtchinnikov and Jennifer A. Scott", title = "A Sparse Symmetric Indefinite Direct Solver for {GPU} Architectures", journal = j-TOMS, volume = "42", number = "1", pages = "1:1--1:25", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2756548", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In recent years, there has been considerable interest in the potential for graphics processing units (GPUs) to speed up the performance of sparse direct linear solvers. Efforts have focused on symmetric positive-definite systems for which no pivoting is required, while little progress has been reported for the much harder indefinite case. We address this challenge by designing and developing a sparse symmetric indefinite solver SSIDS. This new library-quality LDL$^T$ factorization is designed for use on GPU architectures and incorporates threshold partial pivoting within a multifrontal approach. Both the factorize and the solve phases are performed using the GPU. Another important feature is that the solver produces bit-compatible results. Numerical results for indefinite problems arising from a range of practical applications demonstrate that, for large problems, SSIDS achieves performance improvements of up to a factor of 4.6 $ \times $ compared with a state-of-the-art multifrontal solver on a multicore CPU.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bavier:2016:RCR, author = "Eric T. Bavier", title = "{Replicated Computational Results (RCR)} Report for A Sparse Symmetric Indefinite Direct Solver for {GPU} Architectures", journal = j-TOMS, volume = "42", number = "1", pages = "2:1--2:10", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2851489", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A Sparse Symmetric Indefinite Direct Solver for GPU Architectures includes performance results and comparisons of the developed GPU direct solver against a CPU direct solver. New performance data were gathered using software provided by the manuscript authors on two new platforms and compared against the performance of the MUMPS direct solver. After completing this process, the published results have been deemed replicable by the reviewer.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Karney:2016:SEN, author = "Charles F. F. Karney", title = "Sampling Exactly from the Normal Distribution", journal = j-TOMS, volume = "42", number = "1", pages = "3:1--3:14", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2710016", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/compstat.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See improvement in \cite{Du:2021:IES}.", abstract = "An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same base. Thereafter, uniform random digits are copied directly into the representation of the normal deviate. Thus, in contrast to existing methods, it is possible to generate normal deviates exactly rounded to any precision with a mean cost that scales linearly in the precision. The method performs no extended precision arithmetic, calls no transcendental functions, and uses no floating point arithmetic whatsoever; it uses only simple integer operations. It can easily be adapted to sample exactly from the discrete normal distribution whose parameters are rational numbers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Deadman:2016:TMF, author = "Edvin Deadman and Nicholas J. Higham", title = "Testing Matrix Function Algorithms Using Identities", journal = j-TOMS, volume = "42", number = "1", pages = "4:1--4:15", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2723157", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F60", MRnumber = "3472420", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Algorithms for computing matrix functions are typically tested by comparing the forward error with the product of the condition number and the unit roundoff. The forward error is computed with the aid of a reference solution, typically computed at high precision. An alternative approach is to use functional identities such as the ``round-trip tests'' $ e^{\log A} = A $ and $ (A^{1 / p})^p = A $, as are currently employed in a SciPy test module. We show how a linearized perturbation analysis for a functional identity allows the determination of a maximum residual consistent with backward stability of the constituent matrix function evaluations. Comparison of this maximum residual with a computed residual provides a necessary test for backward stability. We also show how the actual linearized backward error for these relations can be computed. Our approach makes use of Fr{\'e}chet derivatives and estimates of their norms. Numerical experiments show that the proposed approaches are able both to detect instability and to confirm stability.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kutyniok:2016:SFD, author = "Gitta Kutyniok and Wang-Q Lim and Rafael Reisenhofer", title = "{ShearLab $3$D}: Faithful Digital Shearlet Transforms Based on Compactly Supported Shearlets", journal = j-TOMS, volume = "42", number = "1", pages = "5:1--5:42", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2740960", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient in sparsely approximating and also in analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this article, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible research, all scripts are accessible on www.ShearLab.org.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Burton:2016:PCD, author = "Benjamin A. Burton and Thomas Lewiner and Jo{\~a}o Paix{\~a}o and Jonathan Spreer", title = "Parameterized Complexity of Discrete {Morse} Theory", journal = j-TOMS, volume = "42", number = "1", pages = "6:1--6:24", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2738034", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Optimal Morse matchings reveal essential structures of cell complexes that lead to powerful tools to study discrete geometrical objects, in particular, discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds through a reduction to the erasability problem. Here, we refine the study of the complexity of problems related to discrete Morse theory in terms of parameterized complexity. On the one hand, we prove that the erasability problem is W [ P ]-complete on the natural parameter. On the other hand, we propose an algorithm for computing optimal Morse matchings on triangulations of 3-manifolds, which is fixed-parameter tractable in the treewidth of the bipartite graph representing the adjacency of the 1- and 2-simplices. This algorithm also shows fixed-parameter tractability for problems such as erasability and maximum alternating cycle-free matching. We further show that these results are also true when the treewidth of the dual graph of the triangulated 3-manifold is bounded. Finally, we discuss the topological significance of the chosen parameters and investigate the respective treewidths of simplicial and generalized triangulations of 3-manifolds.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Giles:2016:AAI, author = "Michael B. Giles", title = "Algorithm 955: Approximation of the Inverse {Poisson} Cumulative Distribution Function", journal = j-TOMS, volume = "42", number = "1", pages = "7:1--7:22", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "New approximations for the inverse of the incomplete gamma function are derived, which are used to develop efficient evaluations of the inverse Poisson cumulative distribution function. An asymptotic approximation based on the standard Normal approximation is particularly good for CPUs with MIMD cores, while for GPUs and other hardware with vector units, a second asymptotic approximation based on Temme's approximation of the incomplete gamma function is more efficient due to conditional branching within each vector. The accuracy and efficiency of the software implementations is assessed on both CPUs and GPUs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aruliah:2016:APP, author = "D. A. Aruliah and Lennaert {Van Veen} and Alex Dubitski", title = "Algorithm 956: {PAMPAC}, A Parallel Adaptive Method for Pseudo-Arclength Continuation", journal = j-TOMS, volume = "42", number = "1", pages = "8:1--8:18", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2714570", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which new approximate solutions are extrapolated from previously converged results and then iteratively refined. Convergence of the iterative corrections is guaranteed only for sufficiently small prediction steps. In high-dimensional systems, corrector steps are extremely costly to compute and the prediction step length must be adapted carefully to avoid failed steps or unnecessarily slow progress. We describe a parallel method for adapting the step length employing several predictor-corrector sequences of different step lengths computed concurrently. In addition, the algorithm permits intermediate results of correction sequences that have not converged to seed new predictions. This strategy results in an aggressive optimization of the step length at the cost of redundancy in the concurrent computation. We present two examples of convoluted solution curves of high-dimensional systems showing that speed-up by a factor of two can be attained on a multicore CPU while a factor of three is attainable on a small cluster.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gautschi:2016:AER, author = "Walter Gautschi", title = "Algorithm 957: Evaluation of the Repeated Integral of the Coerror Function by Half-Range {Gauss--Hermite} Quadrature", journal = j-TOMS, volume = "42", number = "1", pages = "9:1--9:10", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2735626", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Nonstandard Gaussian quadrature is applied to evaluate the repeated integral $ i^n \erfc x $ of the coerror function for $ n \in N_0 $, $ x \in R $ in an appropriate domain of the $ (n, x)$-plane. Relevant software in MATLAB is provided: in particular, two routines evaluating the function to an accuracy of 12 respective 30-decimal digits.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Novoselsky:2016:RAD, author = "Alexander Novoselsky and Eugene Kagan", title = "Remark on {``Algorithm 673: Dynamic Huffman Coding''}", journal = j-TOMS, volume = "42", number = "1", pages = "10:1--10:1", month = feb, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2740959", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Mar 1 17:07:56 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Vitter:1989:ADH}.", abstract = "This remark presents a correction to Algorithm 673 (dynamic Huffman coding) [Vitter 1989] and its translation to MATLAB.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weinstein:2016:STO, author = "Matthew J. Weinstein and Anil V. Rao", title = "A Source Transformation via Operator Overloading Method for the Automatic Differentiation of Mathematical Functions in {MATLAB}", journal = j-TOMS, volume = "42", number = "2", pages = "11:1--11:42", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2699456", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 3 18:52:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A source transformation via operator overloading method is presented for computing derivatives of mathematical functions defined by MATLAB computer programs. The transformed derivative code that results from the method of this article computes a sparse representation of the derivative of the function defined in the original code. As in all source transformation automatic differentiation techniques, an important feature of the method is that any flow control in the original function code is preserved in the derivative code. Furthermore, the resulting derivative code relies solely upon the native MATLAB library. The method is useful in applications where it is required to repeatedly evaluate the derivative of the original function. The approach is demonstrated on several examples and is found to be highly efficient when compared to well-known MATLAB automatic differentiation programs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanZee:2016:BFE, author = "Field G. {Van Zee} and Tyler M. Smith and Bryan Marker and Tze Meng Low and Robert A. {Van De Geijn} and Francisco D. Igual and Mikhail Smelyanskiy and Xianyi Zhang and Michael Kistler and Vernon Austel and John A. Gunnels and Lee Killough", title = "The {BLIS} Framework: Experiments in Portability", journal = j-TOMS, volume = "42", number = "2", pages = "12:1--12:19", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2755561", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 3 18:52:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "BLIS is a new software framework for instantiating high-performance BLAS-like dense linear algebra libraries. We demonstrate how BLIS acts as a productivity multiplier by using it to implement the level-3 BLAS on a variety of current architectures. The systems for which we demonstrate the framework include state-of-the-art general-purpose, low-power, and many-core architectures. We show, with very little effort, how the BLIS framework yields sequential and parallel implementations that are competitive with the performance of ATLAS, OpenBLAS (an effort to maintain and extend the GotoBLAS), and commercial vendor implementations such as AMD's ACML, IBM's ESSL, and Intel's MKL libraries. Although most of this article focuses on single-core implementation, we also provide compelling results that suggest the framework's leverage extends to the multithreaded domain.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mei:2016:CDC, author = "Yi Mei and Mohammad Nabi Omidvar and Xiaodong Li and Xin Yao", title = "A Competitive Divide-and-Conquer Algorithm for Unconstrained Large-Scale Black-Box Optimization", journal = j-TOMS, volume = "42", number = "2", pages = "13:1--13:24", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2791291", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 3 18:52:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article proposes a competitive divide-and-conquer algorithm for solving large-scale black-box optimization problems for which there are thousands of decision variables and the algebraic models of the problems are unavailable. We focus on problems that are partially additively separable, since this type of problem can be further decomposed into a number of smaller independent subproblems. The proposed algorithm addresses two important issues in solving large-scale black-box optimization: (1) the identification of the independent subproblems without explicitly knowing the formula of the objective function and (2) the optimization of the identified black-box subproblems. First, a Global Differential Grouping (GDG) method is proposed to identify the independent subproblems. Then, a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is adopted to solve the subproblems resulting from its rotation invariance property. GDG and CMA-ES work together under the cooperative co-evolution framework. The resultant algorithm, named CC-GDG-CMAES, is then evaluated on the CEC'2010 large-scale global optimization (LSGO) benchmark functions, which have a thousand decision variables and black-box objective functions. The experimental results show that, on most test functions evaluated in this study, GDG manages to obtain an ideal partition of the index set of the decision variables, and CC-GDG-CMAES outperforms the state-of-the-art results. Moreover, the competitive performance of the well-known CMA-ES is extended from low-dimensional to high-dimensional black-box problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sayed:2016:WCR, author = "Wafaa S. Sayed and Hossam A. H. Fahmy", title = "What are the Correct Results for the Special Values of the Operands of the Power Operation?", journal = j-TOMS, volume = "42", number = "2", pages = "14:1--14:17", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2809783", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 3 18:52:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Language standards such as C99 and C11, as well as the IEEE Standard for Floating-Point Arithmetic 754 (IEEE Std 754-2008) specify the expected behavior of binary and decimal floating-point arithmetic in computer-programming environments and the handling of special values and exception conditions. Many researchers focus on verifying the compliance of implementations for binary and decimal floating-point operations with these standards. In this article, we are concerned with the special values of the operands of the power function Z = X$^Y$. We study how the standards define the correct results for this operation, propose a mathematically justified definition for the correct results of the power function on the occurrence of these special values as its operands, test how different software implementations for the power function deal with these special values, and classify the behavior of different programming languages from the viewpoint of how much they conform to the standards and our proposed mathematical definition. We present inconsistencies between the implementations and the standards, and discuss incompatibilities between different versions of the same software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lecuyer:2016:ALB, author = "Pierre L'Ecuyer and David Munger", title = "{Algorithm 958}: {Lattice Builder}: a General Software Tool for Constructing Rank-1 Lattice Rules", journal = j-TOMS, volume = "42", number = "2", pages = "15:1--15:30", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2754929", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 3 18:52:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce a new software tool and library named Lattice Builder, written in C++, that implements a variety of construction algorithms for good rank-1 lattice rules. It supports exhaustive and random searches, as well as component-by-component (CBC) and random CBC constructions, for any number of points, and for various measures of (non)uniformity of the points. The measures currently implemented are all shift-invariant and represent the worst-case integration error for certain classes of integrands. They include, for example, the weighted P $ \alpha $ square discrepancy, the R $ \alpha $ criterion, and figures of merit based on the spectral test, with projection-dependent weights. Each of these measures can be computed as a finite sum. For the P $ \alpha $ and R $ \alpha $ criteria, efficient specializations of the CBC algorithm are provided for projection-dependent, order-dependent, and product weights. For numbers of points that are integer powers of a prime base, the construction of embedded rank-1 lattice rules is supported through any of these algorithms, and through a fast CBC algorithm, with a variety of possibilities for the normalization of the merit values of individual embedded levels and for their combination into a single merit value. The library is extensible, thanks to the decomposition of the algorithms into decoupled components, which makes it easy to implement new types of weights, new search domains, new figures of merit, and so on.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alvarez-Cubero:2016:AVL, author = "Jos{\'e} Antonio {\'A}lvarez-Cubero and Pedro J. Zufiria", title = "{Algorithm 959}: {VBF}: a Library of {C++} Classes for Vector {Boolean} Functions in Cryptography", journal = j-TOMS, volume = "42", number = "2", pages = "16:1--16:22", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2794077", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This implementation uses the NTL library from Victor Shoup, adding new modules that call NTL functions and complement the existing ones, making it better suited to cryptography. The class representing a vector Boolean function can be initialized by several alternative types of data structures such as Truth Table, Trace Representation, and Algebraic Normal Form (ANF), among others. The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity, linearity distance, algebraic degree, linear structures, and frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions are presented. Finally, three real applications of the library are described: the first one analyzes the KASUMI block cipher, the second one analyzes the Mini-AES cipher, and the third one finds Boolean functions with very high nonlinearity, a key property for robustness against linear attacks.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ibanez:2016:PPU, author = "Daniel A. Ibanez and E. Seegyoung Seol and Cameron W. Smith and Mark S. Shephard", title = "{PUMI}: Parallel Unstructured Mesh Infrastructure", journal = j-TOMS, volume = "42", number = "3", pages = "17:1--17:28", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2814935", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The Parallel Unstructured Mesh Infrastructure (PUMI) is designed to support the representation of, and operations on, unstructured meshes as needed for the execution of mesh-based simulations on massively parallel computers. In PUMI, the mesh representation is complete in the sense of being able to provide any adjacency of mesh entities of multiple topologies in O(1) time, and fully distributed to support relationships of mesh entities across multiple memory spaces in a manner consistent with supporting massively parallel simulation workflows. PUMI's mesh maintains links to the high-level model definition in terms of a model topology as produced by CAD systems, and is specifically designed to efficiently support evolving meshes as required for mesh generation and adaptation. To support the needs of parallel unstructured mesh simulations, PUMI also supports a specific set of services such as the migration of mesh entities between parts while maintaining the mesh adjacencies, maintaining read-only mesh entity copies from neighboring parts (ghosting), repartitioning parts as the mesh evolves, and dynamic mesh load balancing. Here we present the overall design, software structures, example programs, and performance results. The effectiveness of PUMI is demonstrated by its applications to massively parallel adaptive simulation workflows.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Abdelfattah:2016:KOL, author = "Ahmad Abdelfattah and David Keyes and Hatem Ltaief", title = "{KBLAS}: an Optimized Library for Dense Matrix-Vector Multiplication on {GPU} Accelerators", journal = j-TOMS, volume = "42", number = "3", pages = "18:1--18:31", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2818311", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "KBLAS is an open-source, high-performance library that provides optimized kernels for a subset of Level 2 BLAS functionalities on CUDA-enabled GPUs. Since performance of dense matrix-vector multiplication is hindered by the overhead of memory accesses, a double-buffering optimization technique is employed to overlap data motion with computation. After identifying a proper set of tuning parameters, KBLAS efficiently runs on various GPU architectures while avoiding code rewriting and retaining compliance with the standard BLAS API. Another optimization technique allows ensuring coalesced memory access when dealing with submatrices, especially for high-level dense linear algebra algorithms. All KBLAS kernels have been leveraged to a multi-GPU environment, which requires the introduction of new APIs. Considering general matrices, KBLAS is very competitive with existing state-of-the-art kernels and provides a smoother performance across a wide range of matrix dimensions. Considering symmetric and Hermitian matrices, the KBLAS performance outperforms existing state-of-the-art implementations on all matrix sizes and achieves asymptotically up to 50\% and 60\% speedup against the best competitor on single GPU and multi-GPUs systems, respectively. Performance results also validate our performance model. A subset of KBLAS high-performance kernels have been integrated into NVIDIA's standard BLAS implementation (cuBLAS) for larger dissemination, starting from version 6.0.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jeannerod:2016:RIE, author = "Claude-Pierre Jeannerod", title = "A Radix-Independent Error Analysis of the {Cornea--Harrison--Tang} Method", journal = j-TOMS, volume = "42", number = "3", pages = "19:1--19:20", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2824252", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Assuming floating-point arithmetic with a fused multiply-add operation and rounding to nearest, the Cornea--Harrison--Tang method aims to evaluate expressions of the form $ a b + c d $ with high relative accuracy. In this article, we provide a rounding error analysis of this method, which unlike previous studies is not restricted to binary floating-point arithmetic but holds for any radix $ \beta $. We show first that an asymptotically optimal bound on the relative error of this method is $ 2 \beta u + 2 u^2 / \beta - 2 u^2 = 2 u + 2 / \beta u^2 + O (u^3) $, where $ u = 1 / 2 \beta^{1 - p} $ is the unit roundoff in radix $ \beta $ and precision $p$. Then we show that the possibility of removing the $ O (u^2)$ term from this bound is governed by the radix parity and the tie-breaking strategy used for rounding: if $ \beta $ is odd or rounding is to nearest even, then the simpler bound $ 2 u$ is obtained, while if $ \beta $ is even and rounding is to nearest away, then there exist floating-point inputs $a$, $b$, $c$, $d$ that lead to a relative error larger than $ 2 u + 2 / \beta u^2 - 4 u^3$. All these results hold provided underflows and overflows do not occur and under some mild assumptions on $p$ satisfied by IEEE 754-2008 formats.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boyer:2016:MMW, author = "Brice Boyer and Jean-Guillaume Dumas", title = "Matrix Multiplication Over Word-Size Modular Rings Using Approximate Formulas", journal = j-TOMS, volume = "42", number = "3", pages = "20:1--20:12", month = jun, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2829947", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:03 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2829947", abstract = "Bini--Capovani--Lotti--Romani approximate formula (or border rank) for matrix multiplication achieves a better complexity than Strassen's matrix multiplication formula. In this article, we show a novel way to use the approximate formula in the special case where the ring is $ \mathbb {Z} / p \mathbb {Z} $. In addition, we show an implementation {\`a} la FFLAS--FFPACK, where $p$ is a word-size modulo, that improves on state-of-the-art $ \mathbb {Z} / p \mathbb {Z}$ matrix multiplication implementations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wang:2016:PGM, author = "Shen Wang and Xiaoye S. Li and Fran{\c{c}}ois-Henry Rouet and Jianlin Xia and Maarten V. {De Hoop}", title = "A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure", journal = j-TOMS, volume = "42", number = "3", pages = "21:1--21:21", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2830569", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a structured parallel geometry-based multifrontal sparse solver using hierarchically semiseparable (HSS) representations and exploiting the inherent low-rank structures. Parallel strategies for nested dissection ordering (taking low rankness into account), symbolic factorization, and structured numerical factorization are shown. In particular, we demonstrate how to manage two layers of tree parallelism to integrate parallel HSS operations within the parallel multifrontal sparse factorization. Such a structured multifrontal factorization algorithm can be shown to have asymptotically lower complexities in both operation counts and memory than the conventional factorization algorithms for certain partial differential equations. We present numerical results from the solution of the anisotropic Helmholtz equations for seismic imaging, and demonstrate that our new solver was able to solve 3D problems up to $600^3$ mesh size, with 216M degrees of freedom in the linear system. For this specific model problem, our solver is both faster and more memory efficient than a geometry-based multifrontal solver (which is further faster than general-purpose algebraic solvers such as MUMPS and SuperLU\_DIST). For the 600$^3$ mesh size, the structured factors from our solver need about 5.9 times less memory.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2016:EHA, author = "Timothy A. Davis and William W. Hager and James T. Hungerford", title = "An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem", journal = j-TOMS, volume = "42", number = "3", pages = "22:1--22:25", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2828635", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush--Kuhn--Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Delgado:2016:APO, author = "Jorge Delgado and Juan Manuel Pe{\~n}a", title = "{Algorithm 960}: {POLYNOMIAL}: an Object-Oriented {Matlab} Library of Fast and Efficient Algorithms for Polynomials", journal = j-TOMS, volume = "42", number = "3", pages = "23:1--23:19", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2814567", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The design and implementation of a Matlab object-oriented software library for working with polynomials is presented. The construction and evaluation of polynomials in Bernstein form are motivated and justified. Efficient constructions for the coefficients of a polynomial in Bernstein form when the polynomial is not given with this representation are provided. The presented adaptive evaluation algorithm uses the VS (Volk and Schumaker) algorithm, the de Casteljau algorithm, and a compensated VS algorithm. In addition, we have completed the library with other algorithms to perform other usual operations with polynomials in Bernstein form.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Benner:2016:AFS, author = "Peter Benner and Vasile Sima and Matthias Voigt", title = "{Algorithm 961}: {Fortran 77} Subroutines for the Solution of Skew-{Hamiltonian\slash Hamiltonian} Eigenproblems", journal = j-TOMS, volume = "42", number = "3", pages = "24:1--24:26", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2818313", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Skew-Hamiltonian/Hamiltonian matrix pencils $ \lambda S - H $ appear in many applications, including linear-quadratic optimal control problems, $ H_\infty $-optimization, certain multibody systems, and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently developed methods exploit and preserve the skew-Hamiltonian/Hamiltonian structure and hence increase the reliability, accuracy, and performance of the computations. In this article, we describe the corresponding algorithms which have been implemented in the style of subroutines of the Subroutine Library in Control Theory (SLICOT). Furthermore, we address some of their applications. We describe variants for real and complex problems, as well as implementation details and perform numerical tests using real-world examples to demonstrate the superiority of the new algorithms compared to standard methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pew:2016:ABB, author = "Jack Pew and Zhi Li and Paul Muir", title = "{Algorithm 962}: {BACOLI}: {B}-spline Adaptive Collocation Software for {PDEs} with Interpolation-Based Spatial Error Control", journal = j-TOMS, volume = "42", number = "3", pages = "25:1--25:17", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2818312", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "BACOL and BACOLR are (Fortran 77) B-spline adaptive collocation packages for the numerical solution of 1D parabolic Partial Differential Equations (PDEs). The packages have been shown to be superior to other similar packages, especially for problems exhibiting sharp, moving spatial layer regions, where a stringent tolerance is imposed. In addition to providing temporal error control through the timestepping software, BACOL and BACOLR feature control of a high-order estimate of the spatial error of the approximate solution, obtained by computing a second approximate solution of one higher order of accuracy; the cost is substantial-execution time and memory usage are almost doubled. In this article, we discuss BACOLI, a new version of BACOL that computes only one approximate solution and uses efficient interpolation-based schemes to obtain a spatial error estimate. In previous studies these schemes have been shown to provide spatial error estimates of comparable quality to those of BACOL. We describe the substantial modification of BACOL needed to obtain BACOLI, and provide numerical results showing that BACOLI is significantly more efficient than BACOL, in some cases by as much as a factor of 2. We also introduce a Fortran 95 wrapper for BACOLI (called BACOLI95) and discuss its simplified user interface.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zaghloul:2016:RAC, author = "Mofreh R. Zaghloul", title = "Remark on {``Algorithm 916: Computing the Faddeyeva and Voigt Functions''}: Efficiency Improvements and {Fortran} Translation", journal = j-TOMS, volume = "42", number = "3", pages = "26:1--26:9", month = may, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2806884", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 23 16:40:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Zaghloul:2011:ACF}.", abstract = "This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of 2. A better accuracy vs efficiency tradeoff scheme is also implemented; this requires the user to supply the number of significant figures desired in the computed values as an extra input argument to the function. Using this tradeoff, it is shown that the efficiency of the algorithm may be further improved significantly while maintaining reasonably accurate and safe results that are free of the pitfalls and complete loss of accuracy seen in other competitive techniques. The current version of the code is provided in Matlab and Scilab in addition to a Fortran translation prepared to meet the needs of real-world problems where very large numbers of function evaluations would require the use of a compiled language. To fulfill this last requirement, a recently proposed reformed version of Huml{\'\i}cek's w4 routine, shown to maintain the claimed accuracy of the algorithm over a wide and fine grid, is implemented in the present Fortran translation for the case of four significant figures. This latter modification assures the reliability of the code in the solution of practical problems requiring numerous evaluation of the function for applications requiring low-accuracy computations ($ < 10^{-4}$).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rouet:2016:DMP, author = "Fran{\c{c}}ois-Henry Rouet and Xiaoye S. Li and Pieter Ghysels and Artem Napov", title = "A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization", journal = j-TOMS, volume = "42", number = "4", pages = "27:1--27:35", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2930660", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2930660", acknowledgement = ack-nhfb, articleno = "27", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meiser:2016:RCR, author = "Dominic Meiser", title = "{Replicated Computational Results (RCR)} Report for {``A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization''}", journal = j-TOMS, volume = "42", number = "4", pages = "28:1--28:5", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2929907", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2929907", acknowledgement = ack-nhfb, articleno = "28", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ledoux:2016:MMT, author = "Veerle Ledoux and Marnix {Van Daele}", title = "{Matslise 2.0}: A {Matlab} Toolbox for {Sturm--Liouville} Computations", journal = j-TOMS, volume = "42", number = "4", pages = "29:1--29:18", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2839299", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2839299", acknowledgement = ack-nhfb, articleno = "29", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Vigna:2016:EEM, author = "Sebastiano Vigna", title = "An Experimental Exploration of {Marsaglia}'s {\tt xorshift} Generators, Scrambled", journal = j-TOMS, volume = "42", number = "4", pages = "30:1--30:23", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2845077", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/tomacs.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2845077", abstract = "Marsaglia proposed xorshift generators are a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's article, showing several weaknesses of such generators. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a nonlinear operation (as originally suggested by Marsaglia). In this article we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's article, finding choices of parameters providing periods of length $ 2^{1024} 1 $ and $ 2^{4096} 1 $. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition, and one multiplication by a constant.", acknowledgement = ack-nhfb, articleno = "30", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Laszlo:2016:MAB, author = "Endre L{\'a}szl{\'o} and Mike Giles and Jeremy Appleyard", title = "Manycore Algorithms for Batch Scalar and Block Tridiagonal Solvers", journal = j-TOMS, volume = "42", number = "4", pages = "31:1--31:36", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2830568", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2830568", acknowledgement = ack-nhfb, articleno = "31", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Prusa:2016:DWT, author = "Zden{\v{e}}k Pr{\ocirc{u}}sa and Peter L. S{\o}ndergaard and Pavel Rajmic", title = "Discrete Wavelet Transforms in the Large Time-Frequency Analysis Toolbox for {MATLAB\slash GNU Octave}", journal = j-TOMS, volume = "42", number = "4", pages = "32:1--32:23", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2839298", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2839298", acknowledgement = ack-nhfb, articleno = "32", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Escobar:2016:AES, author = "Marcos Escobar and Benedikt Rudolph and Rudi Zagst", title = "Algorithm 963: Estimation of Stochastic Covariance Models using a Continuum of Moment Conditions", journal = j-TOMS, volume = "42", number = "4", pages = "33:1--33:26", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2834115", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2834115", acknowledgement = ack-nhfb, articleno = "33", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lozano-Duran:2016:AEA, author = "Adri{\'a}n Lozano-Dur{\'a}n and Guillem Borrell", title = "Algorithm 964: An Efficient Algorithm to Compute the Genus of Discrete Surfaces and Applications to Turbulent Flows", journal = j-TOMS, volume = "42", number = "4", pages = "34:1--34:19", month = jul, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2845076", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:24 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2845076", acknowledgement = ack-nhfb, articleno = "34", journal-URL = "https://dl.acm.org/loi/toms", } @Article{delaCruz:2016:GTU, author = "Luis M. de la Cruz and Eduardo Ramos", title = "General Template Units for the Finite Volume Method in Box-Shaped Domains", journal = j-TOMS, volume = "43", number = "1", pages = "1:1--1:32", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2835175", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2835175", abstract = "In this work, we develop an extension of the Curiously Recurring Template Pattern (CRTP), which allows us to organize three related concepts in a class hierarchy. Generalizations, specializations and special procedures are the concepts that we use to define and implement several tools. We call these tools general template units because they are well-defined building blocks (units) for numerically solving partial differential equations (PDEs), are based on the use of templates of the C++ language, and can be applied in the solution of different kinds of problems. We focus on the solution of PDEs using the Finite Volume Method (FVM) in box-shaped domains. The three concepts just mentioned are intensively used to generate optimized codes for each case study. The convenience of our approach is highlighted in the numerical solutions of the examples of application, including laminar thermal convection, turbulent thermal convection, as well as a two-phase flow model in porous media, all of them in one, two, and three dimensions. The mathematical models of these examples were obtained using the axiomatic formulation, which provides generality, simplicity, and clarity to tackle any continuum mechanics application. The ideas explained in this work are quite simple but powerful in solving fluid dynamics problems, in which the conservativeness of the FVM is an important feature. The techniques developed in this work allow us to swap easily between numerical schemes for computing the coefficients obtained by applying the FVM.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Turcksin:2016:WDP, author = "Bruno Turcksin and Martin Kronbichler and Wolfgang Bangerth", title = "{WorkStream} -- A Design Pattern for Multicore-Enabled Finite Element Computations", journal = j-TOMS, volume = "43", number = "1", pages = "2:1--2:29", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2851488", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2851488", acknowledgement = ack-nhfb, articleno = "2", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kohler:2016:BLI, author = "Martin K{\"o}hler and Jens Saak", title = "On {BLAS} Level-3 Implementations of Common Solvers for (Quasi-) Triangular Generalized {Lyapunov} Equations", journal = j-TOMS, volume = "43", number = "1", pages = "3:1--3:23", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2850415", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2850415", acknowledgement = ack-nhfb, articleno = "3", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Garrett:2016:NAB, author = "C. Kristopher Garrett and Zhaojun Bai and Ren-Cang Li", title = "A Nonlinear {$ Q R $} Algorithm for Banded Nonlinear Eigenvalue Problems", journal = j-TOMS, volume = "43", number = "1", pages = "4:1--4:19", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2870628", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2870628", abstract = "A variation of Kublanovskaya's nonlinear QR method for solving banded nonlinear eigenvalue problems is presented in this article. The new method is iterative and specifically designed for problems too large to use dense linear algebra techniques. For the unstructurally banded nonlinear eigenvalue problem, a new data structure is used for storing the matrices to keep memory and computational costs low. In addition, an algorithm is presented for computing several nearby nonlinear eigenvalues to already-computed ones. Finally, numerical examples are given to show the efficacy of the new methods, and the source code has been made publicly available.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{vanderHoeven:2016:MSA, author = "Joris van der Hoeven and Gr{\'e}goire Lecerf and Guillaume Quintin", title = "Modular {SIMD} arithmetic in {Mathemagix}", journal = j-TOMS, volume = "43", number = "1", pages = "5:1--5:37", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2876503", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2876503", abstract = "Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer operations still require dedicated implementations. In this article, we survey existing algorithms for modular integer arithmetic and present detailed vectorized counterparts. We also describe several applications, such as fast modular Fourier transforms and multiplication of integer polynomials and matrices. The vectorized algorithms have been implemented in C++ inside the free computer algebra and analysis system Mathemagix. The performance of our implementation is illustrated by various benchmarks.", acknowledgement = ack-nhfb, articleno = "5", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sukkari:2016:HPQ, author = "Dalal Sukkari and Hatem Ltaief and David Keyes", title = "A High Performance {QDWH-SVD} Solver Using Hardware Accelerators", journal = j-TOMS, volume = "43", number = "1", pages = "6:1--6:25", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2894747", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2894747", acknowledgement = ack-nhfb, articleno = "6", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Filip:2016:RSI, author = "Silviu-Ioan Filip", title = "A Robust and Scalable Implementation of the {Parks--McClellan} Algorithm for Designing {FIR} Filters", journal = j-TOMS, volume = "43", number = "1", pages = "7:1--7:24", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2904902", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2904902", acknowledgement = ack-nhfb, articleno = "7", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ong:2016:ARM, author = "Benjamin W. Ong and Ronald D. Haynes and Kyle Ladd", title = "Algorithm 965: {RIDC} Methods: A Family of Parallel Time Integrators", journal = j-TOMS, volume = "43", number = "1", pages = "8:1--8:13", month = aug, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2964377", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2964377", acknowledgement = ack-nhfb, articleno = "8", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sluanschi:2016:AAD, author = "Emil I. Slu{\c{s}}anschi and Vlad Dumitrel", title = "{ADiJaC} --- Automatic Differentiation of {Java} Classfiles", journal = j-TOMS, volume = "43", number = "2", pages = "9:1--9:33", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2904901", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/java2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2904901", abstract = "This work presents the current design and implementation of ADiJaC, an automatic differentiation tool for Java classfiles. ADiJaC uses source transformation to generate derivative codes in both the forward and the reverse modes of automatic differentiation. We describe the overall architecture of the tool and present various details and examples for each of the two modes of differentiation. We emphasize the enhancements that have been made over previous versions of ADiJaC and illustrate their influence on the generality of the tool and on the performance of the generated derivative codes. The ADiJaC tool has been used to generate derivatives for a variety of problems, including real-world applications. We evaluate the performance of such codes and compare it to derivatives generated by Tapenade, a well-established automatic differentiation tool for Fortran and C/C++. Additionally, we present a more detailed performance analysis of a real-world application. Apart from being the only general-purpose automatic differentiation tool for Java bytecode, we argue that ADiJaC's features and performance are comparable to those of similar mature tools for other programming languages such as C/C++ or Fortran.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Yamazaki:2016:SPV, author = "Ichitaro Yamazaki and Stanimire Tomov and Jack Dongarra", title = "Stability and Performance of Various Singular Value {$ Q R $} Implementations on Multicore {CPU} with a {GPU}", journal = j-TOMS, volume = "43", number = "2", pages = "10:1--10:18", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2898347", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2898347", acknowledgement = ack-nhfb, articleno = "10", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rupp:2016:PIS, author = "Karl Rupp and Josef Weinbub and Ansgar J{\"u}ngel and Tibor Grasser", title = "Pipelined Iterative Solvers with Kernel Fusion for Graphics Processing Units", journal = j-TOMS, volume = "43", number = "2", pages = "11:1--11:27", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2907944", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2907944", acknowledgement = ack-nhfb, articleno = "11", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Low:2016:AME, author = "Tze Meng Low and Francisco D. Igual and Tyler M. Smith and Enrique S. Quintana-Orti", title = "Analytical Modeling Is Enough for High-Performance {BLIS}", journal = j-TOMS, volume = "43", number = "2", pages = "12:1--12:18", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2925987", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2925987", acknowledgement = ack-nhfb, articleno = "12", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Agullo:2016:IMS, author = "Emmanuel Agullo and Alfredo Buttari and Abdou Guermouche and Florent Lopez", title = "Implementing Multifrontal Sparse Solvers for Multicore Architectures with Sequential Task Flow Runtime Systems", journal = j-TOMS, volume = "43", number = "2", pages = "13:1--13:22", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2898348", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2898348", acknowledgement = ack-nhfb, articleno = "13", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lee:2016:TOI, author = "Mokwon Lee and Kokichi Sugihara and Deok-Soo Kim", title = "Topology-Oriented Incremental Algorithm for the Robust Construction of the {Voronoi} Diagrams of Disks", journal = j-TOMS, volume = "43", number = "2", pages = "14:1--14:23", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2939366", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2939366", acknowledgement = ack-nhfb, articleno = "14", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2016:NPP, author = "Nicholas Gould and Jennifer Scott", title = "A Note on Performance Profiles for Benchmarking Software", journal = j-TOMS, volume = "43", number = "2", pages = "15:1--15:5", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2950048", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2950048", acknowledgement = ack-nhfb, articleno = "15", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tozoni:2016:API, author = "Davi C. Tozoni and Pedro J. De Rezende and Cid C. {De Souza}", title = "{Algorithm 966}: A Practical Iterative Algorithm for the Art Gallery Problem Using Integer Linear Programming", journal = j-TOMS, volume = "43", number = "2", pages = "16:1--16:27", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2890491", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2890491", acknowledgement = ack-nhfb, articleno = "16", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Malhotra:2016:ADM, author = "Dhairya Malhotra and George Biros", title = "{Algorithm 967}: A Distributed-Memory Fast Multipole Method for Volume Potentials", journal = j-TOMS, volume = "43", number = "2", pages = "17:1--17:27", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2898349", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2898349", acknowledgement = ack-nhfb, articleno = "17", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Vallivaara:2016:SAS, author = "Ilari Vallivaara and Katja Poikselk{\"a} and Pauli Rikula and Juha R{\"o}ning", title = "Systematic Alias Sampling: An Efficient and Low-Variance Way to Sample from a Discrete Distribution", journal = j-TOMS, volume = "43", number = "3", pages = "18:1--18:17", month = nov, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2935745", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2935745", abstract = "In this article, we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution: drawing $k$ samples is up to an order of magnitude faster than binary search from the cumulative distribution function (cdf) or inversion methods used in many libraries. The produced empirical distribution function is evaluated using a modified Cram{\'e}r--von Mises goodness-of-fit statistic, showing that the method compares very favorably to multinomial sampling. As continuous distributions can often be approximated with discrete ones, the proposed method can be used as a very general way to efficiently produce random samples for particle filter proposal distributions, for example, for motion models in robotics.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meister:2016:PME, author = "Oliver Meister and Kaveh Rahnema and Michael Bader", title = "Parallel Memory-Efficient Adaptive Mesh Refinement on Structured Triangular Meshes with Billions of Grid Cells", journal = j-TOMS, volume = "43", number = "3", pages = "19:1--19:27", month = sep, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2947668", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2947668", abstract = "We present sam(oa) 2, a software package for a dynamically adaptive, parallel solution of 2D partial differential equations on triangular grids created via newest vertex bisection. An element order imposed by the Sierpinski space-filling curve provides an algorithm for grid generation, refinement, and traversal that is inherently memory efficient. Based purely on stack and stream data structures, it completely avoids random memory access. Using an element-oriented data view suitable for local operators, concrete simulation scenarios are implemented based on control loops and event hooks, which hide the complexity of the underlying traversal scheme. Two case studies are presented: two-phase flow in heterogeneous porous media and tsunami wave propagation, demonstrated on the Tohoku tsunami 2011 in Japan. sam(oa) 2 features hybrid MPI+OpenMP parallelization based on the Sierpinski order induced on the elements. Sections defined by contiguous grid cells define atomic tasks for OpenMP work sharing and stealing, as well as for migration of grid cells between MPI processes. Using optimized communication and load balancing algorithms, sam(oa) 2 achieves 88\% strong scaling efficiency from 16 to 512 cores and 92\% efficiency in a weak scaling test on 8,192 cores with 10 billion elements-all tests including adaptive mesh refinement and load balancing in each time step.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rump:2017:IPK, author = "Siegfried M. Rump", title = "{IEEE754} Precision-$k$ base-$ \beta $ Arithmetic Inherited by Precision-$m$ Base-$ \beta $ Arithmetic for $ k < m$", journal = j-TOMS, volume = "43", number = "3", pages = "20:1--20:15", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2785965", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2785965", abstract = "Suppose an $m$-digit floating-point arithmetic in base $ \beta \geq 2$ following the IEEE754 arithmetic standard is available. We show how a $k$-digit arithmetic with $ k < m$ can be inherited solely using $m$-digit operations. This includes the rounding into $k$ digits, the four basic operations and the square root, all for even or odd base $ \beta $. In particular, we characterize the relation between $k$ and $m$ so that no double rounding occurs when computing in $m$ digits and rounding the result into $k$ digits. We discuss rounding to nearest as well as directed rounding, and our approach covers exceptional values including signed zero. For binary arithmetic, a Matlab toolbox based on binary64 including $k$-bit scalar, vector and matrix operations as well as $k$-bit interval arithmetic is part of Version 8 of INTLAB, the Matlab toolbox for reliable computing.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jacquelin:2017:PDM, author = "Mathias Jacquelin and Lin Lin and Chao Yang", title = "{PSelInv} --- a Distributed Memory Parallel Algorithm for Selected Inversion: The Symmetric Case", journal = j-TOMS, volume = "43", number = "3", pages = "21:1--21:28", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2786977", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2786977", abstract = "We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call PSelInv. The PSelInv method computes selected elements of a general sparse matrix A that can be decomposed as A = LU, where L is lower triangular and U is upper triangular. The implementation described in this article focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization SuperLU\_DIST. However, the underlying data structure and design of PSelInv allows it to be easily combined with other factorization routines, such as PARDISO. We discuss general parallelization strategies such as data and task distribution schemes. In particular, we describe how to exploit the concurrency exposed by the elimination tree associated with the LU factorization of A. We demonstrate the efficiency and accuracy of PSelInv by presenting several numerical experiments. In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix. We also demonstrate how PSelInv can be used to accelerate large-scale electronic structure calculations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fortin:2017:GAG, author = "Pierre Fortin and Mourad Gouicem and Stef Graillat", title = "{GPU}-Accelerated Generation of Correctly Rounded Elementary Functions", journal = j-TOMS, volume = "43", number = "3", pages = "22:1--22:26", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2935746", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2935746", abstract = "The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires solving the Table Maker's Dilemma (TMD), which implies a huge amount of CPU computation time. In this article, we consider accelerating such computations, namely the Lef{\`e}vre algorithm on graphics processing units (GPUs), which are massively parallel architectures with a partial single instruction, multiple data execution. We first propose an analysis of the Lef{\`e}vre hard-to-round argument search using the concept of continued fractions. We then propose a new parallel search algorithm that is much more efficient on GPUs thanks to its more regular control flow. We also present an efficient hybrid CPU-GPU deployment of the generation of the polynomial approximations required in the Lef{\`e}vre algorithm. In the end, we manage to obtain overall speedups up to 53.4 $ \times $ on one GPU over a sequential CPU execution and up to 7.1 $ \times $ over a hex-core CPU, which enable a much faster solution of the TMD for the double-precision format.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Marin:2017:ERF, author = "Manuel Marin and David Defour and Federico Milano", title = "An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions", journal = j-TOMS, volume = "43", number = "3", pages = "23:1--23:22", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2939364", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2939364", abstract = "This article addresses the execution cost of arithmetic operations with a focus on fuzzy arithmetic. Thanks to an appropriate representation format for fuzzy intervals, we show that it is possible to halve the number of operations and divide by 2 to 8 the memory requirements compared to conventional solutions. In addition, we demonstrate the benefit of some hardware features encountered in today's accelerators (GPU) such as static rounding, memory usage, instruction-level parallelism (ILP), and thread-level parallelism (TLP). We then describe a library of fuzzy arithmetic operations written in CUDA and C++. The library is evaluated against traditional approaches using compute-bound and memory-bound benchmarks on Nvidia GPUs, with an observed performance gain of 2 to 20.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rathgeber:2017:FAF, author = "Florian Rathgeber and David A. Ham and Lawrence Mitchell and Michael Lange and Fabio Luporini and Andrew T. T. Mcrae and Gheorghe-Teodor Bercea and Graham R. Markall and Paul H. J. Kelly", title = "{Firedrake}: Automating the Finite Element Method by Composing Abstractions", journal = j-TOMS, volume = "43", number = "3", pages = "24:1--24:27", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2998441", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2998441", abstract = "Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only implementation centered on the composition of several existing and new abstractions for particular aspects of scientific computing. The result is a more complete separation of concerns that eases the incorporation of separate contributions from computer scientists, numerical analysts, and application specialists. These contributions may add functionality or improve performance. Firedrake benefits from automatically applying new optimizations. This includes factorizing mixed function spaces, transforming and vectorizing inner loops, and intrinsically supporting block matrix operations. Importantly, Firedrake presents a simple public API for escaping the UFL abstraction. This allows users to implement common operations that fall outside of pure variational formulations, such as flux limiters.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Calvo:2017:ADM, author = "Manuel Calvo and Juan I. Montijano and Luis R{\'a}ndez", title = "Algorithm 968: {DISODE45}: A {Matlab} {Runge--Kutta} Solver for Piecewise Smooth {IVPs} of {Filippov} Type", journal = j-TOMS, volume = "43", number = "3", pages = "25:1--25:14", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2907054", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=2907054", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gil:2016:ACI, author = "Amparo Gil and Diego Ruiz-Antol{\'\i}n and Javier Segura and Nico M. Temme", title = "{Algorithm 969}: Computation of the Incomplete Gamma Function for Negative Values of the Argument", journal = j-TOMS, volume = "43", number = "3", pages = "26:1--26:9", month = nov, year = "2016", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2972951", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Nov 22 17:45:25 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=2972951", abstract = "An algorithm for computing the incomplete gamma function $ \gamma^(a, z) $ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar{\'e}-type expansions, uniform asymptotic expansions, and recurrence relations, depending on the parameter region. A relative accuracy $ \approx 10^{-13}$ in the parameter region $ (a, z) \in [500, 500] \times [500, 0)$ can be obtained when computing the function $ \gamma^\ast (a, z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sys:2017:AON, author = "Marek S{\'y}s and Zden{\k{e}}k {\v{R}}{\'\i}ha and Vashek Maty{\'a}{\v{s}}", title = "{Algorithm 970}: Optimizing the {NIST Statistical Test Suite} and the {Berlekamp--Massey} Algorithm", journal = j-TOMS, volume = "43", number = "3", pages = "27:1--27:11", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2988228", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:52:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The NIST Statistical Test Suite (NIST STS) is one of the most popular tools for the analysis of randomness. This test battery is widely used, but its implementation is quite inefficient. A complete randomness analysis using the NIST STS can take hours on a standard computer when the tested data volume is on the order of GB. We improved the most time-consuming test (Linear Complexity) from the previous most efficient implementation of the NIST STS. We also optimized other tests and achieved an overall speedup of $ 50.6 \times $ compared with the reference implementation. This means that 20MB of data can be tested within a minute using our new optimized version of the NIST STS. To speed up the Linear Complexity test, we proposed a new version of the Berlekamp--Massey algorithm that computes only the linear complexity of a sequence. This new variant does not construct a linear feedback shift register and is approximately $ 187 \times $ faster than the original NIST implementation of the Berlekamp--Massey algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2017:AIR, author = "Huamin Li and George C. Linderman and Arthur Szlam and Kelly P. Stanton and Yuval Kluger and Mark Tygert", title = "{Algorithm 971}: an Implementation of a Randomized Algorithm for Principal Component Analysis", journal = j-TOMS, volume = "43", number = "3", pages = "28:1--28:14", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3004053", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:52:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Perez:2017:AJI, author = "Juan F. P{\'e}rez and Daniel F. Silva and Julio C. G{\'o}ez and Andr{\'e}s Sarmiento and Andr{\'e}s Sarmiento-Romero and Raha Akhavan-Tabatabaei and Germ{\'a}n Ria{\~n}o", title = "{Algorithm 972}: {jMarkov}: an Integrated Framework for {Markov} Chain Modeling", journal = j-TOMS, volume = "43", number = "3", pages = "29:1--29:22", month = jan, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3009968", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:52:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Markov chains (MC) are a powerful tool for modeling complex stochastic systems. Whereas a number of tools exist for solving different types of MC models, the first step in MC modeling is to define the model parameters. This step is, however, error prone and far from trivial when modeling complex systems. In this article, we introduce jMarkov, a framework for MC modeling that provides the user with the ability to define MC models from the basic rules underlying the system dynamics. From these rules, jMarkov automatically obtains the MC parameters and solves the model to determine steady-state and transient performance measures. The jMarkov framework is composed of four modules: (i) the main module supports MC models with a finite state space; (ii) the jQBD module enables the modeling of Quasi-Birth-and-Death processes, a class of MCs with infinite state space; (iii) the jMDP module offers the capabilities to determine optimal decision rules based on Markov Decision Processes; and (iv) the jPhase module supports the manipulation and inclusion of phase-type variables to represent more general behaviors than that of the standard exponential distribution. In addition, jMarkov is highly extensible, allowing the users to introduce new modeling abstractions and solvers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Filippone:2017:SMV, author = "Salvatore Filippone and Valeria Cardellini and Davide Barbieri and Alessandro Fanfarillo", title = "Sparse Matrix-Vector Multiplication on {GPGPUs}", journal = j-TOMS, volume = "43", number = "4", pages = "30:1--30:49", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3017994", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The multiplication of a sparse matrix by a dense vector (SpMV) is a centerpiece of scientific computing applications: it is the essential kernel for the solution of sparse linear systems and sparse eigenvalue problems by iterative methods. The efficient implementation of the sparse matrix-vector multiplication is therefore crucial and has been the subject of an immense amount of research, with interest renewed with every major new trend in high-performance computing architectures. The introduction of General-Purpose Graphics Processing Units (GPGPUs) is no exception, and many articles have been devoted to this problem. With this article, we provide a review of the techniques for implementing the SpMV kernel on GPGPUs that have appeared in the literature of the last few years. We discuss the issues and tradeoffs that have been encountered by the various researchers, and a list of solutions, organized in categories according to common features. We also provide a performance comparison across different GPGPU models and on a set of test matrices coming from various application domains.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Torun:2017:PMN, author = "F. Sukru Torun and Murat Manguoglu and Cevdet Aykanat", title = "Parallel Minimum Norm Solution of Sparse Block Diagonal Column Overlapped Underdetermined Systems", journal = j-TOMS, volume = "43", number = "4", pages = "31:1--31:21", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3004280", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krislock:2017:BSB, author = "Nathan Krislock and J{\'e}r{\^o}me Malick and Fr{\'e}d{\'e}ric Roupin", title = "{BiqCrunch}: a Semidefinite Branch-and-Bound Method for Solving Binary Quadratic Problems", journal = j-TOMS, volume = "43", number = "4", pages = "32:1--32:23", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3005345", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article presents BiqCrunch, an exact solver for binary quadratic optimization problems. BiqCrunch is a branch-and-bound method that uses an original, efficient semidefinite-optimization-based bounding procedure. It has been successfully tested on a variety of well-known combinatorial optimization problems, such as Max-Cut, Max- k -Cluster, and Max-Independent-Set. The code is publicly available online; a web interface and many conversion tools are also provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aurentz:2017:CCS, author = "Jared L. Aurentz and Lloyd N. Trefethen", title = "Chopping a {Chebyshev} Series", journal = j-TOMS, volume = "43", number = "4", pages = "33:1--33:21", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/2998442", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function $ f(x) $ defined on an interval $ [a, b] $ is ``rounded'' to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem. We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after many years of discussion and the considerations that led to this design.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Magron:2017:CRE, author = "Victor Magron and George Constantinides and Alastair Donaldson", title = "Certified Roundoff Error Bounds Using Semidefinite Programming", journal = j-TOMS, volume = "43", number = "4", pages = "34:1--34:31", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3015465", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely linear operations as non-linearities are inherent to many interesting computational problems in real-world applications. Existing solutions to reasoning possibly lead to either inaccurate bounds or high analysis time in the presence of nonlinear correlations between variables. Furthermore, while it is easy to implement a straightforward method such as interval arithmetic, sophisticated techniques are less straightforward to implement in a formal setting. Thus there is a need for methods that output certificates that can be formally validated inside a proof assistant. We present a framework to provide upper bounds on absolute roundoff errors of floating-point nonlinear programs. This framework is based on optimization techniques employing semidefinite programming and sums of squares certificates, which can be checked inside the Coq theorem prover to provide formal roundoff error bounds for polynomial programs. Our tool covers a wide range of nonlinear programs, including polynomials and transcendental operations as well as conditional statements. We illustrate the efficiency and precision of this tool on non-trivial programs coming from biology, optimization, and space control. Our tool produces more accurate error bounds for 23\% of all programs and yields better performance in 66\% of all programs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Huckelheim:2017:ADC, author = "Jan Christian H{\"u}ckelheim and Laurent Hasco{\"e}t and Jens-Dominik M{\"u}ller", title = "Algorithmic Differentiation of Code with Multiple Context-Specific Activities", journal = j-TOMS, volume = "43", number = "4", pages = "35:1--35:21", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3015464", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Algorithmic differentiation (AD) by source-transformation is an established method for computing derivatives of computational algorithms. Static dataflow analysis is commonly used by AD tools to determine the set of active variables, that is, variables that are influenced by the program input in a differentiable way and have a differentiable influence on the program output. In this work, a context-sensitive static analysis combined with procedure cloning is used to generate specialised versions of differentiated procedures for each call site. This enables better detection and elimination of unused computations and memory storage, resulting in performance improvements of the generated code, in both forward- and reverse-mode AD. The implications of this multi-activity AD approach on the static analysis of an AD tool is shown using dataflow equations. The worst-case cost of multi-activity AD on the differentiation process is analysed and practical remedies to avoid running into this worst case are presented. The method was implemented in the AD tool Tapenade, and we present its application to a 3D unstructured compressible flow solver, for which we generate an adjoint solver that performs significantly faster when multi-activity AD is used.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gould:2017:SAP, author = "Nicholas Gould and Jennifer Scott", title = "The State-of-the-Art of Preconditioners for Sparse Linear Least-Squares Problems", journal = j-TOMS, volume = "43", number = "4", pages = "36:1--36:35", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3014057", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In recent years, a variety of preconditioners have been proposed for use in solving large sparse linear least-squares problems. These include simple diagonal preconditioning, preconditioners based on incomplete factorizations, and stationary inner iterations used with Krylov subspace methods. In this study, we briefly review preconditioners for which software has been made available, then present a numerical evaluation of them using performance profiles and a large set of problems arising from practical applications. Comparisons are made with state-of-the-art sparse direct methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Deckers:2017:AER, author = "Karl Deckers and Ahlem Mougaida and H{\'e}di Belhadjsalah", title = "{Algorithm 973}: Extended Rational {Fej{\'e}r} Quadrature Rules Based on {Chebyshev} Orthogonal Rational Functions", journal = j-TOMS, volume = "43", number = "4", pages = "37:1--37:29", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054077", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a numerical procedure to approximate integrals of the form $ \int^b_a f(x) \, d x $, where $f$ is a function with singularities close to, but outside the interval $ [a, b]$, with $ - \infty \leq a < b \leq + \infty $. The algorithm is based on rational interpolatory Fej{\'e}r quadrature rules, together with a sequence of real and/or complex conjugate poles that are given in advance. Since for n fixed in advance, the accuracy of the computed nodes and weights in the n point rational quadrature formula strongly depends on the given sequence of poles, we propose a small number of iterations over the number of points in the rational quadrature rule, limited by the value $n$ (instead of fixing the number of points in advance) in order to obtain the best approximation among the first $n$. The proposed algorithm is implemented as a Matlab program.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Novoselsky:2017:AOM, author = "Alexander Novoselsky and Eugene Kagan", title = "{Algorithm 974}: The {OutlierLib} --- a {MATLAB} Library for Outliers' Detection", journal = j-TOMS, volume = "43", number = "4", pages = "38:1--38:3", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054078", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The article presents a library of MATLAB functions that implement the widely used algorithms of outlier detection. The library includes the outlier tests for univariate and multivariate data sets with an approximately normal distribution. The software library is accompanied by a brief review of the methods for detecting and treating outliers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Krogh:2017:RAF, author = "Fred T. Krogh and Richard J. Hanson and Philip W. Sharp", title = "Remark on {Algorithm 936: a Fortran Message Processor}", journal = j-TOMS, volume = "43", number = "4", pages = "39:1--39:1", month = mar, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3004279", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 24 08:51:05 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Krogh:2014:AFM}.", abstract = "The Fortran output routine messy enables debugging and error message processing strategies in the design of numerical and mathematical software. It supports separate output from different processes in a parallel computing environment.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Greif:2017:SII, author = "Chen Greif and Shiwen He and Paul Liu", title = "{SYM-ILDL}: Incomplete {$ L D L^T $} Factorization of Symmetric Indefinite and Skew-Symmetric Matrices", journal = j-TOMS, volume = "44", number = "1", pages = "1:1--1:21", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054948", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "SYM-ILDL is a numerical software package that computes incomplete LDL$^T$ (ILDL) factorizations of symmetric indefinite and real skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by Li and Saad [2005]. Our code is economical in terms of storage, and it deals with real skew-symmetric matrices as well as symmetric ones. The package is written in C++ and is templated, is open source, and includes a Matlab interface. The code includes built-in RCM and AMD reordering, two equilibration strategies, threshold Bunch-Kaufman pivoting, and rook pivoting, as well as a wrapper to MC64, a popular matching-based equilibration and reordering algorithm. We also include two built-in iterative solvers: SQMR, preconditioned with ILDL, and MINRES, preconditioned with a symmetric positive definite preconditioner based on the ILDL factorization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reps:2017:CAG, author = "Bram Reps and Tobias Weinzierl", title = "Complex Additive Geometric Multilevel Solvers for {Helmholtz} Equations on Spacetrees", journal = j-TOMS, volume = "44", number = "1", pages = "2:1--2:36", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054946", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce a family of implementations of low-order, additive, geometric multilevel solvers for systems of Helmholtz equations arising from Schr{\o}dinger equations. Both grid spacing and arithmetics may comprise complex numbers, and we thus can apply complex scaling to the indefinite Helmholtz operator. Our implementations are based on the notion of a spacetree and work exclusively with a finite number of precomputed local element matrices. They are globally matrix-free. Combining various relaxation factors with two grid transfer operators allows us to switch from additive multigrid over a hierarchical basis method into a Bramble-Pasciak-Xu (BPX)-type solver, with several multiscale smoothing variants within one code base. Pipelining allows us to realize full approximation storage (FAS) within the additive environment where, amortized, each grid vertex carrying degrees of freedom is read/written only once per iteration. The codes realize a single-touch policy. Among the features facilitated by matrix-free FAS is arbitrary dynamic mesh refinement (AMR) for all solver variants. AMR as an enabler for full multigrid (FMG) cycling the grid unfolds throughout the computation allows us to reduce the cost per unknown. The present work primary contributes toward software realization and design questions. Our experiments show that the consolidation of single-touch FAS, dynamic AMR, and vectorization-friendly, complex scaled, matrix-free FMG cycles delivers a mature implementation blueprint for solvers of Helmholtz equations in general. For this blueprint, we put particular emphasis on a strict implementation formalism as well as some implementation correctness proofs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Luporini:2017:AOF, author = "Fabio Luporini and David A. Ham and Paul H. J. Kelly", title = "An Algorithm for the Optimization of Finite Element Integration Loops", journal = j-TOMS, volume = "44", number = "1", pages = "3:1--3:26", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054944", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present an algorithm for the optimization of a class of finite-element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite-element operators, is proven to achieve a locally optimal operation count. In specified circumstances the optimum achieved is global. Extensive numerical experiments demonstrate significant performance improvements over the state of the art in finite-element code generation in almost all cases. This validates the effectiveness of the algorithm presented here and illustrates its limitations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boldo:2017:RFA, author = "Sylvie Boldo and Stef Graillat and Jean-Michel Muller", title = "On the Robustness of the {2Sum} and {Fast2Sum} Algorithms", journal = j-TOMS, volume = "44", number = "1", pages = "4:1--4:14", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054947", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The 2Sum and Fast2Sum algorithms are important building blocks in numerical computing. They are used (implicitly or explicitly) in many compensated algorithms (such as compensated summation or compensated polynomial evaluation). They are also used for manipulating floating-point expansions. We show that these algorithms are much more robust than it is usually believed: The returned result makes sense even when the rounding function is not round-to-nearest, and they are almost immune to overflow.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Agelek:2017:OEU, author = "Rainer Agelek and Michael Anderson and Wolfgang Bangerth and William L. Barth", title = "On Orienting Edges of Unstructured Two- and Three-Dimensional Meshes", journal = j-TOMS, volume = "44", number = "1", pages = "5:1--5:22", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3061708", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3061708", abstract = "Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each edge relates to that of neighboring cells. However, we can simplify data structures and algorithms if we can a priori orient coordinate systems in such a way that the coordinate systems on the edges follow uniquely from those on the cells by rule. Such rules require that every unstructured mesh allow the assignment of directions to edges that satisfy the convention in adjacent cells. We show that the convention chosen for unstructured quadrilateral meshes in the deal.II library always allows to orient meshes. It can therefore be used to make codes simpler, faster, and less bug prone. We present an algorithm that orients meshes in $ O(N) $ operations. We then show that consistent orientations are not always possible for 3D hexahedral meshes. Thus, cells generally need to store the direction of adjacent edges, but our approach also allows the characterization of cases where this is not necessary. The 3D extension of our algorithm either orients edges consistently, or aborts, both within $ O(N) $ steps.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Porcelli:2017:BTD, author = "Margherita Porcelli and Philippe L. Toint", title = "{BFO}, A Trainable Derivative-free Brute Force Optimizer for Nonlinear Bound-constrained Optimization and Equilibrium Computations with Continuous and Discrete Variables", journal = j-TOMS, volume = "44", number = "1", pages = "6:1--6:25", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3085592", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favorably with that of NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search), a well-known derivative-free optimization package. It is also applicable to multilevel equilibrium- or constrained-type problems. Its easy-to-use interface provides a number of user-oriented features, such as checkpointing and restart, variable scaling, and early termination tools.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanZee:2017:IHP, author = "Field G. {Van Zee} and Tyler M. Smith", title = "Implementing High-performance Complex Matrix Multiplication via the 3m and 4m Methods", journal = j-TOMS, volume = "44", number = "1", pages = "7:1--7:36", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3086466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Oct 4 10:55:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3086466", abstract = "In this article, we explore the implementation of complex matrix multiplication. We begin by briefly identifying various challenges associated with the conventional approach, which calls for a carefully written kernel that implements complex arithmetic at the lowest possible level (i.e., assembly language). We then set out to develop a method of complex matrix multiplication that avoids the need for complex kernels altogether. This constraint promotes code reuse and portability within libraries such as Basic Linear Algebra Subprograms and BLAS-Like Library Instantiation Software (BLIS) and allows kernel developers to focus their efforts on fewer and simpler kernels. We develop two alternative approaches --- one based on the 3m method and one that reflects the classic 4m formulation --- each with multiple variants, all of which rely only on real matrix multiplication kernels. We discuss the performance characteristics of these ``induced'' methods and observe that the assembly-level method actually resides along the 4m spectrum of algorithmic variants. Implementations are developed within the BLIS framework, and testing on modern hardware confirms that while the less numerically stable 3m method yields the fastest runtimes, the more stable (and thus widely applicable) 4m method's performance is somewhat limited due to implementation challenges that appear inherent in nature.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Szo:2017:PET, author = "M{\'a}t{\'e} Sz{\H{o}}ke and Tam{\'a}s Istv{\'a}n J{\'o}zsa and {\'A}d{\'a}m Kolesz{\'a}r and Irene Moulitsas and L{\'a}szl{\'o} K{\"o}n{\"o}zsy", title = "Performance Evaluation of a Two-Dimensional Lattice {Boltzmann} Solver Using {CUDA} and {PGAS UPC} Based Parallelisation", journal = j-TOMS, volume = "44", number = "1", pages = "8:1--8:22", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3085590", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3085590", abstract = "The Unified Parallel C (UPC) language from the Partitioned Global Address Space (PGAS) family unifies the advantages of shared and local memory spaces and offers a relatively straightforward code parallelisation with the Central Processing Unit (CPU). In contrast, the Computer Unified Device Architecture (CUDA) development kit gives a tool to make use of the Graphics Processing Unit (GPU). We provide a detailed comparison between these novel techniques through the parallelisation of a two-dimensional lattice Boltzmann method based fluid flow solver. Our comparison between the CUDA and UPC parallelisation takes into account the required conceptual effort, the performance gain, and the limitations of the approaches from the application oriented developers' point of view. We demonstrated that UPC led to competitive efficiency with the local memory implementation. However, the performance of the shared memory code fell behind our expectations, and we concluded that the investigated UPC compilers could not efficiently treat the shared memory space. The CUDA implementation proved to be more complex compared to the UPC approach mainly because of the complicated memory structure of the graphics card which also makes GPUs suitable for the parallelisation of the lattice Boltzmann method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ganesh:2017:ATM, author = "M. Ganesh and S. C. Hawkins", title = "Algorithm 975: {TMATROM} -- A {$T$}-Matrix Reduced Order Model Software", journal = j-TOMS, volume = "44", number = "1", pages = "9:1--9:18", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3054945", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The T-matrix (TMAT) of a scatterer fully describes the way the scatterer interacts with incident fields and scatters waves, and is therefore used extensively in several science and engineering applications. The T-matrix is independent of several input parameters in a wave propagation model and hence the offline computation of the T-matrix provides an efficient reduced order model (ROM) framework for performing online scattering simulations for various choices of the input parameters. The authors developed and mathematically analyzed a numerically stable formulation for computing the T-matrix (J. Comput. Appl. Math. 234 (2010), 1702--1709). The TMATROM software package provides an object-oriented implementation of the numerically stable formulation and can be used in conjunction with the user's preferred forward solver for the two-dimensional Helmholtz model. We compare TMATROM with standard methods to compute the T-matrix for a range of two-dimensional test scatterers with large aspect ratios and acoustic sizes. Our numerical results demonstrate the robust numerical stability of the TMATROM implementation, even with scatterers for which the standard methods are numerically unstable. The efficiency and flexibility of the TMATROM software package to handle a wide range of two-dimensional scatterers with various shapes and material properties are also demonstrated.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brake:2017:ABN, author = "Daniel A. Brake and Daniel J. Bates and Wenrui Hao and Jonathan D. Hauenstein and Andrew J. Sommese and Charles W. Wampler", title = "Algorithm 976: {Bertini\_real}: Numerical Decomposition of Real Algebraic Curves and Surfaces", journal = j-TOMS, volume = "44", number = "1", pages = "10:1--10:30", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3056528", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Bertini\_real is a compiled command line program for numerically decomposing the real portion of a positive-dimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. The implemented decomposition algorithms are similar to the well-known cylindrical algebraic decomposition (CAD) first established by Collins in that they produce a set of connected cells. In contrast to the CAD, Bertini\_real produces cells with midpoints connected to boundary points by homotopies, which can easily be numerically tracked. Furthermore, the implemented decomposition for surfaces naturally yields a triangulation. This CAD-like decomposition captures the topological information and permits further computation on the real sets, such as sampling, visualization, and three-dimensional printing.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drmac:2017:AQP, author = "Zlatko Drma{\v{c}}", title = "Algorithm 977: a {$ Q R $}-Preconditioned {$ Q R $ SVD} Method for Computing the {SVD} with High Accuracy", journal = j-TOMS, volume = "44", number = "1", pages = "11:1--11:30", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3061709", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jul 14 16:39:28 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A new software for computing the singular value decomposition (SVD) of real or complex matrices is proposed. The method implemented in the code xGESVDQ is essentially the $ Q R $ SVD algorithm available as xGESVD in LAPACK. The novelty is an extra step, the $ Q R $ factorization with column (or complete row and column) pivoting, also already available in LAPACK as xGEQP3. For experts in matrix computations, the combination of the $ Q R $ factorization and an SVD computation routine is not new. However, what seems to be new and important for applications is that the resulting procedure is numerically superior to xGESVD and that it is capable of reaching the accuracy of the Jacobi SVD. Further, when combined with pivoted Cholesky factorization, xGESVDQ provides numerically accurate and fast solvers (designated as xPHEVC, xPSEVC) for the Hermitian positive definite eigenvalue problem. For instance, using accurately computed Cholesky factor, xPSEVC computes all eigenvalues of the $ 200 \times 200 $ Hilbert matrix (whose spectral condition number is greater that $ 10^{300}$) to nearly full machine precision. Furthermore, xGESVDQ can be used for accurate spectral decomposition of general (indefinite) Hermitian matrices.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anderson:2017:ASS, author = "Edward Anderson", title = "{Algorithm 978}: Safe Scaling in the {Level 1 BLAS}", journal = j-TOMS, volume = "44", number = "1", pages = "12:1--12:28", month = jul, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3061665", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:21:07 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3061665", abstract = "The square root of a sum of squares is well known to be prone to overflow and underflow. Ad hoc scaling of intermediate results, as has been done in numerical software such as the BLAS and LAPACK, mostly avoids the problem, but it can still occur at extreme values in the range of representable numbers. More careful scaling, as has been implemented in recent versions of the standard algorithms, may come at the expense of performance or clarity. This work reimplements the vector 2-norm and the generation of Givens rotations from the Level 1 BLAS to improve their performance and design. In addition, support for negative increments is extended to the Level 1 BLAS operations on a single vector, and a comprehensive test suite for all the Level 1 BLAS is included.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hogg:2017:NAO, author = "Jonathan Hogg and Jennifer Scott and Sue Thorne", title = "Numerically Aware Orderings for Sparse Symmetric Indefinite Linear Systems", journal = j-TOMS, volume = "44", number = "2", pages = "13:1--13:22", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3104991", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3104991", abstract = "Sparse symmetric indefinite problems arise in a large number of important application areas; they are often solved through the use of an LDL T factorization via a sparse direct solver. While for many problems prescaling the system matrix A is sufficient to maintain stability of the factorization, for a small but important fraction of problems numerical pivoting is required. Pivoting often incurs a significant overhead, and consequently, a number of techniques have been proposed to try and limit the need for pivoting. In particular, numerically aware ordering algorithms may be used, that is, orderings that depend not only on the sparsity pattern of A but also on the values of its (scaled) entries. Current approaches identify large entries of A and symmetrically permute them onto the subdiagonal, where they can be used as part of a 2 $ \times $ 2 pivot. This is numerically effective, but the fill in the factor L and hence the runtime of the factorization and subsequent triangular solves may be significantly increased over a standard ordering if no pivoting is required. We present a new algorithm that combines a matching-based approach with a numerically aware nested dissection ordering. Numerical comparisons with current approaches for some tough symmetric indefinite problems are given.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Engwer:2017:GRI, author = "Christian Engwer and Andreas N{\"u}{\ss}ing", title = "Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees", journal = j-TOMS, volume = "44", number = "2", pages = "14:1--14:20", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3104989", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3104989", abstract = "Implicitly described domains are a well-established tool in the simulation of time-dependent problems, for example, using level-set methods. To solve partial differential equations on such domains, a range of numerical methods was developed, for example, the Immersed Boundary method, the Unfitted Finite Element or Unfitted Discontinuous Galerkin methods, and the eXtended or Generalised Finite Element methods, just to name a few. Many of these methods involve integration over cut-cells or their boundaries, as they are described by sub-domains of the original level-set mesh. We present a new algorithm to geometrically evaluate the integrals over domains described by a first-order, conforming level-set function. The integration is based on a polyhedral reconstruction of the implicit geometry, following the concepts of the marching cubes algorithm. The algorithm preserves various topological properties of the implicit geometry in its polyhedral reconstruction, making it suitable for Finite Element computations. Numerical experiments show second-order accuracy of the integration. An implementation of the algorithm is available as free software, which allows for an easy incorporation into other projects. The software is in productive use within the DUNE framework (Bastian et al. 2008a).", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Springer:2017:THP, author = "Paul Springer and Jeff R. Hammond and Paolo Bientinesi", title = "{TTC}: A High-Performance Compiler for Tensor Transpositions", journal = j-TOMS, volume = "44", number = "2", pages = "15:1--15:21", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3104988", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3104988", abstract = "We present Tensor Transpose Compiler (TTC), an open-source parallel compiler for multidimensional tensor transpositions. To generate high-performance C++ code, TTC explores a number of optimizations, including software prefetching, blocking, loop-reordering, and explicit vectorization. To evaluate the performance of multidimensional transpositions across a range of possible use-cases, we also release a benchmark covering arbitrary transpositions of up to six dimensions. Performance results show that the routines generated by TTC achieve close to peak memory bandwidth on both the Intel Haswell and the AMD Steamroller architectures and yield significant performance gains over modern compilers. By implementing a set of pruning heuristics, TTC allows users to limit the number of potential solutions; this option is especially useful when dealing with high-dimensional tensors, as the search space might become prohibitively large. Experiments indicate that when only 100 potential solutions are considered, the resulting performance is about 99\% of that achieved with exhaustive search.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Joldes:2017:TRE, author = "Mioara Joldes and Jean-Michel Muller and Valentina Popescu", title = "Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic", journal = j-TOMS, volume = "44", number = "2", pages = "15res:1--15res:27", month = oct, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3121432", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Oct 10 17:52:02 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3121432", abstract = "We analyze several classical basic building blocks of double-word arithmetic (frequently called ``double-double arithmetic'' in the literature): the addition of a double-word number and a floating-point number, the addition of two double-word numbers, the multiplication of a double-word number by a floating-point number, the multiplication of two double-word numbers, the division of a double-word number by a floating-point number, and the division of two double-word numbers. For multiplication and division we get better relative error bounds than the ones previously published. For addition of two double-word numbers, we show that the previously published bound was incorrect, and we provide a new relative error bound. We introduce new algorithms for division. We also give examples that illustrate the tightness of our bounds.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15res", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", remark = "This article is erroneously assigned the same article number as the preceding one!", } @Article{Peise:2017:ARA, author = "Elmar Peise and Paolo Bientinesi", title = "{Algorithm 979}: Recursive Algorithms for Dense Linear Algebra --- The {ReLAPACK} Collection", journal = j-TOMS, volume = "44", number = "2", pages = "16:1--16:19", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3061664", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3061664", abstract = "To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries, such as linear algebra package (LAPACK), commonly implement operations as blocked algorithms. However, to achieve near-optimal performance with such algorithms, significant tuning is required. In contrast, recursive algorithms are virtually tuning free and attain similar performance. In this article, we first analyze and compare blocked and recursive algorithms in terms of performance and then introduce recursive LAPACK (ReLAPACK), an open-source library of recursive algorithms to seamlessly replace many of LAPACK's blocked algorithms. In most scenarios, ReLAPACK outperforms reference LAPACK and in many situations improves upon the performance of optimized libraries.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Yeralan:2017:ASQ, author = "Sencer Nuri Yeralan and Timothy A. Davis and Wissam M. Sid-Lakhdar and Sanjay Ranka", title = "{Algorithm 980}: Sparse {$ Q R $} Factorization on the {GPU}", journal = j-TOMS, volume = "44", number = "2", pages = "17:1--17:29", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3065870", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3065870", abstract = "Sparse matrix factorization involves a mix of regular and irregular computation, which is a particular challenge when trying to obtain high-performance on the highly parallel general-purpose computing cores available on graphics processing units (GPUs). We present a sparse multifrontal $ Q R $ factorization method that meets this challenge and is significantly faster than a highly optimized method on a multicore CPU. Our method factorizes many frontal matrices in parallel and keeps all the data transmitted between frontal matrices on the GPU. A novel bucket scheduler algorithm extends the communication-avoiding $ Q R $ factorization for dense matrices by exploiting more parallelism and by exploiting the staircase form present in the frontal matrices of a sparse multifrontal method.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rizzardi:2017:ATS, author = "Mariarosaria Rizzardi", title = "{Algorithm 981}: {Talbot Suite DE}: Application of Modified {Talbot}'s Method to Solve Differential Problems", journal = j-TOMS, volume = "44", number = "2", pages = "18:1--18:23", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3089248", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3089248", abstract = "In order to solve a differential problem, the Laplace Transform method, when applicable, replaces the problem with a simpler one; the solution is obtained by solving the new problem and then by computing the inverse Laplace Transform of this function. In a numerical context, since the solution of the transformed problem consists of a sequence of Laplace Transform samples, most of the software for the numerical inversion cannot be used since the transform, among parameters, must be passed as a function. To fill this gap, we present Talbot Suite DE, a C software collection for Laplace Transform inversions, specifically designed for these problems and based on Talbot's method. It contains both sequential and parallel implementations; the latter is accomplished by means of OpenMP. We also report some performance results. Aimed at non-expert users, the software is equipped with several examples and a User Guide that includes the external documentation, explains how to use all the sample code, and reports its results about accuracy and efficiency. Some examples are entirely in C and others combine different programming languages (C/MATLAB, C/FORTRAN). The User Guide also contains useful hints to avoid possible errors issued during the compilation or execution of mixed-language code.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Snyder:2017:AES, author = "W. Van Snyder", title = "{Algorithm 982}: Explicit Solutions of Triangular Systems of First-Order Linear Initial-Value Ordinary Differential Equations with Constant Coefficients", journal = j-TOMS, volume = "44", number = "2", pages = "19:1--19:4", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3092892", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3092892", abstract = "A method to compute explicit solutions of homogeneous triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients is described. It is suitable for the limited case of well separated eigenvalues, or for multiple zero eigenvalues provided the entire column corresponding to a zero eigenvalue is zero. The solution for the case of constant inhomogeneity is described. The method requires only the computation of a constant matrix using a simple recurrence. Computing the solutions of the system from that matrix, for values of the independent variable, requires one to exponentiate only the diagonal of a matrix. It is not necessary to compute the exponential of a general triangular matrix. Although this work was motivated by a study of nuclear decay without fission or neutron absorption, which is used throughout as an example, it has wider applicability.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fahmy:2017:AFC, author = "Thierry Fahmy and Arnaud Bell{\'e}toile", title = "{Algorithm 983}: Fast Computation of the Non-Asymptotic {Cochran}'s {$Q$} Statistic for Heterogeneity Detection", journal = j-TOMS, volume = "44", number = "2", pages = "20:1--20:12", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3095076", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3095076", abstract = "The detection of heterogeneity among objects (products, treatments, medical studies) assessed on a series of blocks (consumers, patients, methods, pathologists) is critical in numerous areas such as clinical research, cosmetic studies, or survey analysis. The Cochran's $Q$ test is the most widely used test for identifying heterogeneity on binary data (success vs. failure, cure vs. not cure, 1 vs. 0, etc.). For a large number of blocks, the $Q$ distribution can be approximated by a $ \chi^2$ distribution. Unfortunately, this does not hold for limited sample sizes or sparse tables. In such situations, one has to either run Monte Carlo simulations or compute the exact $Q$ distribution to obtain an accurate and reliable result. However, the latter method is often disregarded in favor of the former due to computational expense considerations. The purpose of this article is to propose an extremely fast implementation of the exact Cochran's $Q$ test so one can benefit from its accuracy at virtually no cost regarding computation time. It is implemented as a part of the XLSTAT statistical software (Addinsoft 2015). After a short presentation of the Cochran's $Q$ test and the motivation for its exact version, we detail our approach and present its actual implementation. We then demonstrate the gain of this algorithm with performance evaluations and measurements. Comparisons against a well-established implementation have shown an increase of the computational velocity by a factor ranging from 100 up to $ 1 \times 10^6$ in the most favorable cases.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weinstein:2017:AAT, author = "Matthew J. Weinstein and Anil V. Rao", title = "Algorithm 984: {ADiGator}, a Toolbox for the Algorithmic Differentiation of Mathematical Functions in {MATLAB} Using Source Transformation via Operator Overloading", journal = j-TOMS, volume = "44", number = "2", pages = "21:1--21:25", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3104990", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3104990", abstract = "A toolbox called ADiGator is described for algorithmically differentiating mathematical functions in MATLAB. ADiGator performs source transformation via operator overloading using forward mode algorithmic differentiation and produces a file that can be evaluated to obtain the derivative of the original function at a numeric value of the input. A convenient by-product of the file generation is the sparsity pattern of the derivative function. Moreover, because both the input and output to the algorithm are source codes, the algorithm may be applied recursively to generate derivatives of any order. A key component of the algorithm is its ability to statically exploit derivative sparsity at the MATLAB operation level to improve runtime performance. The algorithm is applied to four different classes of example problems and is shown to produce runtime efficient derivative code. Due to the static nature of the approach, the algorithm is well suited and intended for use with problems requiring many repeated derivative computations.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zaghloul:2017:ASE, author = "Mofreh R. Zaghloul", title = "Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the {Faddeyeva} Function", journal = j-TOMS, volume = "44", number = "2", pages = "22:1--22:9", month = sep, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3119904", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 19 17:19:59 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://dl.acm.org/citation.cfm?id=3119904", abstract = "We present a new simple algorithm for efficient, and relatively accurate computation of the Faddeyeva function $ w(z) $. The algorithm carefully exploits previous approximations by Hui et al. (1978) and Huml{\'\i}cek (1982) along with asymptotic expressions from Laplace continued fractions. Over a wide and fine grid of the complex argument, $ z = x + i y $, numerical results from the present approximation show a maximum relative error less than $ 4.0 \times 10^{-5} $ for both real and imaginary parts of $w$ while running in a relatively shorter execution time than other competitive techniques. In addition to the calculation of the Faddeyeva function, $w$, partial derivatives of the real and imaginary parts of the function can easily be calculated and returned as optional output.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mehra:2017:ASC, author = "Mani Mehra and Kuldip Singh Patel", title = "{Algorithm 986}: A Suite of Compact Finite Difference Schemes", journal = j-TOMS, volume = "44", number = "2", pages = "23:1--23:31", month = oct, year = "2017", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3119905", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Oct 5 18:31:10 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3119905", abstract = "A collection of Matlab routines that compute derivative approximations of arbitrary functions using high-order compact finite difference schemes is presented. Tenth-order accurate compact finite difference schemes for first and second derivative approximations and sixth-order accurate compact finite difference schemes for third and fourth derivative approximations are discussed for the functions with periodic boundary conditions. Fourier analysis of compact finite difference schemes is explained, and it is observed that compact finite difference schemes have better resolution characteristics when compared to classical finite difference schemes. Compact finite difference schemes for the functions with Dirichlet and Neumann boundary conditions are also discussed. Moreover, compact finite difference schemes for partial derivative approximations of functions in two variables are also given. For each case a Matlab routine is provided to compute the differentiation matrix and results are validated using the test functions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hanson:2018:RAM, author = "Richard J. Hanson and Tim Hopkins", title = "Remark on {Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the {Euclidean} Norm}", journal = j-TOMS, volume = "44", number = "3", pages = "24:1--24:23", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3134441", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Lawson:1979:ABL}.", URL = "https://dl.acm.org/citation.cfm?id=3134441", abstract = "We propose a set of new Fortran reference implementations, based on an algorithm proposed by Kahan, for the Level 1 BLAS routines *NRM2 that compute the Euclidean norm of a real or complex input vector. The principal advantage of these routines over the current offerings is that, rather than losing accuracy as the length of the vector increases, they generate results that are accurate to almost machine precision for vectors of length $ N < N_{\rm max} $ where $ N_{\rm max} $ depends upon the precision of the floating point arithmetic being used. In addition, we make use of intrinsic modules, introduced in the latest Fortran standards, to detect occurrences of non-finite numbers in the input data and return suitable values as well as setting IEEE floating point status flags as appropriate. A set of C interface routines is also provided to allow simple, portable access to the new routines. To improve execution speed, we advocate a hybrid algorithm; a simple loop is used first and, only if IEEE floating point exception flags signal, do we fall back on Kahan's algorithm. Since most input vectors are ``easy,'' i.e., they do not require the sophistication of Kahan's algorithm, the simple loop improves performance while the use of compensated summation ensures high accuracy. We also report on a comprehensive suite of test problems that has been developed to test both our new implementation and existing codes for both accuracy and the appropriate settings of the IEEE arithmetic status flags.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Neirynck:2018:NBA, author = "Niels Neirynck and Willy Govaerts and Yuri A. Kuznetsov and Hil G. E. Meijer", title = "Numerical Bifurcation Analysis of Homoclinic Orbits Embedded in One-Dimensional Manifolds of Maps", journal = j-TOMS, volume = "44", number = "3", pages = "25:1--25:19", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3134443", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3134443", abstract = "We describe new methods for initializing the computation of homoclinic orbits for maps in a state space with arbitrary dimension and for detecting their bifurcations. The initialization methods build on known and improved methods for computing one-dimensional stable and unstable manifolds. The methods are implemented in MatContM, a freely available toolbox in Matlab for numerical analysis of bifurcations of fixed points, periodic orbits, and connecting orbits of smooth nonlinear maps. The bifurcation analysis of homoclinic connections under variation of one parameter is based on continuation methods and allows us to detect all known codimension 1 and 2 bifurcations in three-dimensional (3D) maps, including tangencies and generalized tangencies. MatContM provides a graphical user interface, enabling interactive control for all computations. As the prime new feature, we discuss an algorithm for initializing connecting orbits in the important special case where either the stable or unstable manifold is one-dimensional, allowing us to compute all homoclinic orbits to saddle points in 3D maps. We illustrate this algorithm in the study of the adaptive control map, a 3D map introduced in 1991 by Frouzakis, Adomaitis, and Kevrekidis, to obtain a rather complete bifurcation diagram of the resonance horn in a 1:5 Neimark--Sacker bifurcation point, revealing new features.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Elafrou:2018:SLH, author = "Athena Elafrou and Vasileios Karakasis and Theodoros Gkountouvas and Kornilios Kourtis and Georgios Goumas and Nectarios Koziris", title = "{SparseX}: A Library for High-Performance Sparse Matrix--Vector Multiplication on Multicore Platforms", journal = j-TOMS, volume = "44", number = "3", pages = "26:1--26:32", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3134442", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3134442", abstract = "The Sparse Matrix-Vector Multiplication (SpMV) kernel ranks among the most important and thoroughly studied linear algebra operations, as it lies at the heart of many iterative methods for the solution of sparse linear systems, and often constitutes a severe performance bottleneck. Its optimization, which is intimately associated with the data structures used to store the sparse matrix, has always been of particular interest to the applied mathematics and computer science communities and has attracted further attention since the advent of multicore architectures. In this article, we present SparseX, an open source software package for SpMV targeting multicore platforms, that employs the state-of-the-art Compressed Sparse eXtended (CSX) sparse matrix storage format to deliver high efficiency through a highly usable ``BLAS-like'' interface that requires limited or no tuning. Performance results indicate that our library achieves superior performance over competitive libraries on large-scale problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Doliskani:2018:SCR, author = "Javad Doliskani and Pascal Giorgi and Romain Lebreton and Eric Schost", title = "Simultaneous Conversions with the Residue Number System Using Linear Algebra", journal = j-TOMS, volume = "44", number = "3", pages = "27:1--27:21", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3145573", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3145573", abstract = "We present an algorithm for simultaneous conversions between a given set of integers and their Residue Number System representations based on linear algebra. We provide a highly optimized implementation of the algorithm that exploits the computational features of modern processors. The main application of our algorithm is matrix multiplication over integers. Our speed-up of the conversions to and from the Residue Number System significantly improves the overall running time of matrix multiplication.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Springer:2018:DHP, author = "Paul Springer and Paolo Bientinesi", title = "Design of a High-Performance {GEMM}-like Tensor--Tensor Multiplication", journal = j-TOMS, volume = "44", number = "3", pages = "28:1--28:29", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3157733", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3157733", abstract = "We present ``GEMM-like Tensor--Tensor multiplication'' (GETT), a novel approach for dense tensor contractions that mirrors the design of a high-performance general matrix--matrix multiplication (GEMM). The critical insight behind GETT is the identification of three index sets, involved in the tensor contraction, which enable us to systematically reduce an arbitrary tensor contraction to loops around a highly tuned ``macro-kernel.'' This macro-kernel operates on suitably prepared (``packed'') sub-tensors that reside in a specified level of the cache hierarchy. In contrast to previous approaches to tensor contractions, GETT exhibits desirable features such as unit-stride memory accesses, cache-awareness, as well as full vectorization, without requiring auxiliary memory. We integrate GETT alongside the so-called Transpose-Transpose-GEMM-Transpose and Loops-over-GEMM approaches into an open source ``Tensor Contraction Code Generator.'' The performance results for a wide range of tensor contractions suggest that GETT has the potential of becoming the method of choice: While GETT exhibits excellent performance across the board, its effectiveness for bandwidth-bound tensor contractions is especially impressive, outperforming existing approaches by up to $ 12.4 \times $. More precisely, GETT achieves speedups of up to $ 1.41 \times $ over an equivalent-sized GEMM for bandwidth-bound tensor contractions while attaining up to 91.3\% of peak floating-point performance for compute-bound tensor contractions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sanders:2018:EPR, author = "Peter Sanders and Sebastian Lamm and Lorenz H{\"u}bschle-Schneider and Emanuel Schrade and Carsten Dachsbacher", title = "Efficient Parallel Random Sampling-Vectorized, Cache-Efficient, and Online", journal = j-TOMS, volume = "44", number = "3", pages = "29:1--29:14", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3157734", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3157734", abstract = "We consider the problem of sampling $n$ numbers from the range $ \{ 1, \ldots {}, N \} $ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and leads to a parallel algorithm running in expected time $ O(n / p + \log p)$ on $p$ processors, i.e., scales to massively parallel machines even for moderate values of $n$. The amount of communication between the processors is very small (at most $ O(\log p)$) and independent of the sample size. We also discuss modifications needed for load balancing, online sampling, sampling with replacement, Bernoulli sampling, and vectorization on SIMD units or GPUs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Harase:2018:IBM, author = "Shin Harase and Takamitsu Kimoto", title = "Implementing $ 64$-bit Maximally Equidistributed {$ F_2$}-Linear Generators with {Mersenne} Prime Period", journal = j-TOMS, volume = "44", number = "3", pages = "30:1--30:11", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3159444", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3159444", abstract = "CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. Here, we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters. We provide a table of specific parameters with period lengths from $ 2^{607} - 1 $ to $ 2^{44497} - 1 $.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Birkisson:2018:ARO, author = "{\'A}sgeir Birkisson", title = "Automatic Reformulation of {ODEs} to Systems of First-Order Equations", journal = j-TOMS, volume = "44", number = "3", pages = "31:1--31:18", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3159443", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Jan 22 17:49:32 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3159443", abstract = "Most numerical ODE solvers require problems to be written as systems of first-order differential equations. This normally requires the user to rewrite higher-order differential equations as coupled first-order systems. Here, we introduce the treeVar class, written in object-oriented Matlab, which is capable of algorithmically reformulating higher-order ODEs to equivalent systems of first-order equations. This allows users to specify problems using a more natural syntax and saves them from having to manually derive the first-order reformulation. The technique works by using operator overloading to build up syntax trees of expressions as mathematical programs are evaluated. It then applies a set of rules to the resulting trees to obtain the first-order reformulation, which is returned as another program. This technique has connections with algorithmic/automatic differentiation. We present how treeVar has been incorporated in Chebfun, greatly improving the ODE capabilities of the system.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weinzierl:2018:QMF, author = "Marion Weinzierl and Tobias Weinzierl", title = "Quasi-matrix-free Hybrid Multigrid on Dynamically Adaptive {Cartesian} Grids", journal = j-TOMS, volume = "44", number = "3", pages = "32:1--32:44", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3165280", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:12 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3165280", abstract = "We present a family of spacetree-based multigrid realizations using the tree's multiscale nature to derive coarse grids. They align with matrix-free geometric multigrid solvers as they never assemble the system matrices, which is cumbersome for dynamically adaptive grids and full multigrid. The most sophisticated realizations use BoxMG to construct operator-dependent prolongation and restriction in combination with Galerkin/Petrov--Galerkin coarse-grid operators. This yields robust solvers for nontrivial elliptic problems. We embed the algebraic, problem-dependent, and grid-dependent multigrid operators as stencils into the grid and evaluate all matrix-vector products in situ throughout the grid traversals. Such an approach is not literally matrix-free as the grid carries the matrix. We propose to switch to a hierarchical representation of all operators. Only differences of algebraic operators to their geometric counterparts are held. These hierarchical differences can be stored and exchanged with small memory footprint. Our realizations support arbitrary dynamically adaptive grids while they vertically integrate the multilevel operations through spacetree linearization. This yields good memory access characteristics, while standard colouring of mesh entities with domain decomposition allows us to use parallel many-core clusters. All realization ingredients are detailed such that they can be used by other codes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Babuska:2018:REG, author = "Ivo Babuska and Gustaf S{\"o}derlind", title = "On Roundoff Error Growth in Elliptic Problems", journal = j-TOMS, volume = "44", number = "3", pages = "33:1--33:22", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3134444", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:12 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3134444", abstract = "Large-scale linear systems arise in finite-difference and finite-element discretizations of elliptic problems. With increasing computer performance, ever larger systems are solved using direct methods. How large can such systems be without roundoff compromising accuracy? Here we model roundoff dynamics in standard $ L U $ and $ L D L^T $ decompositions with respect to problem size $N$. For the one-dimensional (1D) Poisson equation with Dirichlet boundary conditions on an equidistant grid, we show that the relative error in the factorized matrix grows like $ O(\epsilon \sqrt N)$ if roundoffs are modeled as independent, expectation zero random variables. With bias, the growth rate changes to $ O(\epsilon N)$. Subsequent back substitution results in typical error growths of $ O(\epsilon > N \sqrt {N})$ and $ O(\epsilon N^2)$, respectively. Error growth is governed by the dynamics of the computational process and by the structure of the boundary conditions rather than by the condition number. Computational results are demonstrated in several examples, including a few fourth-order 1D problems and second-order 2D problems, showing that error accumulation depends strongly on the solution method. Thus, the same $ L U$ solver may exhibit different growth rates for the same 2D Poisson problem, depending on whether the five-point or nine-point FDM operator is used.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Karol:2018:DSL, author = "Sven Karol and Tobias Nett and Jeronimo Castrillon and Ivo F. Sbalzarini", title = "A Domain-Specific Language and Editor for Parallel Particle Methods", journal = j-TOMS, volume = "44", number = "3", pages = "34:1--34:32", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3175659", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:12 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3175659", abstract = "Domain-specific languages (DSLs) are of increasing importance in scientific high-performance computing to reduce development costs, raise the level of abstraction, and, thus, ease scientific programming. However, designing DSLs is not easy, as it requires knowledge of the application domain and experience in language engineering and compilers. Consequently, many DSLs follow a weak approach using macros or text generators, which lack many of the features that make a DSL comfortable for programmers. Some of these features-e.g., syntax highlighting, type inference, error reporting-are easily provided by language workbenches, which combine language engineering techniques and tools in a common ecosystem. In this article, we present the Parallel Particle-Mesh Environment (PPME), a DSL and development environment for numerical simulations based on particle methods and hybrid particle-mesh methods. PPME uses the Meta Programming System, a projectional language workbench. PPME is the successor of the Parallel Particle-Mesh Language, a Fortran-based DSL that uses conventional implementation strategies. We analyze and compare both languages and demonstrate how the programmer's experience is improved using static analyses and projectional editing, i.e., code-structure editing, constrained by syntax, as opposed to free-text editing. We present an explicit domain model for particle abstractions and the first formal type system for particle methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zottou:2018:AMC, author = "Dimitra-Nefeli A. Zottou and Dimitris J. Kavvadias and Frosso S. Makri and Michael N. Vrahatis", title = "Algorithm 987: {MANBIS} --- a {C++} Mathematical Software Package for Locating and Computing Efficiently Many Roots of a Function: Theoretical Issues", journal = j-TOMS, volume = "44", number = "3", pages = "35:1--35:7", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3155744", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:12 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3155744", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Johnson:2018:AAE, author = "Robert W. Johnson", title = "Algorithm 988: {AMGKQ}: An Efficient Implementation of Adaptive Multivariate {Gauss--Kronrod} Quadrature for Simultaneous Integrands in {Octave\slash MATLAB}", journal = j-TOMS, volume = "44", number = "3", pages = "36:1--36:19", month = apr, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3157735", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:12 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3157735", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hwang:2018:CAC, author = "John T. Hwang and Joaquim R. R. A. Martins", title = "A Computational Architecture for Coupling Heterogeneous Numerical Models and Computing Coupled Derivatives", journal = j-TOMS, volume = "44", number = "4", pages = "37:1--37:39", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3182393", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3182393", abstract = "One of the challenges in computational modeling is coupling models to solve multidisciplinary problems. Flow-based computational frameworks alleviate part of the challenge through a modular approach, where data flows from component to component. However, existing flow-based frameworks are inefficient when coupled derivatives are needed for optimization. To address this, we develop the modular analysis and unified derivatives (MAUD) architecture. MAUD formulates the multidisciplinary model as a nonlinear system of equations, which leads to a linear equation that unifies all methods for computing derivatives. This enables flow-based frameworks that use the MAUD architecture to provide a common interface for the chain rule, adjoint method, coupled adjoint method, and hybrid methods; MAUD automatically uses the appropriate method for the problem. A hierarchical, matrix-free approach enables modern solution techniques such as Newton--Krylov solvers to be used within this monolithic formulation without computational overhead. Two demonstration problems are solved using a Python implementation of MAUD: a nanosatellite optimization with more than 2 million unknowns and 25,000 design variables, and an aircraft optimization involving over 6,000 design variables and 23,000 constraints. MAUD is now implemented in the open source framework OpenMDAO, which has been used to solve aircraft, satellite, wind turbine, and turbofan engine design problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Emiris:2018:PPV, author = "Ioannis Z. Emiris and Vissarion Fisikopoulos", title = "Practical Polytope Volume Approximation", journal = j-TOMS, volume = "44", number = "4", pages = "38:1--38:21", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3194656", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3194656", abstract = "We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear halfspaces. We implement and evaluate randomized polynomial-time algorithms for accurately approximating the polytope's volume in high dimensions (e.g., few hundreds) based onhit-and-run random walks. To carry out this efficiently, we experimentally correlate the effect of parameters, such as random walk length and number of sample points, with accuracy and runtime. Our method is based on Monte Carlo algorithms with guaranteed speed and provably high probability of success for arbitrarily high precision. We exploit the problem's features in implementing a practical rounding procedure of polytopes, in computing only partial ``generations'' of random points, and in designing fast polytope boundary oracles. Our publicly available software is significantly faster than exact computation and more accurate than existing approximation methods. For illustration, volume approximations of Birkhoff polytopes $B_{11},\ldots{}, B_{15}$ are computed, in dimensions up to 196, whereas exact methods have only computed volumes of up to $B_{10}$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dambra:2018:BSP, author = "Pasqua D'ambra and Salvatore Filippone and Panayot S. Vassilevski", title = "{BootCMatch}: A Software Package for Bootstrap {AMG} Based on Graph Weighted Matching", journal = j-TOMS, volume = "44", number = "4", pages = "39:1--39:25", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3190647", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3190647", abstract = "This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Escobedo:2018:SDL, author = "Adolfo R. Escobedo and Erick Moreno-Centeno and Christopher Lourenco", title = "Solution of Dense Linear Systems via Roundoff-Error-Free Factorization Algorithms: Theoretical Connections and Computational Comparisons", journal = j-TOMS, volume = "44", number = "4", pages = "40:1--40:24", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3199571", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3199571", abstract = "Exact solving of systems of linear equations (SLEs) is a fundamental subroutine within number theory, formal verification of mathematical proofs, and exact-precision mathematical programming. Moreover, efficient exact SLE solution methods could be valuable for a growing body of science and engineering applications where current fixed-precision standards have been deemed inadequate. This article contains key derivations relating, and computational tests comparing, two exact direct solution frameworks: roundoff-error-free (REF) LU factorization and rational arithmetic LU factorization. Specifically, both approaches solve the linear system Ax = b by factoring the matrix A into the product of a lower triangular (L) and upper triangular (U) matrix, A = LU. Most significantly, the featured findings reveal that the integer-preserving REF factorization framework solves dense SLEs one order of magnitude faster than the exact rational arithmetic approach while requiring half the memory. Since rational LU is utilized for basic solution validation in exact linear and mixed-integer programming, these results offer preliminary evidence of the potential of the REF factorization framework to be utilized within this specific context. Additionally, this article develops and analyzes an efficient streamlined version of Edmonds's Q-matrix approach that can be implemented as another basic solution validation approach. Further experiments demonstrate that the REF factorization framework also outperforms this alternative integer-preserving approach in terms of memory requirements and computational effort. General purpose codes to solve dense SLEs exactly via any of the aforementioned methods have been made available to the research and academic communities.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "40", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Magron:2018:IEU, author = "Victor Magron", title = "Interval Enclosures of Upper Bounds of Roundoff Errors Using Semidefinite Programming", journal = j-TOMS, volume = "44", number = "4", pages = "41:1--41:18", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3206430", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3206430", abstract = "A long-standing problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a particular rounding model. This method applies to numerical programs implementing polynomial functions with box constrained input variables. Our study is based on three different hierarchies, relying respectively on generalized eigenvalue problems, elementary computations, and semidefinite programming (SDP) relaxations. This is complementary of over-approximation frameworks, consisting of obtaining upper bounds on the largest absolute roundoff error. Combining the results of both frameworks allows one to get enclosures for upper bounds on roundoff errors. The under-approximation framework provided by the third hierarchy is based on a new sequence of convergent robust SDP approximations for certain classes of polynomial optimization problems. Each problem in this hierarchy can be solved exactly via SDP. By using this hierarchy, one can provide a monotone nondecreasing sequence of lower bounds converging to the absolute roundoff error of a program implementing a polynomial function, applying for a particular rounding model. We investigate the efficiency and precision of our method on nontrivial polynomial programs coming from space control, optimization, and computational biology.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "41", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Frison:2018:BBL, author = "Gianluca Frison and Dimitris Kouzoupis and Tommaso Sartor and Andrea Zanelli and Moritz Diehl", title = "{BLASFEO}: Basic Linear Algebra Subroutines for Embedded Optimization", journal = j-TOMS, volume = "44", number = "4", pages = "42:1--42:30", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3210754", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3210754", abstract = "Basic Linear Algebra Subroutines for Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and small-scale high-performance computing, in general. A key difference with respect to existing high-performance implementations of BLAS is that the computational performance is optimized for small- to medium-scale matrices, i.e., for sizes up to a few hundred. BLASFEO comes with three different implementations: a high-performance implementation aimed at providing the highest performance for matrices fitting in cache, a reference implementation providing portability and embeddability and optimized for very small matrices, and a wrapper to standard BLAS and LAPACK providing high performance on large matrices. The three implementations of BLASFEO together provide high-performance dense linear algebra routines for matrices ranging from very small to large. Compared to both open-source and proprietary highly tuned BLAS libraries, for matrices of size up to about 100, the high-performance implementation of BLASFEO is about 20--30\% faster than the corresponding level 3 BLAS routines and two to three times faster than the corresponding LAPACK routines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "42", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Huang:2018:ROO, author = "Wen Huang and P.-A. Absil and Kyle A. Gallivan and Paul Hand", title = "{ROPTLIB}: An Object-Oriented {C++} Library for Optimization on {Riemannian} Manifolds", journal = j-TOMS, volume = "44", number = "4", pages = "43:1--43:21", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3218822", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3218822", abstract = "Riemannian optimization is the task of finding an optimum of a real-valued function defined on a Riemannian manifold. Riemannian optimization has been a topic of much interest over the past few years due to many applications including computer vision, signal processing, and numerical linear algebra. The substantial background required to successfully design and apply Riemannian optimization algorithms is a significant impediment for many potential users. Therefore, multiple packages, such as Manopt (in Matlab) and Pymanopt (in Python), have been developed. This article describes ROPTLIB, a C++ library for Riemannian optimization. Unlike prior packages, ROPTLIB simultaneously achieves the following goals: (i) it has user-friendly interfaces in Matlab, Julia, and C++; (ii) users do not need to implement manifold- and algorithm-related objects; (iii) it provides efficient computational time due to its C++ core; (iv) it implements state-of-the-art generic Riemannian optimization algorithms, including quasi-Newton algorithms; and (v) it is based on object-oriented programming, allowing users to rapidly add new algorithms and manifolds.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "43", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brehard:2018:VNE, author = "Florent Br{\'e}hard and Nicolas Brisebarre and Mioara Joldes", title = "Validated and Numerically Efficient {Chebyshev} Spectral Methods for Linear Ordinary Differential Equations", journal = j-TOMS, volume = "44", number = "4", pages = "44:1--44:42", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3208103", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3208103", abstract = "In this work, we develop a validated numeric method for the solution of linear ordinary differential equations (LODEs). A wide range of algorithms (i.e., Runge--Kutta, collocation, spectral methods) exist for numerically computing approximations of the solutions. Most of these come with proofs of asymptotic convergence, but usually, provided error bounds are nonconstructive. However, in some domains like critical systems and computer-aided mathematical proofs, one needs validated effective error bounds. We focus on both the theoretical and practical complexity analysis of a so-called a posteriori quasi-Newton validation method, which mainly relies on a fixed-point argument of a contracting map. Specifically, given a polynomial approximation, obtained by some numerical algorithm and expressed on a Chebyshev basis, our algorithm efficiently computes an accurate and rigorous error bound. For this, we study theoretical properties like compactness, convergence, and invertibility of associated linear integral operators and their truncations in a suitable coefficient space of Chebyshev series. Then, we analyze the almost-banded matrix structure of these operators, which allows for very efficient numerical algorithms for both numerical solutions of LODEs and rigorous computation of the approximation error. Finally, several representative examples show the advantages of our algorithms as well as their theoretical and practical limits.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "44", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Deng:2018:SFE, author = "Lih-Yuan Deng and Jyh-Jen Horng Shiau and Henry Horng-Shing Lu and Dale Bowman", title = "{Secure and Fast Encryption (SAFE)} with Classical Random Number Generators", journal = j-TOMS, volume = "44", number = "4", pages = "45:1--45:17", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3212673", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3212673", abstract = "Pseudo-random number generators (PRNGs) play an important role in both areas of computer simulation and computer security. Currently, there appears to be a huge divide between the types of PRNGs used in these two areas. For PRNGs in computer security applications, the security concern is extremely important. For PRNGs in computer simulation applications, the properties of high-dimensional equi-distribution, efficiency, long period-length, and portability are important. In recent years, there have been many PRNGs proposed in the area of computer simulation satisfying these nice properties. However, most of them are linear generators, thus sharing the same weakness in predictability. The major aim of this article is to propose a general class of secure generators, called SAFE (secure and fast encryption) generators, by properly ``mixing'' two baseline generators with the aforementioned properties to obtain a secure generator that would inherit these nice properties. Specifically, we propose applying a general mutual-shuffling method to certain linear generators, such as the currently most popular MT19937 generator and large-order multiple recursive generators, as well as outputting certain nonlinear transformations of the generated variates to construct secure PRNGS.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "45", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Tan:2018:DIA, author = "Guangming Tan and Junhong Liu and Jiajia Li", title = "Design and Implementation of Adaptive {SpMV} Library for Multicore and Many-Core Architecture", journal = j-TOMS, volume = "44", number = "4", pages = "46:1--46:25", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3218823", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3218823", abstract = "Sparse matrix vector multiplication (SpMV) is an important computational kernel in traditional high-performance computing and emerging data-intensive applications. Previous SpMV libraries are optimized by either application-specific or architecture-specific approaches but present difficulties for use in real applications. In this work, we develop an auto-tuning system (SMATER) to bridge the gap between specific optimizations and general-purpose use. SMATER provides programmers a unified interface based on the compressed sparse row (CSR) sparse matrix format by implicitly choosing the best format and fastest implementation for any input sparse matrix during runtime. SMATER leverages a machine-learning model and retargetable back-end library to quickly predict the optimal combination. Performance parameters are extracted from 2,386 matrices in the SuiteSparse matrix collection. The experiments show that SMATER achieves good performance (up to 10 times that of the Intel Math Kernel Library (MKL) on Intel E5-2680 v3) while being portable on state-of-the-art x86 multicore processors, NVIDIA GPUs, and Intel Xeon Phi accelerators. Compared with the Intel MKL library, SMATER runs faster by more than 2.5 times on average. We further demonstrate its adaptivity in an algebraic multigrid solver from the Hypre library and report greater than 20\% performance improvement.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "46", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Irurozki:2018:APM, author = "Ekhine Irurozki and Josu Ceberio and Josean Santamaria and Roberto Santana and Alexander Mendiburu", title = "Algorithm 989: {\tt perm\_mateda}: a {Matlab} Toolbox of Estimation of Distribution Algorithms for Permutation-based Combinatorial Optimization Problems", journal = j-TOMS, volume = "44", number = "4", pages = "47:1--47:13", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3206429", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3206429", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "47", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ozkan:2018:AEA, author = "Aysegul Ozkan and Rahul Prabhu and Troy Baker and James Pence and J{\"o}rg Peters and Meera Sitharam", title = "Algorithm 990: Efficient Atlasing and Search of Configuration Spaces of Point-Sets Constrained by Distance Intervals", journal = j-TOMS, volume = "44", number = "4", pages = "48:1--48:30", month = aug, year = "2018", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3204472", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65Y15 (65D18)", MRnumber = "3865836", bibdate = "Fri Oct 5 11:23:13 MDT 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/peters-jorg.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3204472", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "48", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aktas:2019:CBM, author = "Mehmet E. Aktas and Esra Akbas", title = "Computing the Braid Monodromy of Completely Reducible $n$-gonal Curves", journal = j-TOMS, volume = "45", number = "1", pages = "1:1--1:11", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3291040", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3291040", abstract = "Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the rectangular braid diagram (RBD) method is proposed to compute the braid monodromy of a completely reducible $n$-gonal curve, i.e., the curves in the form $ (y - y_1 (x)) \ldots {} (y - y_n(x)) = 0$, where $ n \in Z^+$ and $ y_i \in C[x]$. Also, an algorithm is presented to compute the Alexander polynomial of these curve complements using Burau representations of braid groups. Examples for each computation are provided.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amestoy:2019:PSB, author = "Patrick R. Amestoy and Alfredo Buttari and Jean-Yves L'Excellent and Theo Mary", title = "Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures", journal = j-TOMS, volume = "45", number = "1", pages = "2:1--2:26", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3242094", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3242094", abstract = "Matrices coming from elliptic Partial Differential Equations have been shown to have a low-rank property that can be efficiently exploited in multifrontal solvers to provide a substantial reduction of their complexity. Among the possible low-rank formats, the Block Low-Rank format (BLR) is easy to use in a general purpose multifrontal solver and its potential compared to standard (full-rank) solvers has been demonstrated. Recently, new variants have been introduced and it was proved that they can further reduce the complexity but their performance has never been analyzed. In this article, we present a multithreaded BLR factorization and analyze its efficiency and scalability in shared-memory multicore environments. We identify the challenges posed by the use of BLR approximations in multifrontal solvers and put forward several algorithmic variants of the BLR factorization that overcome these challenges by improving its efficiency and scalability. We illustrate the performance analysis of the BLR multifrontal factorization with numerical experiments on a large set of problems coming from a variety of real-life applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Boukaram:2019:HMO, author = "Wajih Boukaram and George Turkiyyah and David Keyes", title = "Hierarchical Matrix Operations on {GPUs}: Matrix--Vector Multiplication and Compression", journal = j-TOMS, volume = "45", number = "1", pages = "3:1--3:28", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3232850", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3232850", abstract = "Hierarchical matrices are space- and time-efficient representations of dense matrices that exploit the low-rank structure of matrix blocks at different levels of granularity. The hierarchically low-rank block partitioning produces representations that can be stored and operated on in near-linear complexity instead of the usual polynomial complexity of dense matrices. In this article, we present high-performance implementations of matrix vector multiplication and compression operations for the H 2 variant of hierarchical matrices on GPUs. The H 2 variant exploits, in addition to the hierarchical block partitioning, hierarchical bases for the block representations and results in a scheme that requires only O ( n ) storage and O ( n ) complexity for the mat-vec and compression kernels. These two operations are at the core of algebraic operations for hierarchical matrices, the mat-vec being a ubiquitous operation in numerical algorithms while compression/recompression represents a key building block for other algebraic operations, which require periodic recompression during execution. The difficulties in developing efficient GPU algorithms come primarily from the irregular tree data structures that underlie the hierarchical representations, and the key to performance is to recast the computations on flattened trees in ways that allow batched linear algebra operations to be performed. This requires marshaling the irregularly laid out data in a way that allows them to be used by the batched routines. Marshaling operations only involve pointer arithmetic with no data movement and as a result have minimal overhead. Our numerical results on covariance matrices from 2D and 3D problems from spatial statistics show the high efficiency our routines achieve over 550GB/s for the bandwidth-limited matrix--vector operation and over 850GFLOPS/s in sustained performance for the compression operation on the P100 Pascal GPU.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Martinsson:2019:RBR, author = "P. G. Martinsson and G. Quintana-Ort{\'\i} and N. Heavner", title = "{randUTV}: A Blocked Randomized Algorithm for Computing a Rank-Revealing {$ U T V $} Factorization", journal = j-TOMS, volume = "45", number = "1", pages = "4:1--4:26", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3242670", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3242670", abstract = "A randomized algorithm for computing a so-called UTV factorization efficiently is presented. Given a matrix A, the algorithm `randUTV' computes a factorization A = UTV *, where U and V have orthonormal columns, and T is triangular (either upper or lower, whichever is preferred). The algorithm randUTV is developed primarily to be a fast and easily parallelized alternative to algorithms for computing the Singular Value Decomposition (SVD). randUTV provides accuracy very close to that of the SVD for problems such as low-rank approximation, solving ill-conditioned linear systems, and determining bases for various subspaces associated with the matrix. Moreover, randUTV produces highly accurate approximations to the singular values of A. Unlike the SVD, the randomized algorithm proposed builds a UTV factorization in an incremental, single-stage, and noniterative way, making it possible to halt the factorization process once a specified tolerance has been met. Numerical experiments comparing the accuracy and speed of randUTV to the SVD are presented. Other experiments also demonstrate that in comparison to column-pivoted QR, which is another factorization that is often used as a relatively economic alternative to the SVD, randUTV compares favorably in terms of speed while providing far higher accuracy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kulisch:2019:MSI, author = "Ulrich Kulisch", title = "Mathematics and Speed for Interval Arithmetic: A Complement to {IEEE 1788}", journal = j-TOMS, volume = "45", number = "1", pages = "5:1--5:22", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3264448", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3264448", abstract = "After a short introduction, the article begins with an axiomatic definition of rounded arithmetic. The concepts of rounding and of rounded arithmetic operations are defined in an axiomatic manner fully independent of special data formats and encodings. Basic properties of floating-point and interval arithmetic can directly be derived from this abstract mathematical model. Interval operations are defined as set operations for elements of the set {\=I}R of closed and connected sets of real numbers. As such, they form an algebraically closed subset of the powerset of the real numbers. This property leads to explicit formulas for the arithmetic operations of floating-point intervals of {\=I}F, which are executable on the computer. Arithmetic for intervals of {\=I}F forms an exception free calculus, i.e., arithmetic operations for intervals of {\=I}F always lead to intervals of {\=I}F again. Later sections are concerned with programming support and hardware for interval arithmetic. Both are a must and absolutely necessary to move interval arithmetic more into the center of scientific computing. With some minor hardware additions, interval operations can be made as fast as simple floating-point operations. In vector and matrix spaces for real, complex, and interval data, the dot product is a fundamental arithmetic operation. Computing the dot product of two vectors with floating-point components exactly substantially speeds up floating-point and interval arithmetic as well as the accuracy of the computed result. Hardware needed for the exact dot product is very modest. The exact dot product is essential for long real and long interval arithmetic. Section 9 illustrates that interval arithmetic as developed in this article already has a long tradition. Products based on these ideas have been available since 1980. Implementing what the article advocates would have a profound effect on mathematical software. Modern processor architecture from Intel, for example, comes quite close to what is requested in this article.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wang:2019:PAA, author = "Shouxiang Wang and Kai Wang and Lei Wu and Chengshan Wang", title = "Polar Affine Arithmetic: Optimal Affine Approximation and Operation Development for Computation in Polar Form Under Uncertainty", journal = j-TOMS, volume = "45", number = "1", pages = "6:1--6:29", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3274659", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3274659", abstract = "Uncertainties practically arise from numerous factors, such as ambiguous information, inaccurate model, and environment disturbance. Interval arithmetic has emerged to solve problems with uncertain parameters, especially in the computational process where only the upper and lower bounds of parameters can be ascertained. In rectangular coordinate systems, the basic interval operations and improved interval algorithms have been developed in the numerical analysis. However, in polar coordinate systems, interval arithmetic still suffers from issues of complex computation and overestimation. This article defines a polar affine variable and develops a polar affine arithmetic (PAA) that extends affine arithmetic to the polar coordinate systems, which performs better in many aspects than the corresponding polar interval arithmetic (PIA). Basic arithmetic operations are developed based on the complex affine arithmetic. The Chebyshev approximation theory and the min-range approximation theory are used to identify the best affine approximation. PAA can accurately keep track of the interdependency among multiple variables throughout the calculation procedure, which prominently reduces the solution conservativeness. Numerical examples implemented in MATLAB programs show that, compared with benchmark results from the Monte Carlo method, the proposed PAA ensures completeness of the exact solution and presents a more compact solution region than PIA when dependency exists in the calculation process. Meanwhile, a comparison of affine arithmetic in polar and rectangular coordinates is presented. An application of PAA in circuit analysis is quantitatively presented and potential applications in other research fields involving complex variables in polar form will be gradually developed.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DaSilva:2019:ULS, author = "Curt {Da Silva} and Felix Herrmann", title = "A Unified {$2$D\slash $3$D} Large-Scale Software Environment for Nonlinear Inverse Problems", journal = j-TOMS, volume = "45", number = "1", pages = "7:1--7:35", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3291042", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3291042", abstract = "Large-scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in inversion frameworks that are technically correct but not scalable to realistically sized problems. On the other hand, the computational demands for realistic problems result in industrial codebases that are geared solely for high performance, rather than comprehensibility or flexibility. We propose a new software design for inverse problems constrained by partial differential equations that bridges the gap between these two seemingly disparate worlds. A hierarchical and modular design reduces the cognitive burden on the user while exploiting high-performance primitives at the lower levels. Our code has the added benefit of actually reflecting the underlying mathematics of the problem, which lowers the cognitive load on the user using it and reduces the initial startup period before a researcher can be fully productive. We also introduce a new preconditioner for the {$3$D} Helmholtz equation that is suitable for fault-tolerant distributed systems. Numerical experiments on a variety of {$2$D} and {$3$D} test problems demonstrate the effectiveness of this approach on scaling algorithms from small- to large-scale problems with minimal code changes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Green:2019:EBS, author = "Kevin R. Green and Raymond J. Spiteri", title = "Extended {BACOLI}: Solving One-Dimensional Multiscale Parabolic {PDE} Systems With Error Control", journal = j-TOMS, volume = "45", number = "1", pages = "8:1--8:19", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3301320", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3301320", abstract = "BACOLI is a Fortran software package for solving one-dimensional parabolic partial differential equations (PDEs) with separated boundary conditions by B-spline adaptive collocation methods. A distinguishing feature of BACOLI is its ability to estimate and control error and correspondingly adapt meshes in both space and time. Many models of scientific interest, however, can be formulated as multiscale parabolic PDE systems, that is, models that couple a system of parabolic PDEs describing dynamics on a global scale with a system of ordinary differential equations describing dynamics on a local scale. This article describes the Fortran software eBACOLI, the extension of BACOLI to solve such multiscale models. The performance of the extended software is demonstrated to be statistically equivalent to the original for purely parabolic PDE systems. Results from eBACOLI are given for various multiscale models from the extended problem class considered.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Walther:2019:VNR, author = "Christoph Walther", title = "Verified {Newton--Raphson} Iteration for Multiplicative Inverses Modulo Powers of Any Base", journal = j-TOMS, volume = "45", number = "1", pages = "9:1--9:7", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3301317", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Dumas:2014:NRI}.", URL = "https://dl.acm.org/citation.cfm?id=3301317", abstract = "We identify two faults in a published algorithm for fast computation of multiplicative inverses modulo prime powers. We patch the algorithm and present machine-assisted proofs of correctness of the repair. Our formal proofs also reveal that being prime is an unnecessary demand for the power base, thus attributing a wider scope of applications to the repaired algorithm.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Springer:2019:SSH, author = "Paul Springer and Devin Matthews and Paolo Bientinesi", title = "Spin Summations: A High-Performance Perspective", journal = j-TOMS, volume = "45", number = "1", pages = "10:1--10:22", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3301319", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3301319", abstract = "In addition to tensor contractions, one of the most pronounced computational bottlenecks in the nonorthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms-including CCSD(T) and CCSDT(Q)-are spin summations. At a first sight, spin summations are operations similar to tensor transpositions, but a closer look reveals additional challenges to high-performance calculations, including temporal locality and scattered memory accesses. This article explores a sequence of algorithmic solutions for spin summations, each exploiting individual properties of either the underlying hardware (e.g., caches, vectorization) or the problem itself (e.g., factorizability). The final algorithm combines the advantages of all the solutions while avoiding their drawbacks; this algorithm achieves high performance through parallelization and vectorization, and by exploiting the temporal locality inherent to spin summations. Combined, these optimizations result in speedups between $2.4 \times $ and $5.5 \times $ over the NCC quantum chemistry software package. In addition to such a performance boost, our algorithm can perform the spin summations in-place, thus reducing the memory footprint by $2 \times $ over an out-of-place variant.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Shterenlikht:2019:QIF, author = "A. Shterenlikht", title = "On Quality of Implementation of {Fortran 2008} Complex Intrinsic Functions on Branch Cuts", journal = j-TOMS, volume = "45", number = "1", pages = "11:1--11:9", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3301318", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3301318", abstract = "Branch cuts in complex functions have important uses in fracture mechanics, jet flow, and aerofoil analysis. This article introduces tests for validating Fortran 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN, ASINH, ACOSH, and ATANH-on branch cuts with arguments of all 3 IEEE floating-point binary formats: binary32, binary64, and binary128, including signed zero and signed infinity. Multiple test failures were revealed, such as wrong signs of results or unexpected overflow, underflow, or NaN. We conclude that the quality of implementation of these Fortran 2008 intrinsics in many compilers is not yet sufficient to remove the need for special code for branch cuts. The electronic appendix contains the full test results with 8 Fortran 2008 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG, and IBM, detailed derivations of the values of these functions on branch cuts and conformal maps of the branch cuts, to be used as a reference. The tests and the results are freely available from https://cmplx.sourceforge.io. This work will be of interest to engineers who use complex functions, as well as to compiler and math library developers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Richardson:2019:ATS, author = "Lee F. Richardson and William F. Eddy", title = "Algorithm 991: The {$2$D} Tree Sliding Window {Discrete Fourier Transform}", journal = j-TOMS, volume = "45", number = "1", pages = "12:1--12:12", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3264426", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3264426", abstract = "We present a new algorithm for the $2$D sliding window discrete Fourier transform. Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley-Tukey fast Fourier transform. For an $N_0 \times N_1$ array and $n_0 \times n_1$ windows, our algorithm takes $O(N_0 N_1 n_0 n_1)$ operations. We provide a C implementation of our algorithm for the Radix-2 case, compare ours to existing algorithms, and show how our algorithm easily extends to higher dimensions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Roth:2019:AOC, author = "{\'A}goston R{\'o}th", title = "Algorithm 992: An {OpenGL}- and {C++}-based Function Library for Curve and Surface Modeling in a Large Class of Extended {Chebyshev} Spaces", journal = j-TOMS, volume = "45", number = "1", pages = "13:1--13:32", month = mar, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3284979", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/multithreading.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Roth:2021:RAO}.", URL = "https://dl.acm.org/citation.cfm?id=3284979", abstract = "We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate, and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that comprises the constants and can be identified with the solution space of a constant-coefficient homogeneous linear differential equation defined on a sufficiently small interval. Using the obtained normalized B-bases, our library can also generate, (partially) differentiate, modify, and visualize a large family of so-called B-curves and tensor product B-surfaces. Moreover, the library also implements methods that can be used to perform dimension elevation, to subdivide B-curves and B-surfaces by means of de Casteljau-like B-algorithms, and to generate basis transformations for the B-representation of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces. Independently of the algebraic, exponential, trigonometric, or mixed type of the applied EC space, the proposed library is numerically stable and efficient up to a reasonable dimension number and may be useful for academics and engineers in the fields of Approximation Theory, Computer Aided Geometric Design, Computer Graphics, and Isogeometric and Numerical Analysis.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Weinzierl:2019:PSP, author = "Tobias Weinzierl", title = "The {Peano} Software --- Parallel, Automaton-based, Dynamically Adaptive Grid Traversals", journal = j-TOMS, volume = "45", number = "2", pages = "14:1--14:41", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3319797", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3319797", abstract = "We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata-one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a `one way to implement things' code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Charara:2019:BTD, author = "Ali Charara and David Keyes and Hatem Ltaief", title = "Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on {GPUs}", journal = j-TOMS, volume = "45", number = "2", pages = "15:1--15:28", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3267101", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3267101", abstract = "Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes (up to 256) using single and multiple GPUs. By deploying recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization, and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dongarra:2019:PPL, author = "Jack Dongarra and Mark Gates and Azzam Haidar and Jakub Kurzak and Piotr Luszczek and Panruo Wu and Ichitaro Yamazaki and Asim Yarkhan and Maksims Abalenkovs and Negin Bagherpour and Sven Hammarling and Jakub S{\'\i}stek and David Stevens and Mawussi Zounon and Samuel D. Relton", title = "{PLASMA}: Parallel Linear Algebra Software for Multicore Using {OpenMP}", journal = j-TOMS, volume = "45", number = "2", pages = "16:1--16:35", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3264491", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3264491", abstract = "The recent version of the Parallel Linear Algebra Software for Multicore Architectures (PLASMA) library is based on tasks with dependencies from the OpenMP standard. The main functionality of the library is presented. Extensive benchmarks are targeted on three recent multicore and manycore architectures, namely, an Intel Xeon, Intel Xeon Phi, and IBM POWER 8 processors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Luporini:2019:ATU, author = "Fabio Luporini and Michael Lange and Christian T. Jacobs and Gerard J. Gorman and J. Ramanujam and Paul H. J. Kelly", title = "Automated Tiling of Unstructured Mesh Computations with Application to Seismological Modeling", journal = j-TOMS, volume = "45", number = "2", pages = "17:1--17:30", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3302256", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3302256", abstract = "Sparse tiling is a technique to fuse loops that access common data, thus increasing data locality. Unlike traditional loop fusion or blocking, the loops may have different iteration spaces and access shared datasets through indirect memory accesses, such as A[map[i]]-hence the name `sparse.' One notable example of such loops arises in discontinuous-Galerkin finite element methods, because of the computation of numerical integrals over different domains (e.g., cells, facets). The major challenge with sparse tiling is implementation --- not only is it cumbersome to understand and synthesize, but it is also onerous to maintain and generalize, as it requires a complete rewrite of the bulk of the numerical computation. In this article, we propose an approach to extend the applicability of sparse tiling based on raising the level of abstraction. Through a sequence of compiler passes, the mathematical specification of a problem is progressively lowered, and eventually sparse-tiled C for-loops are generated. Besides automation, we advance the state-of-the-art by introducing a revisited, more efficient sparse tiling algorithm; support for distributed-memory parallelism; a range of fine-grained optimizations for increased runtime performance; implementation in a publicly available library, SLOPE; and an in-depth study of the performance impact in Seigen, a real-world elastic wave equation solver for seismological problems, which shows speed-ups up to $1.28 \times $ on a platform consisting of 896 Intel Broadwell cores.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sukkari:2019:QBS, author = "Dalal Sukkari and Hatem Ltaief and Aniello Esposito and David Keyes", title = "A {QDWH}-based {SVD} Software Framework on Distributed-memory Manycore Systems", journal = j-TOMS, volume = "45", number = "2", pages = "18:1--18:21", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309548", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Nakatsukasa:2013:SES}.", URL = "https://dl.acm.org/citation.cfm?id=3309548", abstract = "This article presents a high-performance software framework for computing a dense SVD on distributed-memory manycore systems. Originally introduced by Nakatsukasa et al. (2010) and Nakatsukasa and Higham (2013), the SVD solver relies on the polar decomposition using the QR Dynamically Weighted Halley algorithm (QDWH). Although the QDWH-based SVD algorithm performs a significant amount of extra floating-point operations compared to the traditional SVD with the one-stage bidiagonal reduction, the inherent high level of concurrency associated with Level 3 BLAS compute-bound kernels ultimately compensates for the arithmetic complexity overhead. Using the ScaLAPACK two-dimensional block cyclic data distribution with a rectangular processor topology, the resulting QDWH-SVD further reduces excessive communications during the panel factorization, while increasing the degree of parallelism during the update of the trailing submatrix, as opposed to relying on the default square processor grid. After detailing the algorithmic complexity and the memory footprint of the algorithm, we conduct a thorough performance analysis and study the impact of the grid topology on the performance by looking at the communication and computation profiling trade-offs. We report performance results against state-of-the-art existing QDWH software implementations (e.g., Elemental) and their SVD extensions on large-scale distributed-memory manycore systems based on commodity Intel x86 Haswell processors and Knights Landing (KNL) architecture. The QDWH-SVD framework achieves up to 3/8-fold speedups on the Haswell/KNL-based platforms, respectively, against ScaLAPACK PDGESVD and turns out to be a competitive alternative for well- and ill-conditioned matrices. We finally come up herein with a performance model based on these empirical results. Our QDWH-based polar decomposition and its SVD extension are freely available at https://github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively, and have been integrated into the Cray Scientific numerical library LibSci v17.11.1.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Maniezzo:2019:CSC, author = "Vittorio Maniezzo and Marco A. Boschetti and Antonella Carbonaro and Moreno Marzolla and Francesco Strappaveccia", title = "Client-side Computational Optimization", journal = j-TOMS, volume = "45", number = "2", pages = "19:1--19:16", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309549", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3309549", abstract = "Mobile platforms have matured to a point where they can provide the infrastructure required to support sophisticated optimization codes. This opens the possibility to envisage new interest for distributed application codes and the opportunity to intensify research on optimization algorithms requiring limited computational resources, as provided by mobile platforms. In this article, we report on some exploratory experience in this area. We illustrate some practical, real-world cases where running optimization programs on mobile or embedded devices can be useful, with particular emphasis on matheuristics approaches. Then, we discuss a practical use case involving the feasibility version of the generalized assignment problem (GAP). We present a JavaScript implementation of a GAP solver that can be executed inside an ordinary browser supporting ECMAScript. We tested the code on different smartphones of varying age and power, as well as on desktop PCs and other embedded devices. Our experiments confirm the viability of mobile devices for computational intensive tasks.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Porcelli:2019:NUP, author = "Margherita Porcelli and Philippe L. Toint", title = "A Note on Using Performance and Data Profiles for Training Algorithms", journal = j-TOMS, volume = "45", number = "2", pages = "20:1--20:10", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3310362", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3310362", abstract = "This article shows how to use performance and data profile benchmarking tools to improve the performance of algorithms. We propose to achieve this goal by defining and approximately solving suitable optimization problems involving the parameters of the algorithm under consideration. Because these problems do not have derivatives and may involve integer variables, we suggest using a mixed-integer derivative-free optimizer for this task. A numerical illustration is presented (using the BFO package), which indicates that the obtained gains are potentially significant.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Winkelmann:2019:CCA, author = "Jan Winkelmann and Paul Springer and Edoardo {Di Napoli}", title = "{ChASE}: {Chebyshev} Accelerated Subspace Iteration Eigensolver for Sequences of {Hermitian} Eigenvalue Problems", journal = j-TOMS, volume = "45", number = "2", pages = "21:1--21:34", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3313828", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3313828", abstract = "Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties that are pertinent to the entire sequence and not just to the single problem. When such features take the form of correlations between the eigenvectors of consecutive problems, as is the case in many real-world applications, the potential benefit of exploiting them can be substantial. We present the Chebyshev Accelerated Subspace iteration Eigensolver (ChASE), a modern algorithm and library based on subspace iteration with polynomial acceleration. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree that further reduces the necessary floating-point operations. ChASE is written in C++ using the modern software engineering concepts that favor a simple integration in application codes and a straightforward portability over heterogeneous platforms. When solving sequences of Hermitian eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits from the sequence's spectral properties and outperforms direct solvers in many scenarios. The library ships with two distinct parallelization schemes, supports execution over distributed GPUs, and is easily extensible to other parallel computing architectures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fackler:2019:AEC, author = "Paul L. Fackler", title = "Algorithm 993: Efficient Computation with {Kronecker} Products", journal = j-TOMS, volume = "45", number = "2", pages = "22:1--22:9", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3291041", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3291041", abstract = "An algorithm for multiplying a chain of Kronecker products by a matrix is described. The algorithm does not require that the Kronecker chain actually be computed and the main computational work is a series of matrix--matrix multiplications. Use of the algorithm can lead to substantial savings in both memory requirements and computational speed. Although similar algorithms have been described before, this article makes two novel contributions. First, it shows how shuffling of data can be (largely) avoided. Second, it provides a simple method to determine the optimal ordering of the workflow.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Zaghloul:2019:RO, author = "Mofreh R. Zaghloul", title = "Remark on {`Algorithm 680: Evaluation of the Complex Error Function': Cause and Remedy for the Loss of Accuracy Near the Real Axis}", journal = j-TOMS, volume = "45", number = "2", pages = "24:1--24:3", month = apr, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309681", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon May 6 18:23:42 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3309681", abstract = "In this remark, we identify the cause of the loss of accuracy in the computation of the Faddeyeva function, $w(z)$, near the real axis when using Algorithm 680. We provide a simple correction to this problem that allows us to restore this code as one of the important reference routines for accuracy comparisons.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Faz-Hernandez:2019:HPI, author = "Armando Faz-Hern{\'a}ndez and Julio L{\'o}pez and Ricardo Dahab", title = "High-performance Implementation of Elliptic Curve Cryptography Using Vector Instructions", journal = j-TOMS, volume = "45", number = "3", pages = "25:1--25:35", month = jul, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309759", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 31 08:06:08 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3309759", abstract = "Elliptic curve cryptosystems are considered an efficient alternative to conventional systems such as DSA and RSA. Recently, Montgomery and Edwards elliptic curves have been used to implement cryptosystems. In particular, the elliptic curves Curve25519 and Curve448 were used for instantiating Diffie--Hellman protocols named X25519 and X448. Mapping these curves to twisted Edwards curves allowed deriving two new signature instances, called Ed25519 and Ed448, of the Edwards Digital Signature Algorithm. In this work, we focus on the secure and efficient software implementation of these algorithms using SIMD parallel processing. We present software techniques that target the Intel AVX2 vector instruction set for accelerating prime field arithmetic and elliptic curve operations. Our contributions result in a high-performance software library for AVX2-ready processors. For example, our library computes digital signatures 19\% (for Ed25519) and 29\% (for Ed448) faster than previous optimized implementations. Also, our library improves by 10\% and 20\% the execution time of X25519 and X448, respectively.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Naumann:2019:ACD, author = "Uwe Naumann", title = "Adjoint Code Design Patterns", journal = j-TOMS, volume = "45", number = "3", pages = "26:1--26:32", month = jul, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3326162", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 31 08:06:08 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3326162", abstract = "Adjoint methods have become fundamental ingredients of the scientific computing toolbox over the past decades. Large-scale parameter sensitivity analysis, uncertainty quantification, and nonlinear optimization would otherwise turn out computationally infeasible. The symbolic derivation of adjoint mathematical models for relevant problems in science and engineering and their implementation in consistency with the implementation of the underlying primal model frequently proves highly challenging. Hence, an increased interest in algorithmic adjoints can be observed. The algorithmic derivation of adjoint numerical simulation programs shifts some of the problems faced from functional and numerical analysis to computer science. It becomes a highly complex software engineering task requiring expertise in software analysis, transformation, and optimization. Despite rather mature software tool support for algorithmic differentiation, substantial user intervention is typically required when targeting nontrivial numerical programs. A large number of patterns shared by numerous application codes results in repeated duplication of development effort. The adjoint code design patterns introduced in this article aim to reduce this problem through improved formalization from the software engineering perspective. Fully functional reference implementations are provided through github.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hashemi:2019:ECE, author = "Behnam Hashemi", title = "Enclosing {Chebyshev} Expansions in Linear Time", journal = j-TOMS, volume = "45", number = "3", pages = "27:1--27:33", month = jul, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3319395", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 31 08:06:08 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3319395", abstract = "We consider the problem of computing rigorous enclosures for polynomials represented in the Chebyshev basis. Our aim is to compare and develop algorithms with a linear complexity in terms of the polynomial degree. A first category of methods relies on a direct interval evaluation of the given Chebyshev expansion in which Chebyshev polynomials are bounded, e.g., with a divide-and-conquer strategy. Our main category of methods that are based on the Clenshaw recurrence includes interval Clenshaw with defect correction (ICDC), and the spectral transformation of Clenshaw recurrence rewritten as a discrete dynamical system. An extension of the barycentric representation to interval arithmetic is also considered that has a log-linear complexity as it takes advantage of a verified discrete cosine transform. We compare different methods and provide illustrative numerical experiments. In particular, our eigenvalue-based methods are interesting for bounding the range of high-degree interval polynomials. Some of the methods rigorously compute narrow enclosures for high-degree Chebyshev expansions at thousands of points in a few seconds on an average computer. We also illustrate how to employ our methods as an automatic a posteriori forward error analysis tool to monitor the accuracy of the Chebfun feval command.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lee:2019:ICA, author = "Christopher T. Lee and John B. Moody and Rommie E. Amaro and J. Andrew Mccammon and Michael J. Holst", title = "The Implementation of the Colored Abstract Simplicial Complex and Its Application to Mesh Generation", journal = j-TOMS, volume = "45", number = "3", pages = "28:1--28:20", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3321515", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3321515", abstract = "We introduce the Colored Abstract Simplicial Complex library (CASC): a new, modern, and header-only C++ library that provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively, CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata-aware decimation algorithm, which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kronbichler:2019:FMF, author = "Martin Kronbichler and Katharina Kormann", title = "Fast Matrix-Free Evaluation of Discontinuous {Galerkin} Finite Element Operators", journal = j-TOMS, volume = "45", number = "3", pages = "29:1--29:40", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3325864", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3325864", abstract = "We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators. It relies on fast quadrature with sum factorization on quadrilateral and hexahedral meshes, targeting general weak forms of linear and nonlinear partial differential equations. Different algorithms and data structures are compared in an in-depth performance analysis. The implementations of the local integrals are optimized by vectorization over several cells and faces and an even-odd decomposition of the one-dimensional interpolations. Up to 60\% of the arithmetic peak on Intel Haswell, Broadwell, and Knights Landing processors is reached when running from caches and up to 40\% of peak when also considering the access to vectors from main memory. On 2$ \times $14 Broadwell cores, the throughput is up to 2.2 billion unknowns per second for the 3D Laplacian and up to 4 billion unknowns per second for the 3D advection on affine geometries, close to a simple copy operation at 4.7 billion unknowns per second. Our experiments show that MPI ghost exchange has a considerable impact on performance and we present strategies to mitigate this effect. Finally, various options for evaluating geometry terms and their performance are discussed. Our implementations are publicly available through the deal.II finite element library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Johansson:2019:CHF, author = "Fredrik Johansson", title = "Computing Hypergeometric Functions Rigorously", journal = j-TOMS, volume = "45", number = "3", pages = "30:1--30:26", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3328732", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3328732", abstract = "We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions $_0 F_1$, $_1 F_1$, $_2 F_1$, and $_2 F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and argument, and, by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function $_p F_q$ and computation of high-order parameter derivatives.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Dieguez:2019:TPR, author = "Adri{\'a}n P. Di{\'e}guez and Margarita Amor and Ram{\'o}n Doallo", title = "Tree Partitioning Reduction: A New Parallel Partition Method for Solving Tridiagonal Systems", journal = j-TOMS, volume = "45", number = "3", pages = "31:1--31:26", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3328731", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3328731", abstract = "Solving tridiagonal linear-equation systems is a fundamental computing kernel in a wide range of scientific and engineering applications, and its computation can be modeled with parallel algorithms. These parallel solvers are typically designed to compute problems whose data fit in a common shared-memory space where all the cores taking part in the computation have access. However, when the problem size is large, data cannot be entirely stored in the common shared-memory space, and a high number of high-latency communications are performed. One alternative is to partition the problem among different memory spaces. At this point, conventional parallel algorithms do not facilitate the partition of computation in independent tiles, since each reduction depends on equations that may be in different tiles. This article proposes an algorithm based on a tree reduction, called the Tree Partitioning Reduction (TPR) method, which partitions the problem into independent slices that can be partially computed in parallel within different common shared-memory spaces. The TPR method can be implemented for any parallel and distributed programming paradigm. Furthermore, in this work, TPR is efficiently implemented for CUDA GPUs to solve large size problems, providing highly competitive performance results with respect to existing packages, being, on average, 22.03$ \times $ faster than CUSPARSE.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cartis:2019:IFR, author = "Coralia Cartis and Jan Fiala and Benjamin Marteau and Lindon Roberts", title = "Improving the Flexibility and Robustness of Model-based Derivative-free Optimization Solvers", journal = j-TOMS, volume = "45", number = "3", pages = "32:1--32:41", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3338517", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3338517", abstract = "We present two software packages for derivative-free optimization (DFO): DFO-LS for nonlinear least-squares problems and Py-BOBYQA for general objectives, both with optional bound constraints. Inspired by the Gauss--Newton method, DFO-LS constructs simplified linear regression models for the residuals and allows flexible initialization for expensive problems, whereby it can begin making progress after as few as two objective evaluations. Numerical results show DFO-LS can gain reasonable progress on some medium-scale problems with fewer objective evaluations than is needed for one gradient evaluation. DFO-LS has improved robustness to noise, allowing sample averaging, regression-based model construction, and multiple restart strategies with an auto-detection mechanism. Our extensive numerical experimentation shows that restarting the solver when stagnation is detected is a cheap and effective mechanism for achieving robustness, with superior performance over sampling and regression techniques. The package Py-BOBYQA is a Python implementation of BOBYQA (Powell 2009), with novel features such as the implementation of robustness to noise strategies. Our numerical experiments show that Py-BOBYQA is comparable to or better than existing general DFO solvers for noisy problems. In our comparisons, we introduce an adaptive accuracy measure for data profiles of noisy functions, striking a balance between measuring the true and the noisy objective improvement.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pardue:2019:AEP, author = "Juliette Pardue and Andrey Chernikov", title = "{Algorithm 995}: An Efficient Parallel Anisotropic {Delaunay} Mesh Generator for Two-Dimensional Finite Element Analysis", journal = j-TOMS, volume = "45", number = "3", pages = "33:1--33:30", month = jul, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3301321", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 31 08:06:08 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3301321", abstract = "A bottom-up approach to parallel anisotropic mesh generation is presented by building a mesh generator starting from the basic operations of vertex insertion and Delaunay triangles. Applications focusing on high-lift design or dynamic stall, or numerical methods and modeling test cases, still focus on two-dimensional domains. This automated parallel mesh generation approach can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field. The anisotropy requirement adds a level of complexity to a parallel meshing algorithm by making computation depend on the local alignment of elements, which in turn is dictated by geometric boundaries and the density functions- one-dimensional spacing functions generated from an exponential distribution. This approach yields computational savings in mesh generation and flow solution through well-shaped anisotropic triangles instead of isotropic triangles. The validity of the meshes is shown through solution characteristic comparisons to verified reference solutions. A 79\% parallel weak scaling efficiency on 1,024 distributed memory nodes, and a 72\% parallel efficiency over the fastest sequential isotropic mesh generator on 512 distributed memory nodes, is shown through numerical experiments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ito:2019:ABS, author = "Naoki Ito and Sunyoung Kim and Masakazu Kojima and Akiko Takeda and Kim-Chuan Toh", title = "{Algorithm 996}: {BBCPOP}: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems With Binary, Box, and Complementarity Constraints", journal = j-TOMS, volume = "45", number = "3", pages = "34:1--34:16", month = jul, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3309988", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 31 08:06:08 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3309988", abstract = "The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box, and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a doubly nonnegative relaxation of the POP, and then solves the COP by applying the bisection and projection method. The COP is expressed with a linear objective function and constraints described as a single hyperplane and two cones, which are the Cartesian product of positive semidefinite cones and a polyhedral cone induced from the BBC constraints. BBCPOP aims to compute a tight lower bound for the optimal value of a large-scale POP in the class that is beyond the comfort zone of existing software packages. The robustness, reliability, and efficiency of BBCPOP are demonstrated in comparison to the state-of-the-art software SDP package SDPNAL+ on randomly generated sparse POPs of degree 2 and 3 with up to a few thousands variables, and ones of degree from 5 to 8 with up to a few hundred variables. Numerical results on BBC-constrained POPs that arise from quadratic assignment problems are also reported. The software package BBCPOP is available at https://sites.google.com/site/bbcpop1/.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Speck:2019:APP, author = "Robert Speck", title = "{Algorithm 997}: {pySDC}-Prototyping Spectral Deferred Corrections", journal = j-TOMS, volume = "45", number = "3", pages = "35:1--35:23", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3310410", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3310410", abstract = "In this article, we present the Python framework pySDC for solving collocation problems with spectral deferred correction (SDC) methods and their time-parallel variant PFASST, the parallel full approximation scheme in space and time. pySDC features many implementations of SDC and PFASST, from simple implicit timestepping to high-order implicit-explicit or multi-implicit splitting and multilevel SDCs. The software package comes with many different, preimplemented examples and has seven tutorials to help new users with their first steps. Time parallelism is implemented either in an emulated way for debugging and prototyping or using MPI for benchmarking. The code is fully documented and tested using continuous integration, including most results of previous publications. Here, we describe the structure of the code by taking two different perspectives: those of the user and those of the developer. The first sheds light on the front-end, the examples, and the tutorials, and the second is used to describe the underlying implementation and the data structures. We show three different examples to highlight various aspects of the implementation, the capabilities, and the usage of pySDC. In addition, couplings to the FEniCS framework and PETSc, the latter including spatial parallelism with MPI, are described.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Agulhari:2019:ARL, author = "Cristiano M. Agulhari and Alexandre Felipe and Ricardo C. L. F. Oliveira and Pedro L. D. Peres", title = "{Algorithm 998}: The Robust {LMI} Parser --- a Toolbox to Construct {LMI} Conditions for Uncertain Systems", journal = j-TOMS, volume = "45", number = "3", pages = "36:1--36:25", month = aug, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3323925", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Sep 3 17:49:22 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3323925", abstract = "The ROLMIP (Robust LMI Parser) is a toolbox specialized in control theory for uncertain linear systems, built to work under MATLAB jointly with YALMIP, to ease the programming of sufficient Linear Matrix Inequality (LMI) conditions that, if feasible, assure the validity of parameter-dependent LMIs in the entire set of uncertainty considered. This article presents the new version of the ROLMIP toolbox, which was completely remodeled to provide a high-level user-friendly interface to cope with distinct uncertain domains (hypercube and multi-simplex) and to treat time-varying parameters in discrete- and continuous-time. By means of simple commands, the user is able to define polynomial matrices as well as to describe the desired parameter-dependent LMIs in an easy way, considerably reducing the programming time to end up with implementable LMI conditions. Therefore, ROLMIP helps the popularization of the state-of-the-art robust control methods for uncertain systems based on LMIs among graduate students, researchers, and engineers in control systems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{LucambioPerez:2019:WLS, author = "L. R. {Lucambio P{\'e}rez} and L. F. Prudente", title = "A {Wolfe} Line Search Algorithm for Vector Optimization", journal = j-TOMS, volume = "45", number = "4", pages = "37:1--37:23", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3342104", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3342104", abstract = "In a recent article, Lucambio P{\'e}rez and Prudente extended the Wolfe conditions for the vector-valued optimization. Here, we propose a line search algorithm for finding a step size satisfying the strong Wolfe conditions in the vector optimization setting. Well definedness and finite termination results are provided. We discuss practical aspects related to the algorithm and present some numerical experiments illustrating its applicability. Codes supporting this article are written in Fortran 90 and are freely available for download.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sagebaum:2019:HPD, author = "Max Sagebaum and Tim Albring and Nicolas R. Gauger", title = "High-Performance Derivative Computations using {CoDiPack}", journal = j-TOMS, volume = "45", number = "4", pages = "38:1--38:27", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3356900", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3356900", abstract = "There are several AD tools available that all implement different strategies for the reverse mode of AD. The most common strategies are primal value taping (implemented e.g. by ADOL-C) and Jacobian taping (implemented e.g. by Adept and dco/c++). Particularly for Jacobian taping, recent advances using expression templates make it very attractive for large scale software. However, the current implementations are either closed source or miss essential features and flexibility. Therefore, we present the new AD tool CoDiPack (Code Differentiation Package) in this paper. It is specifically designed for minimal memory consumption and optimal runtime, such that it can be used for the differentiation of large scale software. An essential part of the design of CoDiPack is the modular layout and the recursive data structures which not only allow the efficient implementation of the Jacobian taping approach but will also enable other approaches like the primal value taping or new research ideas. We will finally present the performance values of CoDiPack on a generic PDE example and on the SU2 code.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hisil:2019:KLF, author = "Huseyin Hisil and Joost Renes", title = "On {Kummer} Lines with Full Rational 2-torsion and Their Usage in Cryptography", journal = j-TOMS, volume = "45", number = "4", pages = "39:1--39:17", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3361680", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3361680", abstract = "A paper by Karati and Sarkar at Asiacrypt'17 has pointed out the potential for Kummer lines in genus 1, by observing that their SIMD-friendly arithmetic is competitive with the status quo. A more recent preprint explores the connection with (twisted) Edwards curves. In this article, we extend this work and significantly simplify the treatment of Karati and Sarkar. We show that their Kummer line is the x -line of a Montgomery curve translated by a point of order two, and exhibit a natural isomorphism to the y -line of a twisted Edwards curve. Moreover, we show that the Kummer line presented by Gaudry and Lubicz can be obtained via the action of a point of order two on the y -line of an Edwards curve. The maps connecting these curves and lines are all very simple. As a result, a cryptographic implementation can use the arithmetic that is optimal for its instruction set at negligible cost.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Flegar:2019:FCL, author = "Goran Flegar and Florian Scheidegger and Vedran Novakovi{\'c} and Giovani Mariani and Andr{\'e}s E. Tom{\'a}s and A. Cristiano I. Malossi and Enrique S. Quintana-Ort{\'\i}", title = "{FloatX}: A {C++} Library for Customized Floating-Point Arithmetic", journal = j-TOMS, volume = "45", number = "4", pages = "40:1--40:23", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3368086", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3368086", abstract = "We present FloatX (Float eXtended), a C ++ framework to investigate the effect of leveraging customized floating-point formats in numerical applications. FloatX formats are based on binary IEEE 754 with smaller significand and exponent bit counts specified by the user. Among other properties, FloatX facilitates an incremental transformation of the code, relies on hardware-supported floating-point types as back-end to preserve efficiency, and incurs no storage overhead. The article discusses in detail the design principles, programming interface, and datatype casting rules behind FloatX. Furthermore, it demonstrates FloatX's usage and benefits via several case studies from well-known numerical dense linear algebra libraries, such as BLAS and LAPACK; the Ginkgo library for sparse linear systems; and two neural network applications related with image processing and text recognition.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "40", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2019:CGG, author = "Robert C. Kirby and Lawrence Mitchell", title = "Code Generation for Generally Mapped Finite Elements", journal = j-TOMS, volume = "45", number = "4", pages = "41:1--41:23", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3361745", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See also replication report \cite{Lindquist:2019:RCR}.", URL = "https://dl.acm.org/citation.cfm?id=3361745", abstract = "Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite-element transformations in FInAT and hence into the Firedrake finite-element system. Numerical results evaluate the new elements, comparing them to existing methods for classical problems. For a second-order model problem, we find that new elements give smooth solutions at a mild increase in cost over standard Lagrange elements. For fourth-order problems, however, the newly enabled methods significantly outperform interior penalty formulations. We also give some advanced use cases, solving the nonlinear Cahn--Hilliard equation and some biharmonic eigenvalue problems (including Chladni plates) using C 1 discretizations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "41", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lindquist:2019:RCR, author = "Neil Lindquist", title = "Replicated Computational Results {(RCR)} Report for {``\booktitle{Code Generation for Generally Mapped Finite Elements}''}", journal = j-TOMS, volume = "45", number = "4", pages = "42:1--42:7", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3360984", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Kirby:2019:CGG}.", URL = "https://dl.acm.org/citation.cfm?id=3360984", abstract = "``\booktitle{Code Generation for Generally Mapped Finite Elements}'' includes performance results for the finite element methods discussed in that manuscript. The authors provided a Zenodo archive with the Firedrake components and dependencies used, as well as the scripts that generated the results. The software was installed on two similar platforms; then, new results were gathered and compared to the original results. After completing this process, the results have been deemed replicable by the reviewer.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "42", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Speleers:2019:ACM, author = "Hendrik Speleers", title = "{Algorithm 999}: {Computation} of Multi-Degree {B}-Splines", journal = j-TOMS, volume = "45", number = "4", pages = "43:1--43:15", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3321514", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3321514", abstract = "Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines with similar properties to standard B-splines. These basis functions are called multi-degree B-splines (or MDB-splines ). The construction relies on an extraction operator that represents all MDB-splines as linear combinations of local B-splines of different degrees. This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context of multi-degree splines. A M ATLAB implementation is provided to illustrate the computation and use of MDB-splines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "43", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2019:ASG, author = "Timothy A. Davis", title = "{Algorithm 1000}: {SuiteSparse:GraphBLAS}: Graph Algorithms in the Language of Sparse Linear Algebra", journal = j-TOMS, volume = "45", number = "4", pages = "44:1--44:25", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3322125", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3322125", abstract = "SuiteSparse:GraphBLAS is a full implementation of the GraphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. GraphBLAS provides a powerful and expressive framework for creating graph algorithms based on the elegant mathematics of sparse matrix operations on a semiring. An overview of the GraphBLAS specification is given, followed by a description of the key features and performance of its implementation in the SuiteSparse:GraphBLAS package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "44", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Burgel:2019:AIM, author = "Florian B{\"u}rgel and Kamil S. Kazimierski and Armin Lechleiter", title = "{Algorithm 1001}: {IPscatt} --- a {MATLAB} Toolbox for the Inverse Medium Problem in Scattering", journal = j-TOMS, volume = "45", number = "4", pages = "45:1--45:20", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3328525", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3328525", abstract = "IPscatt is a free, open-source MATLAB toolbox facilitating the solution for time-independent scattering (also known as time-harmonic scattering) in two- and three-dimensional settings. The toolbox has three main application cases: simulation of the scattered field for a given transmitter-receiver geometry; the generation of simulated data as well as the handling of the real-world data from Institute Fresnel; and the reconstruction of the contrast from several measured, scattered fields. In each case, a variety of options tailored to the needs of practitioners is provided. For example, the toolbox allows the simulation of the scattered near field as well as of the far field. Also, it provides methods for the modeling of the incident field as point sources as well as plane waves. Finally, many common geometries of transmitters and receivers are included out of the box. Regarding the reconstruction, the provided functions implement the regularization scheme that relies on a primal-dual algorithm and was introduced by F. B{\"u}rgel, K. S. Kazimierski, and A. Lechleiter [ Journal of Computational Physics 339 (2017), 1-30]. This article provides a survey of the mathematical concepts in scattering, connects them with the provided implementation, gives an overview of the software framework as well as its application areas, and compares it with existing software packages solving the same problem.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "45", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kara:2019:AGC, author = "G{\"o}k{\c{c}}ehan Kara and Can {\"O}zturan", title = "{Algorithm 1002}: {Graph} Coloring Based Parallel Push-relabel Algorithm for the Maximum Flow Problem", journal = j-TOMS, volume = "45", number = "4", pages = "46:1--46:28", month = dec, year = "2019", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3330481", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Dec 27 14:56:25 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/citation.cfm?id=3330481", abstract = "The maximum flow problem is one of the most common network flow problems. This problem involves finding the maximum possible amount of flow between two designated nodes on a network with arcs having flow capacities. The push-relabel algorithm is one of the fastest algorithms to solve this problem. We present a shared memory parallel push-relabel algorithm. Graph coloring is used to avoid collisions between threads for concurrent push and relabel operations. In addition, excess values of target nodes are updated using atomic instructions to prevent race conditions. The experiments show that our algorithm is competitive for wide graphs with low diameters. Results from three different data sets are included, computer vision problems, DIMACS challenge problems, and KaHIP partitioning problems. These are compared with existing push-relabel and pseudoflow implementations. We show that high speedup rates are possible using our coloring based parallelization technique on sparse networks. However, we also observe that the pseudoflow algorithm runs faster than the push-relabel algorithm on dense and long networks.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "46", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Huang:2020:SAR, author = "Jianyu Huang and Chenhan D. Yu and Robert A. van de Geijn", title = "{Strassen}'s Algorithm Reloaded on {GPUs}", journal = j-TOMS, volume = "46", number = "1", pages = "1:1--1:22", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3372419", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3372419", abstract = "Conventional Graphics Processing Unit (GPU) implementations of Strassen's algorithm (Strassen) rely on the existing high-performance matrix multiplication (gemm), trading space for time. As a result, such approaches can only achieve practical speedup or relatively large, ``squarish'' matrices due to the extra memory overhead, and their usages are limited due to the considerable workspace. We present novel Strassen primitives for GPUs that can be composed to generate a family of Strassen algorithms. Our algorithms utilize both the memory and thread hierarchies on GPUs, reusing shared memory and register files inherited from gemm, fusing additional operations, and avoiding extra workspace. We further exploit intra- and inter-kernel parallelism by batching, streaming, and employing atomic operations. We develop a performance model for NVIDIA Volta GPUs to select the appropriate blocking parameters and predict the performance for gemm and Strassen. Overall, our 1-level Strassen can achieve up to $ 1.11 \times $ speedup with a crossover point as small as 1,536 compared to cublasSgemm on a NVIDIA Tesla V100 GPU. With additional workspace, our 2-level Strassen can achieve $ 1.19 \times $ speedup with a crossover point at 7,680.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Arevalo:2020:SPA, author = "Carmen Ar{\'e}valo and Erik Jonsson-Glans and Josefine Olander and Monica Selva Soto and Gustaf S{\"o}derlind", title = "A Software Platform for Adaptive High Order Multistep Methods", journal = j-TOMS, volume = "46", number = "1", pages = "2:1--2:17", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3372159", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3372159", abstract = "We present a software package, Modes, offering $h$-adaptive and $p$-adaptive linear multistep methods for first order initial value problems in ordinary differential equations. The implementation is based on a new parametric, grid-independent representation of multistep methods [Ar{\'e}valo and S{\"o}derlind 2017]. Parameters are supplied for over 60 methods. For nonstiff problems, all maximal order methods ($ p = k$ for explicit and $ p = k + 1$ for implicit methods) are supported. For stiff computation, implicit methods of order $ p = k$ are included.\par A collection of step-size controllers based on digital filters is provided, generating smooth step-size sequences offering improved computational stability. Controllers may be selected to match method and problem classes. A new system for automatic order control is also provided for designated families of multistep methods, offering simultaneous $h$- and $p$-adaptivity.\par Implemented as a Matlab toolbox, the software covers high order computations with linear multistep methods within a unified, generic framework. Computational experiments show that the new software is competitive and offers qualitative improvements. Modes is available for downloading and is primarily intended as a platform for developing a new generation of state-of-the-art multistep solvers, as well as for true ceteris paribus evaluation of algorithmic components. This also enables method comparisons within a single implementation environment.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cui:2020:HON, author = "Tao Cui and Wei Leng and Huaqing Liu and Linbo Zhang and Weiying Zheng", title = "High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface", journal = j-TOMS, volume = "46", number = "1", pages = "3:1--3:18", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3372144", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3372144", abstract = "Given a shape regular tetrahedron and a curved surface that is defined implicitly by a nonlinear level set function and divides the tetrahedron into two sub-domains, a general-purpose, robust, and high-order numerical algorithm is proposed in this article for computing both volume integrals in the sub-domains and surface integrals on their common boundary. The algorithm uses a direct approach that decomposes 3D volume integrals or 2D surface integrals into multiple 1D integrals and computes the 1D integrals with Gaussian quadratures. It only requires finding roots of univariate nonlinear functions in given intervals and evaluating the integrand, the level set function, and the gradient of the level set function at given points. It can achieve arbitrarily high accuracy by increasing the orders of Gaussian quadratures, and it does not need extra a priori knowledge about the integrand and the level set function. The code for the algorithm is freely available in the open-source finite element toolbox Parallel Hierarchical Grid (PHG) and can serve as a basic building block for implementing 3D high-order numerical algorithms involving implicit interfaces or boundaries.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Betcke:2020:PAG, author = "Timo Betcke and Matthew W. Scroggs and Wojciech 'Smigaj", title = "Product Algebras for {Galerkin} Discretisations of Boundary Integral Operators and their Applications", journal = j-TOMS, volume = "46", number = "1", pages = "4:1--4:22", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3368618", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3368618", abstract = "Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Abhyankar:2020:PDL, author = "Shrirang Abhyankar and Getnet Betrie and Daniel Adrian Maldonado and Lois C. Mcinnes and Barry Smith and Hong Zhang", title = "{PETSc DMNetwork}: a Library for Scalable Network {PDE}-Based Multiphysics Simulations", journal = j-TOMS, volume = "46", number = "1", pages = "5:1--5:24", month = apr, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3344587", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 29 08:09:49 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3344587", abstract = "We present DMNetwork, a high-level package included in the PETSc library for the simulation of multiphysics phenomena over large-scale networked systems. The library aims at applications that have networked structures such as those in electrical, gas, nd water distribution systems. DMNetwork provides data and topology management, parallelization for multiphysics systems over a network, and hierarchical and composable solvers to exploit the problem structure. DMNetwork eases the simulation development cycle by providing the necessary infrastructure through simple abstractions to define and query the network components. This article presents the design of DMNetwork, illustrates its user interface, and demonstrates its ability to solve multiphysics systems, such as an electric circuit, a network of power grid and water subnetworks, and transient hydraulic systems over large networks with more than 2 billion variables on extreme-scale computers using up to 30,000 processors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Luporini:2020:APD, author = "Fabio Luporini and Mathias Louboutin and Michael Lange and Navjot Kukreja and Philipp Witte and Jan H{\"u}ckelheim and Charles Yount and Paul H. J. Kelly and Felix J. Herrmann and Gerard J. Gorman", title = "Architecture and Performance of {Devito}, a System for Automated Stencil Computation", journal = j-TOMS, volume = "46", number = "1", pages = "6:1--6:28", month = apr, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3374916", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Apr 29 08:09:49 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3374916", abstract = "Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of generating highly optimized code given symbolic equations expressed in Python, specialized in, but not limited to, affine (stencil) codes. The lowering process --- from mathematical equations down to C++ code --- is performed by the Devito compiler through a series of intermediate representations. Several performance optimizations are introduced, including advanced common sub-expressions elimination, tiling, and parallelization. Some of these are obtained through well-established stencil optimizers, integrated in the backend of the Devito compiler. The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented. The effectiveness of such performance optimizations is demonstrated using operators drawn from seismic imaging applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2020:AMG, author = "Timothy A. Davis and William W. Hager and Scott P. Kolodziej and S. Nuri Yeralan", title = "{Algorithm 1003}: {Mongoose}, a Graph Coarsening and Partitioning Library", journal = j-TOMS, volume = "46", number = "1", pages = "7:1--7:18", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3337792", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3337792", abstract = "Partitioning graphs is a common and useful operation in many areas, from parallel computing to VLSI design to sparse matrix algorithms. In this article, we introduce Mongoose, a multilevel hybrid graph partitioning algorithm and library. Building on previous work in multilevel partitioning frameworks and combinatoric approaches, we introduce novel stall-reducing and stall-free coarsening strategies, as well as an efficient hybrid algorithm leveraging (1) traditional combinatoric methods and (2) continuous quadratic programming formulations. We demonstrate how this new hybrid algorithm outperforms either strategy in isolation, and we also compare Mongoose to METIS and demonstrate its effectiveness on large and social networking (power law) graphs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reizenstein:2020:AIL, author = "Jeremy F. Reizenstein and Benjamin Graham", title = "{Algorithm 1004}: The {Iisignature} Library: Efficient Calculation of Iterated-Integral Signatures and Log Signatures", journal = j-TOMS, volume = "46", number = "1", pages = "8:1--8:21", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3371237", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3371237", abstract = "Iterated-integral signatures and log signatures are sequences calculated from a path that characterizes its shape. They originate from the work of K. T. Chen and have become important through Terry Lyons's theory of differential equations driven by rough paths, which is an important developing area of stochastic analysis. They have applications in statistics and machine learning, where there can be a need to calculate finite parts of them quickly for many paths. We introduce the signature and the most basic information (displacement and signed areas) that it contains. We present algorithms for efficiently calculating these signatures. For log signatures this requires consideration of the structure of free Lie algebras. We benchmark the performance of the algorithms. The methods are implemented in C++ and released as a Python extension package, which also supports differentiation. In combination with a machine learning library (Tensorflow, PyTorch, or Theano), this allows end-to-end learning of neural networks involving signatures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jonasson:2020:AFS, author = "Kristjan Jonasson and Sven Sigurdsson and Hordur Freyr Yngvason and Petur Orri Ragnarsson and Pall Melsted", title = "{Algorithm 1005}: {Fortran} Subroutines for Reverse Mode Algorithmic Differentiation of {BLAS} Matrix Operations", journal = j-TOMS, volume = "46", number = "1", pages = "9:1--9:20", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3382191", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3382191", abstract = "A set of Fortran subroutines for reverse mode algorithmic (or automatic) differentiation of the basic linear algebra subprograms (BLAS) is presented. This is preceded by a description of the mathematical tools used to obtain the formulae of these derivatives, with emphasis on special matrices supported by the BLAS: triangular, symmetric, and band. All single and double precision BLAS derivatives have been implemented, together with the Cholesky factorization from Linear Algebra Package (LAPACK). The subroutines are written in Fortran 2003 with a Fortran 77 interface to allow use from C and C++, as well as dynamic languages such as R, Python, Matlab, and Octave. The subroutines are all implemented by calling BLAS, thereby attaining fast runtime. Timing results show derivative runtimes that are about twice those of the corresponding BLAS, in line with theory. The emphasis is on reverse mode because it is more important for the main application that we have in mind, numerical optimization. Two examples are presented, one dealing with the least squares modeling of groundwater, and the other dealing with the maximum likelihood estimation of the parameters of a vector autoregressive time series. The article contains comprehensive tables of formulae for the BLAS derivatives as well as for several non-BLAS matrix operations commonly used in optimization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Abergel:2020:AFA, author = "R{\'e}my Abergel and Lionel Moisan", title = "{Algorithm 1006}: Fast and Accurate Evaluation of a Generalized Incomplete Gamma Function", journal = j-TOMS, volume = "46", number = "1", pages = "10:1--10:24", month = mar, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3365983", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 7 10:39:23 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365983", abstract = "We present a computational procedure to evaluate the integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for $ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p > 0 $, which generalizes the lower $ (x = 0) $ and upper $ (y = + \infty) $ incomplete gamma functions. To allow for large values of $x$, $y$, and $p$ while avoiding under\slash overflow issues in the standard double precision floating point arithmetic, we use an explicit normalization that is much more efficient than the classical ratio with the complete gamma function. The generalized incomplete gamma function is estimated with continued fractions, with integrations by parts, or, when $ x \approx y$, with the Romberg numerical integration algorithm. We show that the accuracy reached by our algorithm improves a recent state-of-the-art method by two orders of magnitude, and it is essentially optimal considering the limitations imposed by floating point arithmetic. Moreover, the admissible parameter range of our algorithm $ (0 \leq p, x, y \leq 10^{15})$ is much larger than competing algorithms, and its robustness is assessed through massive usage in an image processing application.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brisebarre:2020:EAS, author = "Nicolas Brisebarre and Mioara Joldes and Jean-Michel Muller and Ana-Maria Nanes and Joris Picot", title = "Error Analysis of Some Operations Involved in the {Cooley--Tukey Fast Fourier Transform}", journal = j-TOMS, volume = "46", number = "2", pages = "11:1--11:27", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3368619", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3368619", abstract = "We are interested in obtaining error bounds for the classical Cooley--Tukey fast Fourier transform algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. For that purpose, we also give some results on the relative error of the complex multiplication by a root of unity, and on the largest value that can take the real or imaginary part of one term of the fast Fourier transform of a vector $x$, assuming that all terms of $x$ have real and imaginary parts less than some value $b$.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Herrmann:2020:HRF, author = "Julien Herrmann and Guillaume Pallez (Aupy)", title = "{H-Revolve}: a Framework for Adjoint Computation on Synchronous Hierarchical Platforms", journal = j-TOMS, volume = "46", number = "2", pages = "12:1--12:25", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3378672", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378672", abstract = "We study the problem of checkpointing strategies for adjoint computation on synchronous hierarchical platforms, specifically computational platforms with several levels of storage with different writing and reading costs. When reversing a large adjoint chain, choosing which data to checkpoint and where is a critical decision for the overall performance of the computation. We introduce H-Revolve, an optimal algorithm for this problem. We make it available in a public Python library along with the implementation of several state-of-the-art algorithms for the variant of the problem with two levels of storage. We provide a detailed description of how one can use this library in an adjoint computation software in the field of automatic differentiation or backpropagation. Finally, we evaluate the performance of H-Revolve and other checkpointing heuristics though an extensive campaign of simulation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ballard:2020:TPC, author = "Grey Ballard and Alicia Klinvex and Tamara G. Kolda", title = "{TuckerMPI}: a Parallel {C++\slash MPI} Software Package for Large-scale Data Compression via the {Tucker} Tensor Decomposition", journal = j-TOMS, volume = "46", number = "2", pages = "13:1--13:31", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3378445", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378445", abstract = "Our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100 s of nodes (1,000 s of MPI processes), achieving compression ratios between 100 and 200,000$ \times $, which equates to 99--99.999\% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Marques:2020:BSC, author = "Osni Marques and James Demmel and Paulo B. Vasconcelos", title = "Bidiagonal {SVD} Computation via an Associated Tridiagonal Eigenproblem", journal = j-TOMS, volume = "46", number = "2", pages = "14:1--14:25", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3361746", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3361746", abstract = "The Singular Value Decomposition (SVD) is widely used in numerical analysis and scientific computing applications, including dimensionality reduction, data compression and clustering, and computation of pseudo-inverses. In many cases, a crucial part of the SVD of a general matrix is to find the SVD of an associated bidiagonal matrix. This article discusses an algorithm to compute the SVD of a bidiagonal matrix through the eigenpairs of an associated symmetric tridiagonal matrix. The algorithm enables the computation of only a subset of singular values and corresponding vectors, with potential performance gains. The article focuses on a sequential version of the algorithm, and discusses special cases and implementation details. The implementation, called BDSVDX, has been included in the LAPACK library. We use a large set of bidiagonal matrices to assess the accuracy of the implementation, both in single and double precision, as well as to identify potential shortcomings. The results show that BDSVDX can be up to three orders of magnitude faster than existing algorithms, which are limited to the computation of a full SVD. We also show comparisons of an implementation that uses BDSVDX as a building block for the computation of the SVD of general matrices.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Frison:2020:BAB, author = "Gianluca Frison and Tommaso Sartor and Andrea Zanelli and Moritz Diehl", title = "The {BLAS API} of {BLASFEO}: Optimizing Performance for Small Matrices", journal = j-TOMS, volume = "46", number = "2", pages = "15:1--15:36", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3378671", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/java2020.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378671", abstract = "Basic Linear Algebra Subroutines For Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and other applications targeting relatively small matrices. BLASFEO defines an application programming interface (API) which uses a packed matrix format as its native format. This format is analogous to the internal memory buffers of optimized BLAS, but it is exposed to the user and it removes the packing cost from the routine call. For matrices fitting in cache, BLASFEO outperforms optimized BLAS implementations, both open source and proprietary. This article investigates the addition of a standard BLAS API to the BLASFEO framework, and proposes an implementation switching between two or more algorithms optimized for different matrix sizes. Thanks to the modular assembly framework in BLASFEO, tailored linear algebra kernels with mixed column- and panel-major arguments are easily developed. This BLAS API has lower performance than the BLASFEO API, but it nonetheless outperforms optimized BLAS and especially LAPACK libraries for matrices fitting in cache. Therefore, it can boost a wide range of applications, where standard BLAS and LAPACK libraries are employed and the matrix size is moderate. In particular, this article investigates the benefits in scientific programming languages such as Octave, SciPy, and Julia.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Michail:2020:JJL, author = "Dimitrios Michail and Joris Kinable and Barak Naveh and John V. Sichi", title = "{JGraphT} --- a {Java} Library for Graph Data Structures and Algorithms", journal = j-TOMS, volume = "46", number = "2", pages = "16:1--16:29", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3381449", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/java2020.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381449", abstract = "Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze, and query graphs are crucial in an era where large-scale spatial, societal, and economic network data are abundantly available. One such package is JGraphT, programming library that contains very efficient and generic graph data structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability, and performance in mind. A distinctive feature of this library is its ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks, including transportation, social, and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism, matching and flow problems, approximation algorithms for NP-hard problems such as independent set and the traveling salesman problem, and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial products, as well as noncommercial and academic research projects.\par In this work, we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus several similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amos:2020:AQQ, author = "Brandon D. Amos and David R. Easterling and Layne T. Watson and William I. Thacker and Brent S. Castle and Michael W. Trosset", title = "{Algorithm 1007}: {QNSTOP} --- Quasi-{Newton} Algorithm for Stochastic Optimization", journal = j-TOMS, volume = "46", number = "2", pages = "17:1--17:20", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3374219", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3374219", abstract = "QNSTOP consists of serial and parallel (OpenMP) Fortran 2003 codes for the quasi-Newton stochastic optimization method of Castle and Trosset for stochastic search problems. A complete description of QNSTOP for both local search with stochastic objective and global search with ``noisy'' deterministic objective is given here, to the best of our knowledge, for the first time. For stochastic search problems, some convergence theory exists for particular algorithmic choices and parameter values. Both the parallel driver subroutine, which offers several parallel decomposition strategies, and the serial driver subroutine can be used for local stochastic search or global deterministic search, based on an input switch. Some performance data for computational systems biology problems is given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Casado:2020:AMN, author = "Jose Maria Varas Casado and Rob Hewson", title = "{Algorithm 1008}: {Multicomplex} Number Class for {Matlab}, with a Focus on the Accurate Calculation of Small Imaginary Terms for Multicomplex Step Sensitivity Calculations", journal = j-TOMS, volume = "46", number = "2", pages = "18:1--18:26", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3378542", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378542", abstract = "A Matlab class for multicomplex numbers was developed with particular attention paid to the robust and accurate handling of small imaginary components. This is primarily to allow the class to be used to obtain n order derivative information using the multicomplex step method for, among other applications, gradient-based optimization and optimum control problems. The algebra of multicomplex numbers is described, as is its accurate computational implementation, considering small term approximations and the identification of principal values. The implementation of the method in Matlab is studied, and a class definition is constructed. This new class definition enables Matlab to handle $n$-order multicomplex numbers and perform arithmetic functions. It was found that with this method, the step size could be arbitrarily decreased toward machine precision. Use of the method to obtain up to the seventh derivative of functions is presented, as is timing data to demonstrate the efficiency of the class implementation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hawkins:2020:AMO, author = "Stuart C. Hawkins", title = "{Algorithm 1009}: {MieSolver} --- an Object-Oriented {Mie} Series Software for Wave Scattering by Cylinders", journal = j-TOMS, volume = "46", number = "2", pages = "19:1--19:28", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3381537", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381537", abstract = "MieSolver provides an efficient solver for the problem of wave propagation through a heterogeneous configuration of nonidentical circular cylinders. MieSolver allows great flexibility in the physical properties of each cylinder, and the cylinders may have opaque or penetrable cores, as well as an arbitrary number of penetrable layers. The wave propagation is governed by the two-dimensional Helmholtz equation and models electromagnetic, acoustic, and elastic waves. The solver is based on the Mie series solution for scattering by a single circular cylinder and hence is numerically stable and highly accurate. We demonstrate the accuracy of our software with extensive numerical experiments over a wide range of frequencies (about five orders of magnitude) and up to 60 cylinders.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Orellana:2020:ABE, author = "Alberto Giacomo Orellana and Cristiano {De Michele}", title = "{Algorithm 1010}: {Boosting} Efficiency in Solving Quartic Equations with No Compromise in Accuracy", journal = j-TOMS, volume = "46", number = "2", pages = "20:1--20:28", month = jun, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3386241", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Jun 12 07:37:53 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See improvement \cite{DeMichele:2022:RAB}.", URL = "https://dl.acm.org/doi/abs/10.1145/3386241", abstract = "Aiming to provide a very accurate, efficient, and robust quartic equation solver for physical applications, we have proposed an algorithm that builds on the previous works of P. Strobach and S. L. Shmakov. It is based on the decomposition of the quartic polynomial into two quadratics, whose coefficients are first accurately estimated by handling carefully numerical errors and afterward refined through the use of the Newton--Raphson method. Our algorithm is very accurate in comparison with other state-of-the-art solvers that can be found in the literature, but (most importantly) it turns out to be very efficient according to our timing tests. A crucial issue for us is the robustness of the algorithm, i.e., its ability to cope with the detrimental effect of round-off errors, no matter what set of quartic coefficients is provided in a practical application. In this respect, we extensively tested our algorithm in comparison to other quartic equation solvers both by considering specific extreme cases and by carrying out a statistical analysis over a very large set of quartics. Our algorithm has also been heavily tested in a physical application, i.e., simulations of hard cylinders, where it proved its absolute reliability as well as its efficiency.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lange:2020:FRF, author = "Marko Lange and Siegfried M. Rump", title = "Faithfully Rounded Floating-point Computations", journal = j-TOMS, volume = "46", number = "3", pages = "21:1--21:20", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3290955", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3290955", abstract = "We present a pair arithmetic for the four basic operations and square root. It can be regarded as a simplified, more-efficient double-double arithmetic. The central assumption on the underlying arithmetic is the first standard model for error analysis for operations on a discrete set of real numbers. Neither do we require a floating-point grid nor a rounding to nearest property. Based on that, we define a relative rounding error unit $u$ and prove rigorous error bounds for the computed result of an arbitrary arithmetic expression depending on $u$, the size of the expression, and possibly a condition measure. In the second part of this note, we extend the error analysis by examining requirements to ensure faithfully rounded outputs and apply our results to IEEE 754 standard conform floating-point systems. For a class of mathematical expressions, using an IEEE 754 standard conform arithmetic with base $ \beta $, the result is proved to be faithfully rounded for up to $ 1 / \sqrt {\beta u - 2}$ operations. Our findings cover a number of previously published algorithms to compute faithfully rounded results, among them Horner's scheme, products, sums, dot products, or Euclidean norm. Beyond that, several other problems can be analyzed, such as polynomial interpolation, orientation problems, Householder transformations, or the smallest singular value of Hilbert matrices of large size.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ahrens:2020:AER, author = "Peter Ahrens and James Demmel and Hong Diep Nguyen", title = "Algorithms for Efficient Reproducible Floating Point Summation", journal = j-TOMS, volume = "46", number = "3", pages = "22:1--22:49", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3389360", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3389360", abstract = "We define ``reproducibility'' as getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should not affect the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociative floating point addition, makes reproducibility challenging even for summation, or operations like the BLAS. We describe a ``reproducible accumulator'' data structure (the ``binned number'') and associated algorithms to reproducibly sum binary floating point numbers, independent of summation order. We use a subset of the IEEE Floating Point Standard 754-2008 and bitwise operations on the standard representations in memory. Our approach requires only one read-only pass over the data, and one reduction in parallel, using a 6-word reproducible accumulator (more words can be used for higher accuracy), enabling standard tiling optimization techniques. Summing $n$ words with a 6-word reproducible accumulator requires approximately $ 9 n$ floating point operations (arithmetic, comparison, and absolute value) and approximately $ 3 n$ bitwise operations. The final error bound with a 6-word reproducible accumulator and our default settings can be up to 229 times smaller than the error bound for conventional (recursive) summation on ill-conditioned double-precision inputs", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accurate floating-point summation", } @Article{Aguirre-Mesa:2020:MLC, author = "Andres M. Aguirre-Mesa and Manuel J. Garcia and Harry Millwater", title = "{MultiZ}: a Library for Computation of High-order Derivatives Using Multicomplex or Multidual Numbers", journal = j-TOMS, volume = "46", number = "3", pages = "23:1--23:30", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3378538", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3378538", abstract = "Multicomplex and multidual numbers are two generalizations of complex numbers with multiple imaginary axes, useful for numerical computation of derivatives with machine precision. The similarities between multicomplex and multidual algebras allowed us to create a unified library to use either one for sensitivity analysis. This library can be used to compute arbitrary order derivates of functions of a single variable or multiple variables. The storage of matrix representations of multicomplex and multidual numbers is avoided using a combination of one-dimensional resizable arrays and an indexation method based on binary bitwise operations. To provide high computational efficiency and low memory usage, the multiplication of hypercomplex numbers up to sixth order is carried out using a hard-coded algorithm. For higher hypercomplex orders, the library uses by default a multiplication method based on binary bitwise operations. The computation of algebraic and transcendental functions is achieved using a Taylor series approximation. Fortran and Python versions were developed, and extensions to other languages are self-evident.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Avramidis:2020:SOS, author = "Eleftherios Avramidis and Marta Lalik and Ozgur E. Akman", title = "{SODECL}: an Open-Source Library for Calculating Multiple Orbits of a System of Stochastic Differential Equations in Parallel", journal = j-TOMS, volume = "46", number = "3", pages = "24:1--24:21", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3385076", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3385076", abstract = "Stochastic differential equations (SDEs) are widely used to model systems affected by random processes. In general, the analysis of an SDE model requires numerical solutions to be generated many times over multiple parameter combinations. However, this process often requires considerable computational resources to be practicable. Due to the embarrassingly parallel nature of the task, devices such as multi-core processors and graphics processing units (GPUs) can be employed for acceleration.\par Here, we present SODECL (https://github.com/avramidis/sodecl), a software library that utilizes such devices to calculate multiple orbits of an SDE model. To evaluate the acceleration provided by SODECL, we compared the time required to calculate multiple orbits of an exemplar stochastic model when one CPU core is used, to the time required when using all CPU cores or a GPU. In addition, to assess scalability, we investigated how model size affected execution time on different parallel compute devices.\par Our results show that when using all 32 CPU cores of a high-end high-performance computing node, the task is accelerated by a factor of up to 6.7, compared to when using a single CPU core. Executing the task on a high-end GPU yielded accelerations of up to 4.5, compared to a single CPU core.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Agamawi:2020:CCS, author = "Yunus M. Agamawi and Anil V. Rao", title = "{CGPOPS}: a {C++} Software for Solving Multiple-Phase Optimal Control Problems Using Adaptive {Gaussian} Quadrature Collocation and Sparse Nonlinear Programming", journal = j-TOMS, volume = "46", number = "3", pages = "25:1--25:38", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3390463", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3390463", abstract = "A general-purpose C++ software program called CGPOPS is described for solving multiple-phase optimal control problems using adaptive direct orthogonal collocation methods. The software employs a Legendre--Gauss--Radau direct orthogonal collocation method o transcribe the continuous optimal control problem into a large sparse nonlinear programming problem (NLP). A class of hp mesh refinement methods are implemented that determine the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy tolerance. The software is interfaced with the open source Newton NLP solver IPOPT. All derivatives required by the NLP solver are computed via central finite differencing, bicomplex-step derivative approximations, hyper-dual derivative approximations, or automatic differentiation. The key components of the software are described in detail, and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a transitional platform to solve a wide variety of complex constrained optimal control problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2020:APE, author = "Brisa N. Davis and Randall J. LeVeque", title = "Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic {PDEs} Using {Clawpack}", journal = j-TOMS, volume = "46", number = "3", pages = "26:1--26:28", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3392775", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3392775", abstract = "Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can selectively refine areas to track discontinuities in the solution. The open source Clawpack software implements block-structured AMR to refine around propagating waves in the AMRClaw package. For problems where the solution must be computed over a large domain but is only of interest in a small area, this approach often refines waves that will not impact the target area. We seek a method that enables the identification and refinement of only the waves that will influence the target area.\par Here we show that solving the time-dependent adjoint equation and using a suitable inner product allows for a more precise refinement of the relevant waves. We present the adjoint methodology in general and give details on the implementation of this method in AMRClaw. Examples and a computational performance analysis for linear acoustics equations are presented. The adjoint method is compared to AMR methods already available in AMRClaw, and the advantages and disadvantages are discussed. The approach presented here is implemented in Clawpack, in Version 5.6.1, and code for all examples presented is archived on Github.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bleyer:2020:AFR, author = "Jeremy Bleyer", title = "Automating the Formulation and Resolution of Convex Variational Problems: Applications from Image Processing to Computational Mechanics", journal = j-TOMS, volume = "46", number = "3", pages = "27:1--27:33", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3393881", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3393881", abstract = "Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms, which require well-designed optimization algorithms for their resolution. The present manuscript presents the Python package called fenics\_optim built on top of the FEniCS finite element software, which enables one to automate the formulation and resolution of various convex variational problems. Formulating such a problem relies on FEniCS domain-specific language and the representation of convex functions, in particular, non-smooth ones, in the conic programming framework. The discrete formulation of the corresponding optimization problems hinges on the finite element discretization capabilities offered by FEniCS, while their numerical resolution is carried out by the interior-point solver Mosek. Through various illustrative examples, we show that convex optimization problems can be formulated using only a few lines of code, discretized in a very simple manner, and solved extremely efficiently.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ewart:2020:PES, author = "Timoth{\'e}e Ewart and Francesco Cremonesi and Felix Sch{\"u}rmann and Fabien Delalondre", title = "Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function $ e^x $", journal = j-TOMS, volume = "46", number = "3", pages = "28:1--28:22", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3408893", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3408893", abstract = "The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. In addition, we have completed this work with a factorization method, which is surprisingly neglected in the literature. This work focuses on out-of-order Intel processors, amongst others, of which computational units are available. Moreover, we applied our work on the elementary function $e^x$ that requires, in the current implementation, an evaluation of a polynomial of degree 10 for a satisfying precision and performance. Our results show that the factorization scheme is the fastest in benchmarks, and that latency and throughput are intrinsically dependent on each other on superscalar architecture.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mejstrik:2020:AII, author = "Thomas Mejstrik", title = "{Algorithm 1011}: {Improved} Invariant Polytope Algorithm and Applications", journal = j-TOMS, volume = "46", number = "3", pages = "29:1--29:26", month = sep, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3408891", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Sep 26 07:28:19 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3408891", abstract = "In several papers of 2013--2016, Guglielmi and Protasov made a breakthrough in the problem of the joint spectral radius computation, developing the invariant polytope algorithm that for most matrix families finds the exact value of the joint spectral radius. This algorithm found many applications in problems of functional analysis, approximation theory, combinatorics, and so on. In this article, we propose a modification of the invariant polytope algorithm making it roughly 3 times faster (single threaded), suitable for higher dimensions, and parallelise it. The modified version works for most matrix families of dimensions up to 25, for non-negative matrices up to 3,000. In addition, we introduce a new, fast algorithm, called modified Gripenberg algorithm, for computing good lower bounds for the joint spectral radius. The corresponding examples and statistics of numerical results are provided. Several applications of our algorithms are presented. In particular, we find the exact values of the regularity exponents of Daubechies wavelets up to order 42 and the capacities of codes that avoid certain difference patterns.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drmac:2020:NNA, author = "Zlatko Drma{\v{c}} and Ivana {\v{S}}ain Glibi{\'c}", title = "New Numerical Algorithm for Deflation of Infinite and Zero Eigenvalues and Full Solution of Quadratic Eigenvalue Problems", journal = j-TOMS, volume = "46", number = "4", pages = "30:1--30:32", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3401831", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3401831", abstract = "This article presents a new method for computing all eigenvalues and eigenvectors of quadratic matrix pencil $ Q (\lambda) = \lambda^2 M + \lambda C + K $. It is an upgrade of the quadeig algorithm by Hammarling et al., which attempts to reveal and remove by deflation a certain number of zero and infinite eigenvalues before QZ iterations. Proposed modifications of the quadeig framework are designed to enhance backward stability and to make the process of deflating infinite and zero eigenvalues more numerically robust. In particular, careful preprocessing allows scaling invariant\slash component-wise backward error and thus a better condition number. Further, using an upper triangular version of the Kronecker canonical form enables deflating additional infinite eigenvalues, in addition to those inferred from the rank of M. Theoretical analysis and empirical evidence from thorough testing of the software implementation confirm superior numerical performances of the proposed method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Thies:2020:PPH, author = "Jonas Thies and Melven R{\"o}hrig-Z{\"o}llner and Nigel Overmars and Achim Basermann and Dominik Ernst and Georg Hager and Gerhard Wellein", title = "{PHIST}: a Pipelined, Hybrid-Parallel Iterative Solver Toolkit", journal = j-TOMS, volume = "46", number = "4", pages = "31:1--31:26", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3402227", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3402227", abstract = "The increasing complexity of hardware and software environments in high-performance computing poses big challenges on the development of sustainable and hardware-efficient numerical software. This article addresses these challenges in the context of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Burstedde:2020:PTA, author = "Carsten Burstedde", title = "Parallel Tree Algorithms for {AMR} and Non-Standard Data Access", journal = j-TOMS, volume = "46", number = "4", pages = "32:1--32:31", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3401990", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3401990", abstract = "We introduce several parallel algorithms operating on a distributed forest of adaptive quadtrees/octrees. They are targeted at large-scale applications relying on data layouts that are more complex than required for standard finite elements, such as hp -. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pinto:2020:VSS, author = "Severiano Gonz{\'a}lez Pinto and Domingo Hern{\'a}ndez Abreu and Juan Ignacio Montijano", title = "Variable Step-Size Control Based on Two-Steps for {Radau IIA} Methods", journal = j-TOMS, volume = "46", number = "4", pages = "33:1--33:24", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3408892", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3408892", abstract = "Two-step embedded methods of order s based on s -stage Radau IIA formulas are considered for the variable step-size integration of stiff differential equations. These embedded methods are aimed at local error control and are computed through a linear \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Uphoff:2020:YAT, author = "Carsten Uphoff and Michael Bader", title = "Yet Another Tensor Toolbox for Discontinuous {Galerkin} Methods and Other Applications", journal = j-TOMS, volume = "46", number = "4", pages = "34:1--34:40", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3406835", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3406835", abstract = "The numerical solution of partial differential equations is at the heart of many grand challenges in supercomputing. Solvers based on high-order discontinuous Galerkin (DG) discretisation have been shown to scale on large supercomputers with excellent \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Williams-Young:2020:SSS, author = "David B. Williams-Young and Paul G. Beckman and Chao Yang", title = "A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation", journal = j-TOMS, volume = "46", number = "4", pages = "35:1--35:31", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3409571", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3409571", abstract = "The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and $k$-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Spring:2020:FCS, author = "Braegan S. Spring and Eric Polizzi and Ahmed H. Sameh", title = "A Feature-complete {SPIKE} Dense Banded Solver", journal = j-TOMS, volume = "46", number = "4", pages = "36:1--36:35", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3410153", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3410153", abstract = "This article presents a parallel, effective, and feature-complete recursive SPIKE algorithm that achieves near feature-parity with the standard linear algebra package banded linear system solver. First, we present a flexible parallel implementation of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Barabasz:2020:EAI, author = "Barbara Barabasz and Andrew Anderson and Kirk M. Soodhalter and David Gregg", title = "Error Analysis and Improving the Accuracy of {Winograd} Convolution for Deep Neural Networks", journal = j-TOMS, volume = "46", number = "4", pages = "37:1--37:33", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3412380", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3412380", abstract = "Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is used in many DNN software frameworks. However,. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chang:2020:ADI, author = "Tyler H. Chang and Layne T. Watson and Thomas C. H. Lux and Ali R. Butt and Kirk W. Cameron and Yili Hong", title = "{Algorithm 1012}: {DELAUNAYSPARSE}: Interpolation via a Sparse Subset of the {Delaunay} Triangulation in Medium to High Dimensions", journal = j-TOMS, volume = "46", number = "4", pages = "38:1--38:20", month = nov, year = "2020", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3422818", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 14 07:15:52 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See remark \cite{Chang:2024:RAC}.", URL = "https://dl.acm.org/doi/10.1145/3422818", abstract = "DELAUNAYSPARSE contains both serial and parallel codes written in Fortran 2003 (with OpenMP) for performing medium- to high-dimensional interpolation via the Delaunay triangulation. To accommodate the exponential growth in the size of the Delaunay \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2021:SLS, author = "Jennifer Scott and Miroslav Tuma", title = "Strengths and Limitations of Stretching for Least-squares Problems with Some Dense Rows", journal = j-TOMS, volume = "47", number = "1", pages = "1:1--1:25", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3412559", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3412559", abstract = "We recently introduced a sparse stretching strategy for handling dense rows that can arise in large-scale linear least-squares problems and make such problems challenging to solve. Sparse stretching is designed to limit the amount of fill within the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lebrun-Grandie:2021:APP, author = "D. Lebrun-Grandi{\'e} and A. Prokopenko and B. Turcksin and S. R. Slattery", title = "{ArborX}: a Performance Portable Geometric Search Library", journal = j-TOMS, volume = "47", number = "1", pages = "2:1--2:15", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3412558", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3412558", abstract = "Searching for geometric objects that are close in space is a fundamental component of many applications. The performance of search algorithms comes to the forefront as the size of a problem increases both in terms of total object count as well as in the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Huang:2021:HHP, author = "Hua Huang and Xin Xing and Edmond Chow", title = "{H2Pack}: High-performance {$ H^2 $} Matrix Package for Kernel Matrices Using the Proxy Point Method", journal = j-TOMS, volume = "47", number = "1", pages = "3:1--3:29", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3412850", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3412850", abstract = "Dense kernel matrices represented in H$^2$ matrix format typically require less storage and have faster matrix--vector multiplications than when these matrices are represented in the standard dense format. In this article, we present H2Pack, a high-performance, shared-memory library for constructing and operating with $ H^2$ matrix representations for kernel matrices defined by non-oscillatory, translationally invariant kernel functions. Using a hybrid analytic-algebraic compression method called the proxy point method, H2Pack can efficiently construct an $ H^2$ matrix representation with linear computational complexity. Storage and matrix--vector multiplication also have linear complexity. H2Pack also introduces the concept of ``partially admissible blocks'' for $ H^2$ matrices to make $ H^2$ matrix--vector multiplication mathematically identical to the fast multipole method (FMM) if analytic expansions are used. We optimize H2Pack from both the algorithm and software perspectives. Compared to existing FMM libraries, H2Pack generally has much faster $ H^2$ matrix--vector multiplications, since the proxy point method is more effective at producing block low-rank approximations than the analytic methods used in FMM. As a tradeoff, $ H^2$ matrix construction in H2Pack is typically more expensive than the setup cost in FMM libraries. Thus, H2Pack is ideal for applications that need a large number of matrix--vector multiplications for a given configuration of data points.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Renard:2021:GAF, author = "Yves Renard and Konstantinos Poulios", title = "{GetFEM}: Automated {FE} Modeling of Multiphysics Problems Based on a Generic Weak Form Language", journal = j-TOMS, volume = "47", number = "1", pages = "4:1--4:31", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3412849", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3412849", abstract = "This article presents the major mathematical and implementation features of a weak form language (GWFL) for an automated finite-element (FE) solution of partial differential equation systems. The language is implemented in the GetFEM framework and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Oliveira:2021:EBM, author = "I. F. D. Oliveira and R. H. C. Takahashi", title = "An Enhancement of the Bisection Method Average Performance Preserving Minmax Optimality", journal = j-TOMS, volume = "47", number = "1", pages = "5:1--5:24", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3423597", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3423597", abstract = "We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kempf:2021:ACG, author = "Dominic Kempf and Ren{\'e} He{\ss} and Steffen M{\"u}thing and Peter Bastian", title = "Automatic Code Generation for High-performance Discontinuous {Galerkin} Methods on Modern Architectures", journal = j-TOMS, volume = "47", number = "1", pages = "6:1--6:31", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3424144", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3424144", abstract = "SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software's sustainability. In this publication, we solve this sustainability and performance \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Clevenger:2021:FPA, author = "Thomas C. Clevenger and Timo Heister and Guido Kanschat and Martin Kronbichler", title = "A Flexible, Parallel, Adaptive Geometric Multigrid Method for {FEM}", journal = j-TOMS, volume = "47", number = "1", pages = "7:1--7:27", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3425193", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3425193", abstract = "We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by using a space \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Arroyo:2021:ARI, author = "Daisy Arroyo and Xavier Emery", title = "{Algorithm 1013}: an {R} Implementation of a Continuous Spectral Algorithm for Simulating Vector {Gaussian} Random Fields in {Euclidean} Spaces", journal = j-TOMS, volume = "47", number = "1", pages = "8:1--8:25", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3421316", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3421316", abstract = "A continuous spectral algorithm and computer routines in the R programming environment that enable the simulation of second-order stationary and intrinsic (i.e., with second-order stationary increments or generalized increments) vector Gaussian random in Euclidean spaces are presented. The simulation is obtained by computing a weighted sum of cosine and sine waves, with weights that depend on the matrix-valued spectral density associated with the spatial correlation structure of the random field to simulate. The computational cost is proportional to the number of locations targeted for simulation, below that of sequential, matrix decomposition and discrete spectral algorithms. Also, the implementation is versatile, as there is no restriction on the number of vector components, workspace dimension, number and geometrical configuration of the target locations. The computer routines are illustrated with synthetic examples and statistical testing is proposed to check the normality of the distribution of the simulated random field or of its generalized increments. A by-product of this work is a spectral representation of spherical, cubic, penta, Askey, J-Bessel, Cauchy, Laguerre, hypergeometric, iterated exponential, gamma, and stable covariance models in the $d$-dimensional Euclidean space..", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Borges:2021:AIA, author = "Carlos F. Borges", title = "{Algorithm 1014}: an Improved Algorithm for {\tt hypot(x,y)}", journal = j-TOMS, volume = "47", number = "1", pages = "9:1--9:12", month = jan, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3428446", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jan 7 10:31:04 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3428446", abstract = "We develop fast and accurate algorithms for evaluating $ \sqrt {x^2 + y^2} $ for two floating-point numbers $x$ and $y$. Library functions that perform this computation are generally named {\tt hypot(x,y)}. We compare five approaches that we will develop in this article to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will investigate the accuracy of our algorithms by simulation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sohier:2021:CIS, author = "Devan Sohier and Pablo {De Oliveira Castro} and Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re and Eric Petit and Olivier Jamond", title = "Confidence Intervals for Stochastic Arithmetic", journal = j-TOMS, volume = "47", number = "2", pages = "10:1--10:33", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3432184", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3432184", abstract = "Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results.\par In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and code\aster.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Soylu:2021:IAC, author = "G{\"u}ltekin Soylu", title = "Improved Arithmetic of Complex Fans", journal = j-TOMS, volume = "47", number = "2", pages = "11:1--11:10", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3434400", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3434400", abstract = "Complex fans are sets of complex numbers whose magnitudes and angles range in closed intervals. The fact that the sum of two fans is a disordered shape gives rise to the need for computational methods to find the minimal enclosing fan. Cases where the sum of two fans contains the origin of the complex plane as a boundary point are of special interest. The result of the addition is then enclosed by circles in current methods, but under certain circumstances this turns out to be an overestimate. The focus of this article is the diagnosis and treatment of such cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{VanZee:2021:SMD, author = "Field G. {Van Zee} and Devangi N. Parikh and Robert A. {Van De Geijn}", title = "Supporting Mixed-domain Mixed-precision Matrix Multiplication within the {BLIS} Framework", journal = j-TOMS, volume = "47", number = "2", pages = "12:1--12:26", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3402225", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3402225", abstract = "We approach the problem of implementing mixed-datatype support within the general matrix multiplication (gemm) operation of the BLAS-like Library Instantiation Software framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or complex values. Another factor of complexity, whereby the matrix product and accumulation are allowed to take place in a precision different from the storage precisions of either A or B, is also discussed. We first break the problem into orthogonal dimensions, considering the mixing of domains separately from mixing precisions. Support for all combinations of matrix operands stored in either the real or complex domain is mapped out by enumerating the cases and describing an implementation approach for each. Supporting all combinations of storage and computation precisions is handled by typecasting the matrices at key stages of the computation --- during packing and/or accumulation, as needed. Several optional optimizations are also documented. Performance results gathered on a 56-core Marvell ThunderX2 and a 52-core Intel Xeon Platinum demonstrate that high performance is mostly preserved, with modest slowdowns incurred from unavoidable typecast instructions. The mixed-datatype implementation confirms that combinatorial intractability is avoided, with the framework relying on only two assembly microkernels to implement 128 datatype combinations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Daas:2021:RKS, author = "Hussam {Al Daas} and Laura Grigori and Pascal H{\'e}non and Philippe Ricoux", title = "Recycling {Krylov} Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems", journal = j-TOMS, volume = "47", number = "2", pages = "13:1--13:30", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3439746", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3439746", abstract = "This article presents deflation strategies related to recycling Krylov subspace methods for solving one or a sequence of linear systems of equations. Besides well-known strategies of deflation, Ritz-, and harmonic Ritz-based deflation, we introduce a Singular Value Decomposition based deflation technique. We consider the recycling in two contexts: recycling the Krylov subspace between the restart cycles and recycling a deflation subspace when the matrix changes in a sequence of linear systems. Numerical experiments on real-life reservoir simulation demonstrate the impact of our proposed strategy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Flegar:2021:APB, author = "Goran Flegar and Hartwig Anzt and Terry Cojean and Enrique S. Quintana-Ort{\'\i}", title = "Adaptive Precision Block-{Jacobi} for High Performance Preconditioning in the {Ginkgo} Linear Algebra Software", journal = j-TOMS, volume = "47", number = "2", pages = "14:1--14:28", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3441850", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3441850", abstract = "The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator --- like a preconditioner --- in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Osborn:2021:RCR, author = "Sarah Osborn", title = "Replicated Computational Results {(RCR)} Report for {``Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software''}", journal = j-TOMS, volume = "47", number = "2", pages = "15:1--15:4", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3446000", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3446000", abstract = "The article by Flegar et al. titled ``Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software'' presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library.\par In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo's Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Villa:2021:HES, author = "Umberto Villa and Noemi Petra and Omar Ghattas", title = "{hIPPYlib}: an Extensible Software Framework for Large-Scale Inverse Problems Governed by {PDEs}: {Part I}: Deterministic Inversion and Linearized {Bayesian} Inference", journal = j-TOMS, volume = "47", number = "2", pages = "16:1--16:34", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3428447", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3428447", abstract = "We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also discussed. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Theisen:2021:FTM, author = "Lambert Theisen and Manuel Torrilhon", title = "{fenicsR13}: a Tensorial Mixed Finite Element Solver for the Linear {R13} Equations Using the {FEniCS} Computing Platform", journal = j-TOMS, volume = "47", number = "2", pages = "17:1--17:29", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3442378", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3442378", abstract = "We present a mixed finite element solver for the linearized regularized 13-moment equations of non-equilibrium gas dynamics. The Python implementation builds upon the software tools provided by the FEniCS computing platform. We describe a new tensorial approach utilizing the extension capabilities of FEniCS' Unified Form Language to define required differential operators for tensors above second degree. The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse. Using the software abstraction levels provided by the Unified Form Language allows an almost one-to-one correspondence between the underlying mathematics and the resulting source code. Test cases support the correctness of the proposed method using validation with exact solutions. To justify the usage of extended gas flow models, we discuss typical application cases involving rarefaction effects. We provide the documented and validated solver publicly.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Guthe:2021:AFS, author = "Stefan Guthe and Daniel Thuerck", title = "{Algorithm 1015}: a Fast Scalable Solver for the Dense Linear (Sum) Assignment Problem", journal = j-TOMS, volume = "47", number = "2", pages = "18:1--18:27", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3442348", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3442348", abstract = "We present a new algorithm for solving the dense linear (sum) assignment problem and an efficient, parallel implementation that is based on the successive shortest path algorithm. More specifically, we introduce the well-known epsilon scaling approach used in the Auction algorithm to approximate the dual variables of the successive shortest path algorithm prior to solving the assignment problem to limit the complexity of the path search. This improves the runtime by several orders of magnitude for hard-to-solve real-world problems, making the runtime virtually independent of how hard the assignment is to find. In addition, our approach allows for using accelerators and/or external compute resources to calculate individual rows of the cost matrix. This enables us to solve problems that are larger than what has been reported in the past, including the ability to efficiently solve problems whose cost matrix exceeds the available systems memory. To our knowledge, this is the first implementation that is able to solve problems with more than one trillion arcs in less than 100 hours on a single machine.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hahne:2021:APP, author = "Jens Hahne and Stephanie Friedhoff and Matthias Bolten", title = "{Algorithm 1016}: {PyMGRIT}: a {Python} Package for the Parallel-in-time Method {MGRIT}", journal = j-TOMS, volume = "47", number = "2", pages = "19:1--19:22", month = apr, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3446979", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 27 08:23:28 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3446979", abstract = "In this article, we introduce the Python framework PyMGRIT, which implements the multigrid-reduction-in-time (MGRIT) algorithm for solving (non-)linear systems arising from the discretization of time-dependent problems. The MGRIT algorithm is a reduction-based iterative method that allows parallel-in-time simulations, i.e., calculating multiple time steps simultaneously in a simulation, using a time-grid hierarchy. The PyMGRIT framework includes many different variants of the MGRIT algorithm, ranging from different multigrid cycle types and relaxation schemes, various coarsening strategies, including time-only and space-time coarsening, and the ability to utilize different time integrators on different levels in the multigrid hierarchy. The comprehensive documentation with tutorials and many examples and the fully documented code allow an easy start into the work with the package. The functionality of the code is ensured by automated serial and parallel tests using continuous integration. PyMGRIT supports serial runs suitable for prototyping and testing of new approaches, as well as parallel runs using the Message Passing Interface (MPI). In this manuscript, we describe the implementation of the MGRIT algorithm in PyMGRIT and present the usage from both a user and a developer point of view. Three examples illustrate different aspects of the package itself, especially running tests with pure time parallelism, as well as space-time parallelism through the coupling of PyMGRIT with PETSc or Firedrake.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Eswar:2021:PPL, author = "Srinivas Eswar and Koby Hayashi and Grey Ballard and Ramakrishnan Kannan and Michael A. Matheson and Haesun Park", title = "{PLANC}: Parallel Low-rank Approximation with Nonnegativity Constraints", journal = j-TOMS, volume = "47", number = "3", pages = "20:1--20:37", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3432185", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3432185", abstract = "We consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Abdelfattah:2021:SBB, author = "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra and Mark Gates and Azzam Haidar and Sven Hammarling and Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek and Stanimire Tomov and Mawussi Zounon", title = "A Set of Batched Basic Linear Algebra Subprograms and {LAPACK} Routines", journal = j-TOMS, volume = "47", number = "3", pages = "21:1--21:23", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3431921", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3431921", abstract = "This article describes a standard API for a set of Batched Basic Linear Algebra Subprograms (Batched BLAS or BBLAS). The focus is on many independent BLAS operations on small matrices that are grouped together and processed by a single routine, called a Batched BLAS routine. The matrices are grouped together in uniformly sized groups, with just one group if all the matrices are of equal size. The aim is to provide more efficient, but portable, implementations of algorithms on high-performance many-core platforms. These include multicore and many-core CPU processors, GPUs and coprocessors, and other hardware accelerators with floating-point compute facility. As well as the standard types of single and double precision, we also include half and quadruple precision in the standard. In particular, half precision is used in many very large scale applications, such as those associated with machine learning.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Barthels:2021:LAG, author = "Henrik Barthels and Christos Psarras and Paolo Bientinesi", title = "{Linnea}: Automatic Generation of Efficient Linear Algebra Programs", journal = j-TOMS, volume = "47", number = "3", pages = "22:1--22:26", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3446632", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3446632", abstract = "The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for matrix computations (e.g., Matlab, Eigen) internally use optimized kernels such as those provided by BLAS and LAPACK; however, their translation algorithms are often too simplistic and thus lead to a suboptimal use of said kernels, resulting in significant performance losses. To combine the productivity offered by high-level languages, and the performance of low-level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem; as output, it returns an efficient sequence of calls to high-performance kernels. Linnea uses a custom best-first search algorithm to find a first solution in less than a second, and increasingly better solutions when given more time. In 125 test problems, the code generated by Linnea almost always outperforms Matlab, Julia, Eigen, and Armadillo, with speedups up to and exceeding $ 10 \times $.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Campos:2021:NMP, author = "Carmen Campos and Jose E. Roman", title = "{NEP}: a Module for the Parallel Solution of Nonlinear Eigenvalue Problems in {SLEPc}", journal = j-TOMS, volume = "47", number = "3", pages = "23:1--23:29", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3447544", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3447544", abstract = "SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. Over the past few years, we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These problems can be defined by means of a matrix-valued function that depends nonlinearly on a single scalar parameter. We do not consider the particular case of polynomial eigenvalue problems (which are implemented in a different module in SLEPc) and focus here on rational eigenvalue problems and other general nonlinear eigenproblems involving square roots or any other nonlinear function. The article discusses how the NEP module has been designed to fit the needs of applications and provides a description of the available solvers, including some implementation details such as parallelization. Several test problems coming from real applications are used to evaluate the performance and reliability of the solvers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pruua:2021:FMP, author = "Zdenek Pruua and Nicki Holighaus and Peter Balazs", title = "Fast Matching Pursuit with Multi-{Gabor} Dictionaries", journal = j-TOMS, volume = "47", number = "3", pages = "24:1--24:20", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3447958", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3447958", abstract = "Finding the best K-sparse approximation of a signal in a redundant dictionary is an NP-hard problem. Suboptimal greedy matching pursuit algorithms are generally used for this task. In this work, we present an acceleration technique and an implementation of the matching pursuit algorithm acting on a multi-Gabor dictionary, i.e., a concatenation of several Gabor-type time-frequency dictionaries, each of which consists of translations and modulations of a possibly different window and time and frequency shift parameters. The technique is based on pre-computing and thresholding inner products between atoms and on updating the residual directly in the coefficient domain, i.e., without the round-trip to the signal domain. Since the proposed acceleration technique involves an approximate update step, we provide theoretical and experimental results illustrating the convergence of the resulting algorithm. The implementation is written in C (compatible with C99 and C++11), and we also provide Matlab and GNU Octave interfaces. For some settings, the implementation is up to 70 times faster than the standard Matching Pursuit Toolkit.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Farrell:2021:PST, author = "Patrick E. Farrell and Matthew G. Knepley and Lawrence Mitchell and Florian Wechsung", title = "{PCPATCH}: Software for the Topological Construction of Multigrid Relaxation Methods", journal = j-TOMS, volume = "47", number = "3", pages = "25:1--25:22", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3445791", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3445791", abstract = "Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gau{\ss}--Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lyu:2021:FFA, author = "Xing-long Lyu and Tiexiang Li and Tsung-ming Huang and Jia-wei Lin and Wen-wei Lin and Sheng Wang", title = "{FAME}: Fast Algorithms for {Maxwell}'s Equations for Three-dimensional Photonic Crystals", journal = j-TOMS, volume = "47", number = "3", pages = "26:1--26:24", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3446329", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3446329", abstract = "In this article, we propose the Fast Algorithms for Maxwell's Equations (FAME) package for solving Maxwell's equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee's discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only $ 0.33 $ and $ 3.6 \times 10^{-3} $ seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lakhmiri:2021:HHO, author = "Dounia Lakhmiri and S{\'e}bastien {Le Digabel} and Christophe Tribes", title = "{HyperNOMAD}: Hyperparameter Optimization of Deep Neural Networks Using Mesh Adaptive Direct Search", journal = j-TOMS, volume = "47", number = "3", pages = "27:1--27:27", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3450975", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3450975", abstract = "The performance of deep neural networks is highly sensitive to the choice of the hyperparameters that define the structure of the network and the learning process. When facing a new application, tuning a deep neural network is a tedious and time-consuming process that is often described as a ``dark art.'' This explains the necessity of automating the calibration of these hyperparameters. Derivative-free optimization is a field that develops methods designed to optimize time-consuming functions without relying on derivatives. This work introduces the HyperNOMAD package, an extension of the NOMAD software that applies the MADS algorithm [7] to simultaneously tune the hyperparameters responsible for both the architecture and the learning process of a deep neural network (DNN). This generic approach allows for an important flexibility in the exploration of the search space by taking advantage of categorical variables. HyperNOMAD is tested on the MNIST, Fashion-MNIST, and CIFAR-10 datasets and achieves results comparable to the current state of the art.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Slak:2021:MCL, author = "Jure Slak and Gregor Kosec", title = "{Medusa}: a {C++} Library for Solving {PDEs} Using Strong Form Mesh-free Methods", journal = j-TOMS, volume = "47", number = "3", pages = "28:1--28:25", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3450966", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3450966", abstract = "Medusa, a novel library for implementation of non-particle strong form mesh-free methods, such as GFDM or RBF-FD, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection, and stencil weight computation. Many different algorithms exist for each part and the possible combinations offer a plethora of possibilities for improvements of solution procedures that are far from fully understood. As a consequence there are still many unanswered questions in the mesh-free community resulting in vivid ongoing research in the field. Medusa implements the core mesh-free elements as independent blocks, which offers users great flexibility in experimenting with the method they are developing, as well as easily comparing it with other existing methods. The article describes the chosen abstractions and their usage, illustrates aspects of the philosophy and design, offers some executions time benchmarks and demonstrates the application of the library on cases from linear elasticity and fluid flow in irregular 2D and 3D domains.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Skrabanek:2021:AFR, author = "Pavel Skrab{\'a}nek and Nat{\'a}lia Mart{\'\i}nkov{\'a}", title = "{Algorithm 1017}: \pkg{fuzzyreg}: an {R} Package for Fitting Fuzzy Regression Models", journal = j-TOMS, volume = "47", number = "3", pages = "29:1--29:18", month = jun, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3451389", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sun Jun 27 07:42:02 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3451389", abstract = "Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Farrell:2021:IAR, author = "Patrick E. Farrell and Robert C. Kirby and Jorge Marchena-Men{\'e}ndez", title = "Irksome: Automating {Runge--Kutta} Time-stepping for Finite Element Methods", journal = j-TOMS, volume = "47", number = "4", pages = "30:1--30:26", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3466168", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3466168", abstract = "While implicit Runge--Kutta (RK) methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebraic system at each time step are frequently cited as impediments. We present Irksome, a high-level library for manipulating UFL (Unified Form Language) expressions of semidiscrete variational forms to obtain UFL expressions for the coupled Runge--Kutta stage equations at each time step. Irksome works with the Firedrake package to enable the efficient solution of the resulting coupled algebraic systems. Numerical examples confirm the efficacy of the software and our solver techniques for various problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Daversin-Catty:2021:AAA, author = "C{\'e}cile Daversin-Catty and Chris N. Richardson and Ada J. Ellingsrud and Marie E. Rognes", title = "Abstractions and Automated Algorithms for Mixed Domain Finite Element Methods", journal = j-TOMS, volume = "47", number = "4", pages = "31:1--31:36", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3471138", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3471138", abstract = "Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology, physiology, biology, and fracture mechanics. Mixed dimensional PDEs are also commonly encountered when imposing non-standard conditions over a subspace of lower dimension, e.g., through a Lagrange multiplier. In this article, we present general abstractions and algorithms for finite element discretizations of mixed domain and mixed dimensional PDEs of codimension up to one (i.e., nD-mD with $ |n - m| \leq 1$). We introduce high-level mathematical software abstractions together with lower-level algorithms for expressing and efficiently solving such coupled systems. The concepts introduced here have also been implemented in the context of the FEniCS finite element software. We illustrate the new features through a range of examples, including a constrained Poisson problem, a set of Stokes-type flow models, and a model for ionic electrodiffusion.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Heltai:2021:PGI, author = "Luca Heltai and Wolfgang Bangerth and Martin Kronbichler and Andrea Mola", title = "Propagating Geometry Information to Finite Element Computations", journal = j-TOMS, volume = "47", number = "4", pages = "32:1--32:30", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3468428", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3468428", abstract = "The traditional workflow in continuum mechanics simulations is that a geometry description --- for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) tools --- forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original, ``underlying'' geometry. However, many modern techniques --- for example, adaptive mesh refinement and the use of higher order geometry approximation methods --- really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that nearly all geometry-related needs inside the simulators can be satisfied by just two ``primitives'': elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Munch:2021:HDE, author = "Peter Munch and Katharina Kormann and Martin Kronbichler", title = "\pkg{hyper.deal}: an Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations", journal = j-TOMS, volume = "47", number = "4", pages = "33:1--33:34", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3469720", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3469720", abstract = "This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper.deal are reported for high-dimensional advection problems and for the solution of the Vlasov--Poisson equation in up to six-dimensional phase space.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ramachandran:2021:PPB, author = "Prabhu Ramachandran and Aditya Bhosale and Kunal Puri and Pawan Negi and Abhinav Muta and A. Dinesh and Dileep Menon and Rahul Govind and Suraj Sanka and Amal S. Sebastian and Ananyo Sen and Rohan Kaushik and Anshuman Kumar and Vikas Kurapati and Mrinalgouda Patil and Deep Tavker and Pankaj Pandey and Chandrashekhar Kaushik and Arkopal Dutt and Arpit Agarwal", title = "{PySPH}: a {Python}-based Framework for Smoothed Particle Hydrodynamics", journal = j-TOMS, volume = "47", number = "4", pages = "34:1--34:38", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3460773", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3460773", abstract = "PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is generated from this high-level Python code and executed on either multiple cores, or on GPUs, seamlessly. It also supports distributed execution using MPI. PySPH supports a wide variety of SPH schemes and formulations. These include, incompressible and compressible fluid flow, elastic dynamics, rigid body dynamics, shallow water equations, and other problems. PySPH supports a variety of boundary conditions including mirror, periodic, solid wall, and inlet/outlet boundary conditions. The package is written to facilitate reuse and reproducibility. This article discusses the overall design of PySPH and demonstrates many of its features. Several example results are shown to demonstrate the range of features that PySPH provides.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Peres:2021:ECT, author = "Noah Peres and Andrew Ray Lee and Uri Keich", title = "Exactly Computing the Tail of the {Poisson}-Binomial Distribution", journal = j-TOMS, volume = "47", number = "4", pages = "35:1--35:19", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3460774", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3460774", abstract = "We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Blackman:2021:SLP, author = "David Blackman and Sebastiano Vigna", title = "Scrambled Linear Pseudorandom Number Generators", journal = j-TOMS, volume = "47", number = "4", pages = "36:1--36:32", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3460772", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3460772", abstract = "$F_2$-linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer from linear artifacts that show as failures in linearity-related statistical tests such as the binary-rank and the linear-complexity test. In this article, we give two new contributions. First, we introduce two new $F_2$-linear transformations that have been handcrafted to have good statistical properties and at the same time to be programmable very efficiently on superscalar processors, or even directly in hardware. Then, we describe some scramblers, that is, nonlinear functions applied to the state array that reduce or delete the linear artifacts, and propose combinations of linear transformations and scramblers that give extremely fast pseudorandom number generators of high quality. A novelty in our approach is that we use ideas from the theory of filtered linear-feedback shift registers to prove some properties of our scramblers, rather than relying purely on heuristics. In the end, we provide simple, extremely fast generators that use a few hundred bits of memory, have provable properties, and pass strong statistical tests.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Snyder:2021:CRA, author = "W. Van Snyder", title = "Corrigendum: {Remark on Algorithm 723: Fresnel Integrals}", journal = j-TOMS, volume = "47", number = "4", pages = "37:1--37:1", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3452336", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Snyder:1993:AFI}.", URL = "https://dl.acm.org/doi/10.1145/3452336", abstract = "There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals, which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Roth:2021:RAO, author = "{\'A}goston R{\'o}th", title = "Remark on {Algorithm 992}: an {OpenGL}- and {C++}-based Function Library for Curve and Surface Modeling in a Large Class of Extended {Chebyshev} Spaces", journal = j-TOMS, volume = "47", number = "4", pages = "38:1--38:2", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3461643", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Roth:2019:AOC}.", URL = "https://dl.acm.org/doi/10.1145/3461643", abstract = "We provide a number of corrections to the software component that accompanied this Algorithm submission [3]. An updated version of the code is available from the ACM Collected Algorithms site [1].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gia:2021:AFF, author = "Quoc T. Le Gia and Ming Li and Yu Guang Wang", title = "{Algorithm 1018}: \pkg{FaVeST} --- Fast Vector Spherical Harmonic Transforms", journal = j-TOMS, volume = "47", number = "4", pages = "39:1--39:24", month = dec, year = "2021", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3458470", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Sep 29 06:58:41 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3458470", abstract = "Vector spherical harmonics on the unit sphere of $ \mathbb {R}^3 $ have broad applications in geophysics, quantum mechanics, and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this article, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to $ N \log \sqrt {N} $ for $N$ number of evaluation points. The adjoint FaVeST, which evaluates a linear combination of vector spherical harmonics with a degree up to $ \dot M$ for $M$ evaluation points, has cost proportional to $ M \log \sqrt {M}$. Numerical examples of simulated tangent fields illustrate the accuracy, efficiency, and stability of FaVeST.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Yang:2022:GHP, author = "Carl Yang and Aydin Bulu{\c{c}} and John D. Owens", title = "\pkg{GraphBLAST}: a High-Performance Linear Algebra-based Graph Framework on the {GPU}", journal = j-TOMS, volume = "48", number = "1", pages = "1:1--1:51", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3466795", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3466795", abstract = "High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which allow graph algorithms to be expressed in a performant, succinct, composable, and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in ``GraphBLAST'', the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anzt:2022:GML, author = "Hartwig Anzt and Terry Cojean and Goran Flegar and Fritz G{\"o}bel and Thomas Gr{\"u}tzmacher and Pratik Nayak and Tobias Ribizel and Yuhsiang Mike Tsai and Enrique S. Quintana-Ort{\'\i}", title = "\pkg{Ginkgo}: a Modern Linear Operator Algebra Framework for High Performance Computing", journal = j-TOMS, volume = "48", number = "1", pages = "2:1--2:33", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3480935", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3480935", abstract = "In this article, we present Ginkgo, a modern C++ math library for scientific high performance computing. While classical linear algebra libraries act on matrix and vector objects, Ginkgo's design principle abstracts all functionality as ``linear operators,'' motivating the notation of a ``linear operator algebra library.'' Ginkgo's current focus is oriented toward providing sparse linear algebra functionality for high performance graphics processing unit (GPU) architectures, but given the library design, this focus can be easily extended to accommodate other algorithms and hardware architectures. We introduce this sophisticated software architecture that separates core algorithms from architecture-specific backends and provide details on extensibility and sustainability measures. We also demonstrate Ginkgo's usability by providing examples on how to use its functionality inside the MFEM and deal.ii finite element ecosystems. Finally, we offer a practical demonstration of Ginkgo's high performance on state-of-the-art GPU architectures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Balos:2022:RCR, author = "Cody J. Balos", title = "Reproduced Computational Results Report for {``\pkg{Ginkgo}: a Modern Linear Operator Algebra Framework for High Performance Computing''}", journal = j-TOMS, volume = "48", number = "1", pages = "3:1--3:7", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3480936", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3480936", abstract = "The article titled ``Ginkgo: A Modern Linear Operator Algebra Framework for High Performance Computing'' by Anzt et al. presents a modern, linear operator centric, C++ library for sparse linear algebra. Experimental results in the article demonstrate that Ginkgo is a flexible and user-friendly framework capable of achieving high-performance on state-of-the-art GPU architectures.In this report, the Ginkgo library is installed and a subset of the experimental results are reproduced. Specifically, the experiment that shows the achieved memory bandwidth of the Ginkgo Krylov linear solvers on NVIDIA A100 and AMD MI100 GPUs is redone and the results are compared to what presented in the published article. Upon completion of the comparison, the published results are deemed reproducible.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drmac:2022:ACS, author = "Zlatko Drmac and Ivana Sain Glibi{\'c}", title = "An Algorithm for the Complete Solution of the Quartic Eigenvalue Problem", journal = j-TOMS, volume = "48", number = "1", pages = "4:1--4:34", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3494528", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3494528", abstract = "The quartic eigenvalue problem $ (\lambda^4 A + \lambda^3 B + \lambda^2 C + \lambda^D + E) x = 0 $ naturally arises in a plethora of applications, such as when solving the Orr Sommerfeld equation in the stability analysis of the Poiseuille flow, in theoretical analysis and experimental design of locally resonant phononic plates, modeling a robot with electric motors in the joints, calibration of catadioptric vision system, or, for example, computation of the guided and leaky modes of a planar waveguide. This article proposes a new numerical method for the full solution (all eigenvalues and all left and right eigenvectors) that, starting with a suitable linearization, uses an initial, structure-preserving reduction designed to reveal and deflate a certain number of zero and infinite eigenvalues before the final linearization is forwarded to the QZ algorithm. The backward error in the reduction phase is bounded column wise in each coefficient matrix, which is advantageous if the coefficient matrices are graded. Numerical examples show that the proposed algorithm is capable of computing the eigenpairs with small residuals, and that it is competitive with the available state-of-the-art methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2022:CSU, author = "Jennifer Scott and Miroslav Tuma", title = "A Computational Study of Using Black-box {$ Q R $} Solvers for Large-scale Sparse-dense Linear Least Squares Problems", journal = j-TOMS, volume = "48", number = "1", pages = "5:1--5:24", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3494527", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3494527", abstract = "Large-scale overdetermined linear least squares problems arise in many practical applications. One popular solution method is based on the backward stable QR factorization of the system matrix A. This article focuses on sparse-dense least squares problems in which A is sparse except from a small number of rows that are considered dense. For large-scale problems, the direct application of a QR solver either fails because of insufficient memory or is unacceptably slow. We study several solution approaches based on using a sparse QR solver without modification, focussing on the case that the sparse part of A is rank deficient. We discuss partial matrix stretching and regularization and propose extending the augmented system formulation with iterative refinement for sparse problems to sparse-dense problems, optionally incorporating multi-precision arithmetic. In summary, our computational study shows that, before applying a black-box QR factorization, a check should be made for rows that are classified as dense and, if such rows are identified, then A should be split into sparse and dense blocks; a number of ways to use a black-box QR factorization to exploit this splitting are possible, with no single method found to be the best in all cases.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Porcelli:2022:EPS, author = "Margherita Porcelli and Philippe L. Toint", title = "Exploiting Problem Structure in Derivative Free Optimization", journal = j-TOMS, volume = "48", number = "1", pages = "6:1--6:25", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3474054", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3474054", abstract = "A structured version of derivative-free random pattern search optimization algorithms is introduced, which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems. This technique improves performance by orders of magnitude and makes it possible to solve large problems that otherwise are totally intractable by other derivative-free methods. A library of interpolation-based modelling tools is also described, which can be associated with the structured or unstructured versions of the initial pattern search algorithm. The use of the library further enhances performance, especially when associated with structure. The significant gains in performance associated with these two techniques are illustrated using a new freely-available release of the Brute Force Optimizer (BFO) package firstly introduced in [Porcelli and Toint 2017], which incorporates them. An interesting conclusion of the numerical results presented is that providing global structural information on a problem can result in significantly less evaluations of the objective function than attempting to building local Taylor-like models.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Huckelheim:2022:SSA, author = "Jan H{\"u}ckelheim and Laurent Hasco{\"e}t", title = "Source-to-Source Automatic Differentiation of {OpenMP} Parallel Loops", journal = j-TOMS, volume = "48", number = "1", pages = "7:1--7:32", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3472796", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3472796", abstract = "differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are crucial in optimization, uncertainty quantification, and machine learning. The computational cost to compute gradients is a common bottleneck in practice. For applications that are parallelized for multicore CPUs or GPUs using OpenMP, one also wishes to compute the gradients in parallel. We propose a framework to reason about the correctness of the generated derivative code, from which we justify our OpenMP extension to the differentiation model. We implement this model in the automatic differentiation tool Tapenade and present test cases that are differentiated following our extended differentiation procedure. Performance of the generated derivative programs in forward and reverse mode is better than sequential, although our reverse mode often scales worse than the input programs.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Crum:2022:BTS, author = "Justin Crum and Cyrus Cheng and David A. Ham and Lawrence Mitchell and Robert C. Kirby and Joshua A. Levine and Andrew Gillette", title = "Bringing Trimmed Serendipity Methods to Computational Practice in \pkg{Firedrake}", journal = j-TOMS, volume = "48", number = "1", pages = "8:1--8:19", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3490485", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3490485", abstract = "We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H1, H(curl), or H(div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Muller:2022:FDW, author = "Jean-Michel Muller and Laurence Rideau", title = "Formalization of Double-Word Arithmetic, and Comments on {``Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic''}", journal = j-TOMS, volume = "48", number = "1", pages = "9:1--9:24", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3484514", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3484514", abstract = "Recently, a complete set of algorithms for manipulating double-word numbers (some classical, some new) was analyzed [16]. We have formally proven all the theorems given in that article, using the Coq proof assistant. The formal proof work led us to: (i) locate mistakes in some of the original paper proofs (mistakes that, however, do not hinder the validity of the algorithms), (ii) significantly improve some error bounds, and (iii) generalize some results by showing that they are still valid if we slightly change the rounding mode. The consequence is that the algorithms presented in [16] can be used with high confidence, and that some of them are even more accurate than what was believed before. This illustrates what formal proof can bring to computer arithmetic: beyond mere (yet extremely useful) verification, correction, and consolidation of already known results, it can help to find new properties. All our formal proofs are freely available.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Snyder:2022:RAE, author = "W. Van Snyder", title = "Remark on {Algorithm 982: Explicit Solutions of Triangular Systems of First-order Linear Initial-value Ordinary Differential Equations with Constant Coefficients}", journal = j-TOMS, volume = "48", number = "1", pages = "10:1--10:4", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3479429", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3479429", abstract = "Algorithm 982: Explicit solutions of triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients provides an explicit solution for an homogeneous system, and a brief description of how to compute a solution for the inhomogeneous case. The method described is not directly useful if the coefficient matrix is singular. This remark explains more completely how to compute the solution for the inhomogeneous case and for the singular coefficient matrix case.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Myllykoski:2022:ATB, author = "Mirko Myllykoski", title = "{Algorithm 1019}: a Task-based Multi-shift {$ Q R $ \slash $ Q Z $} Algorithm with Aggressive Early Deflation", journal = j-TOMS, volume = "48", number = "1", pages = "11:1--11:36", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3495005", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3495005", abstract = "The $ Q R $ algorithm is one of the three phases in the process of computing the eigenvalues and the eigenvectors of a dense nonsymmetric matrix. This paper describes a task-based $ Q R $ algorithm for reducing an upper Hessenberg matrix to real Schur form. The task-based algorithm also supports generalized eigenvalue problems ($ Q Z $ algorithm) but this paper concentrates on the standard case. The task-based algorithm adopts previous algorithmic improvements, such as tightly-coupled multi-shifts and Aggressive Early Deflation (AED), and also incorporates several new ideas that significantly improve the performance. This includes, but is not limited to, the elimination of several synchronization points, the dynamic merging of previously separate computational steps, the shortening and the prioritization of the critical path, and experimental GPU support. The task-based implementation is demonstrated to be multiple times faster than multi-threaded LAPACK and ScaLAPACK in both single-node and multi-node configurations on two different machines based on Intel and AMD CPUs. The implementation is built on top of the StarPU runtime system and is part of the open-source StarNEig library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Speleers:2022:ACM, author = "Hendrik Speleers", title = "{Algorithm 1020}: Computation of Multi-Degree {Tchebycheffian} {B}-Splines", journal = j-TOMS, volume = "48", number = "1", pages = "12:1--12:31", month = mar, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3478686", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Feb 17 08:00:57 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3478686", abstract = "Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab. The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Nath:2022:KVM, author = "Kaushik Nath and Palash Sarkar", title = "{Kummer} versus {Montgomery} Face-off over Prime Order Fields", journal = j-TOMS, volume = "48", number = "2", pages = "13:1--13:28", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3503536", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3503536", abstract = "This paper makes a comprehensive comparison of the efficiencies of vectorized implementations of Kummer lines and Montgomery curves at various security levels. For the comparison, nine Kummer lines are considered, out of which eight are new, and new assembly implementations of all nine Kummer lines have been made. Seven previously proposed Montgomery curves are considered and new vectorized assembly implementations have been made for three of them. Our comparisons show that for all security levels, Kummer lines are consistently faster than Montgomery curves, though the speed-up gap is not much.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Eifler:2022:SCF, author = "Leon Eifler and Ambros Gleixner and Jonad Pulaj", title = "A Safe Computational Framework for Integer Programming Applied to {Chv{\'a}tal's Conjecture}", journal = j-TOMS, volume = "48", number = "2", pages = "14:1--14:12", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3485630", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3485630", abstract = "We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a rational branch-and-bound certificate produced by an exact integer programming solver, SCIP, in order to circumvent floating-point round-off errors present in most state-of-the-art solvers for mixed-integer programs. The resulting certificates are self-contained and checker software exists that can verify their correctness independently of the integer programming solver used to produce the certificate. This acts as a safeguard against programming errors that may be present in complex solver software. The viability of this approach is tested by applying it to finite cases of Chv{\'a}tal's conjecture, a long-standing open question in extremal combinatorics. We take particular care to verify also the correctness of the input for this specific problem, using the Coq formal proof assistant. As a result, we are able to provide the first machine-assisted proof that Chv{\'a}tal's conjecture holds for all downsets whose union of sets contains seven elements or less.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gusmeroli:2022:BPB, author = "Nicol{\`o} Gusmeroli and Timotej Hrga and Borut Luzar and Janez Povh and Melanie Siebenhofer and Angelika Wiegele", title = "{BiqBin}: a Parallel Branch-and-bound Solver for Binary Quadratic Problems with Linear Constraints", journal = j-TOMS, volume = "48", number = "2", pages = "15:1--15:31", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3514039", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3514039", abstract = "We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the Max-Cut problem by a branch-and-bound algorithm. All the main ingredients are carefully developed using new semidefinite programming relaxations obtained by strengthening the existing relaxations with a set of hypermetric inequalities, applying the bundle method as the bounding routine and using new strategies for exploring the branch-and-bound tree.\par Furthermore, an efficient C implementation of a sequential and a parallel branch-and-bound algorithm is presented. The latter is based on a load coordinator-worker scheme using MPI for multi-node parallelization and is evaluated on a high-performance computer.\par The new solver is benchmarked against BiqCrunch, GUROBI, and SCIP on four families of (linearly constrained) binary quadratic problems. Numerical results demonstrate that BiqBin is a highly competitive solver. The serial version outperforms the other three solvers on the majority of the benchmark instances. We also evaluate the parallel solver and show that it has good scaling properties. The general audience can use it as an on-line service available at http://www.biqbin.eu.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Charumathi:2022:FAP, author = "V. Charumathi and M. Ramakrishna and Vinita Vasudevan", title = "Fast and Accurate Proper Orthogonal Decomposition using Efficient Sampling and Iterative Techniques for Singular Value Decomposition", journal = j-TOMS, volume = "48", number = "2", pages = "16:1--16:24", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3506691", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3506691", abstract = "In this article, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique is used to update the dominant POD modes in each iteration. We derive bounds for the spectral norm of the error introduced by a series of merging operations. We use an existing theorem to get an approximate measure of the quality of subspaces obtained on convergence of the iteration. Results on various datasets indicate that the POD modes and/or the subspaces are approximated with excellent accuracy with a significant runtime improvement over computing the truncated SVD. We also propose a method to compute the POD modes of large matrices that do not fit in the RAM using this iterative sampling and merging algorithms.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mccoid:2022:PRA, author = "Conor Mccoid and Martin J. Gander", title = "A Provably Robust Algorithm for Triangle--triangle Intersections in Floating-point Arithmetic", journal = j-TOMS, volume = "48", number = "2", pages = "17:1--17:30", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3513264", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3513264", abstract = "Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new triangle intersection algorithm ensures consistency and parsimony across three types of calculations. The set of intersections produced by the algorithm, called representations, is shown to match the set of geometric intersections, called models. The article concludes with a comparison between the old and new intersection algorithms for PANG using an example found to reliably generate failures in the former.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scroggs:2022:CAO, author = "Matthew W. Scroggs and J{\o}rgen S. Dokken and Chris N. Richardson and Garth N. Wells", title = "Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes", journal = j-TOMS, volume = "48", number = "2", pages = "18:1--18:23", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3524456", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3524456", abstract = "We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Trotter:2022:MTO, author = "James D. Trotter and Xing Cai and Simon W. Funke", title = "On Memory Traffic and Optimisations for Low-order Finite Element Assembly Algorithms on Multi-core {CPUs}", journal = j-TOMS, volume = "48", number = "2", pages = "19:1--19:31", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3503925", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3503925", abstract = "Motivated by the wish to understand the achievable performance of finite element assembly on unstructured computational meshes, we dissect the standard cellwise assembly algorithm into four kernels, two of which are dominated by irregular memory traffic. Several optimisation schemes are studied together with associated lower and upper bounds on the estimated memory traffic volume. Apart from properly reordering the mesh entities, the two most significant optimisations include adopting a lookup table in adding element matrices or vectors to their global counterparts, and using a row-wise assembly algorithm for multi-threaded parallelisation. Rigorous benchmarking shows that, due to the various optimisations, the actual volumes of memory traffic are in many cases very close to the estimated lower bounds. These results confirm the effectiveness of the optimisations, while also providing a recipe for developing efficient software for finite element assembly.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lourenco:2022:ASL, author = "Christopher Lourenco and Jinhao Chen and Erick Moreno-Centeno and Timothy A. Davis", title = "{Algorithm 1021}: {SPEX} Left {LU}, Exactly Solving Sparse Linear Systems via a Sparse Left-looking Integer-preserving {LU} Factorization", journal = j-TOMS, volume = "48", number = "2", pages = "20:1--20:23", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3519024", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3519024", abstract = "SPEX Left LU is a software package for exactly solving unsymmetric sparse linear systems. As a component of the sparse exact (SPEX) software package, SPEX Left LU can be applied to any input matrix, A, whose entries are integral, rational, or decimal, and provides a solution to the system $ A x = b$, which is either exact or accurate to user-specified precision. SPEX Left LU preorders the matrix A with a user-specified fill-reducing ordering and computes a left-looking LU factorization with the special property that each operation used to compute the L and U matrices is integral. Notable additional applications of this package include benchmarking the stability and accuracy of state-of-the-art linear solvers and determining whether singular-to-double-precision matrices are indeed singular. Computationally, this article evaluates the impact of several novel pivoting schemes in exact arithmetic, benchmarks the exact iterative solvers within Linbox, and benchmarks the accuracy of MATLAB sparse backslash. Most importantly, it is shown that SPEX Left LU outperforms the exact iterative solvers in run time on easy instances and in stability as the iterative solver fails on a sizeable subset of the tested (both easy and hard) instances. The SPEX Left LU package is written in ANSI C, comes with a MATLAB interface, and is distributed via GitHub, as a component of the SPEX software package, and as a component of SuiteSparse.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Heavner:2022:AEA, author = "N. Heavner and F. D. Igual and G. Quintana-Ort{\'\i} and P. G. Martinsson", title = "{Algorithm 1022}: {Efficient} Algorithms for Computing a Rank-Revealing {UTV} Factorization on Parallel Computing Architectures", journal = j-TOMS, volume = "48", number = "2", pages = "21:1--21:42", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3507466", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3507466", abstract = "Randomized singular value decomposition (RSVD) is by now a well-established technique for efficiently computing an approximate singular value decomposition of a matrix. Building on the ideas that underpin RSVD, the recently proposed algorithm ``randUTV'' computes a full factorization of a given matrix that provides low-rank approximations with near-optimal error. Because the bulk of randUTV is cast in terms of communication-efficient operations such as matrix-matrix multiplication and unpivoted QR factorizations, it is faster than competing rank-revealing factorization methods such as column-pivoted QR in most high-performance computational settings. In this article, optimized randUTV implementations are presented for both shared-memory and distributed-memory computing environments. For shared memory, randUTV is redesigned in terms of an algorithm-by-blocks that, together with a runtime task scheduler, eliminates bottlenecks from data synchronization points to achieve acceleration over the standard blocked algorithm based on a purely fork-join approach. The distributed-memory implementation is based on the ScaLAPACK library. The performance of our new codes compares favorably with competing factorizations available on both shared-memory and distributed-memory architectures", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Korablev:2022:ARF, author = "Yuriy Korablev", title = "{Algorithm 1023}: {Restoration} of Function by Integrals with Cubic Integral Smoothing Spline in {R}", journal = j-TOMS, volume = "48", number = "2", pages = "22:1--22:17", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3519384", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3519384", abstract = "In this paper, a cubic integral smoothing spline with roughness penalty for restoring a function by integrals is described. A mathematical method for building such a spline is described in detail. The method is based on cubic integral spline with a penalty function, which minimizes the sum of squares of the difference between the observed integrals of the unknown function and the integrals of the spline being constructed, plus an additional penalty for the nonlinearity (roughness) of the spline. This method has a matrix form, and this paper shows in detail how to fill in each matrix. The parameter $ \alpha $ governs the desired smoothness of the restored function. Spline knots can be chosen independently of observations, and a weight can be defined for each observation for more control over the resulting spline shape. An implementation in the R language as function int\_spline is given. The function int\_spline is easy to use, with all arguments completely described and corresponding examples given. An example of the application of the method in rare event analysis and forecasting is given.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kalantari:2022:AST, author = "Bahman Kalantari and Yikai Zhang", title = "{Algorithm 1024}: Spherical Triangle Algorithm: a Fast Oracle for Convex Hull Membership Queries", journal = j-TOMS, volume = "48", number = "2", pages = "23:1--23:32", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3516520", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3516520", abstract = "The Convex Hull Membership (CHM) tests whether $ p \in conv(S) $, where p and the n points of S lie in $ \mathbb { R}^m $. CHM finds applications in Linear Programming, Computational Geometry, and Machine Learning. The Triangle Algorithm (TA), previously developed, in $ O(1 / \epsilon^2) $ iterations computes $ p' \in \conv (S) $, either an $ \epsilon $-approximate solution, or a witness certifying p \not \in conv(S). We first prove the equivalence of exact and approximate versions of CHM and Spherical-CHM, where $ p = 0$ and $ ||v|| = 1$ for each $v$ in $S$. If for some $ M \geq 1$ every non-witness with $ ||p'|| > \epsilon $ admits $ v \in S$ satisfying $ ||p' - v|| \geq \sqrt {1 + \epsilon / M}$, we prove the number of iterations improves to $ O(M / \epsilon)$ and $ M \leq 1 / \epsilon $ always holds. Equivalence of CHM and Spherical-CHM implies {\em Minimum Enclosing Ball\/} (MEB) algorithms can be modified to solve CHM. However, we prove $ (1 + \epsilon)$-approximation in MEB is $ \Omega (\sqrt {\epsilon })$-approximation in Spherical-CHM. Thus, even $ O(1 / \epsilon) $ iteration MEB algorithms are not superior to Spherical-TA. Similar weakness is proved for MEB core sets. Spherical-TA also results a variant of the {\em All Vertex Triangle Algorithm\/} (AVTA) for computing all vertices of $ \conv (S)$. Substantial computations on distinct problems demonstrate that TA and Spherical-TA generally achieve superior efficiency over algorithms such as Frank--Wolfe, MEB, and LP-Solver.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pokuri:2022:APS, author = "Balaji Sesha Sarath Pokuri and Alec Lofquist and Chad Risko and Baskar Ganapathysubramanian", title = "{Algorithm 1025}: {PARyOpt}: a Software for Parallel Asynchronous Remote {Bayesian} Optimization", journal = j-TOMS, volume = "48", number = "2", pages = "24:1--24:15", month = jun, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3529517", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed Jul 20 07:04:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3529517", abstract = "PARyOpt $^1$ is a Python based implementation of the Bayesian optimization routine designed for remote and asynchronous function evaluations. Bayesian optimization is especially attractive for computational optimization due to its low cost function footprint as well as the ability to account for uncertainties in data. A key challenge to efficiently deploy any optimization strategy on distributed computing systems is the synchronization step, where data from multiple function calls is assimilated to identify the next campaign of function calls. Bayesian optimization provides an elegant approach to overcome this issue via asynchronous updates. We formulate, develop and implement a parallel, asynchronous variant of Bayesian optimization. The framework is robust and resilient to external failures. We show how such asynchronous evaluations help reduce the total optimization wall clock time for a suite of test problems. Additionally, we show how the software design of the framework allows easy extension to response surface reconstruction (Kriging), providing a high performance software for autonomous exploration. The software is available on PyPI, with examples and documentation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Schwarz:2022:RLB, author = "Angelika Schwarz", title = "Robust level-3 {BLAS} Inverse Iteration from the {Hessenberg} Matrix", journal = j-TOMS, volume = "48", number = "3", pages = "25:1--25:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3544789", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3544789", abstract = "Inverse iteration is known to be an effective method for computing eigenvectors corresponding to simple and well-separated eigenvalues. In the non-symmetric case, the solution of shifted Hessenberg systems is a central step. Existing inverse iteration solvers approach the solution of the shifted Hessenberg systems with either RQ or LU factorizations and, once factored, solve the corresponding systems. This approach has limited level-3 BLAS potential since distinct shifts have distinct factorizations. This paper rearranges the RQ approach such that data shared between distinct shifts can be exploited. Thereby the backward substitution with the triangular R factor can be expressed mostly with matrix--matrix multiplications (level-3 BLAS). The resulting algorithm computes eigenvectors in a tiled, overflow-free, and task-parallel fashion. The numerical experiments show that the new algorithm outperforms existing inverse iteration solvers for the computation of both real and complex eigenvectors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Psarras:2022:LAM, author = "Christos Psarras and Henrik Barthels and Paolo Bientinesi", title = "The Linear Algebra Mapping Problem. {Current} State of Linear Algebra Languages and Libraries", journal = j-TOMS, volume = "48", number = "3", pages = "26:1--26:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3549935", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3549935", abstract = "We observe a disconnect between developers and end-users of linear algebra libraries. On the one hand, developers invest significant effort in creating sophisticated numerical kernels. On the other hand, end-users are progressively less likely to go through the time consuming process of directly using said kernels; instead, languages and libraries, which offer a higher level of abstraction, are becoming increasingly popular. These languages offer mechanisms that internally map the input program to lower level kernels. Unfortunately, our experience suggests that, in terms of performance, this translation is typically suboptimal.\par In this paper, we define the problem of mapping a linear algebra expression to a set of available building blocks as the ``Linear Algebra Mapping Problem'' (LAMP); we discuss its NP-complete nature, and investigate how effectively a benchmark of test problems is solved by popular high-level programming languages and libraries. Specifically, we consider Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++), and NumPy (Python); the benchmark is meant to test both compiler optimizations, as well as linear algebra specific optimizations, such as the optimal parenthesization of matrix products. The aim of this study is to facilitate the development of languages and libraries that support linear algebra computations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Apriansyah:2022:PQF, author = "M. Ridwan Apriansyah and Rio Yokota", title = "Parallel {$ Q R $} Factorization of Block Low-rank Matrices", journal = j-TOMS, volume = "48", number = "3", pages = "27:1--27:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3538647", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3538647", abstract = "We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR structure to achieve arithmetic complexity of $ O(m n) $, while the tiled BLR-QR exhibits $ O(mn^{1.5}) $ complexity. However, the tiled BLR-QR has finer task granularity that allows parallel task-based execution on shared memory systems. We compare the block-column-wise BLR-QR using fork-join parallelism with tiled BLR-QR using task-based parallelism. We also compare these two implementations of Householder BLR-QR with a block-column-wise Modified Gram--Schmidt (MGS) BLR-QR using fork-join parallelism and a state-of-the-art vendor-optimized dense Householder QR in Intel MKL. For a matrix of size 131k $ \times $ 65k, all BLR methods are more than an order of magnitude faster than the dense QR in MKL. Our methods are also robust to ill conditioning and produce better orthogonal factors than the existing MGS-based method. On a CPU with 64 cores, our parallel tiled Householder and block-column-wise Householder algorithms show a speedup of 50 and 37 times, respectively", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lange:2022:TAF, author = "Marko Lange", title = "Toward Accurate and Fast Summation", journal = j-TOMS, volume = "48", number = "3", pages = "28:1--28:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3544488", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3544488", abstract = "We introduce a new accurate summation algorithm based on the error-free summation into floating-point buckets. Our algorithm exploits ideas from Zhu and Hayes' OnlineExactSum, but it uses a significantly smaller number of accumulators and has a better instruction-level parallelism. In the default setting, our implementation aaaSum returns a faithfully rounded floating-point approximation of the true sum. We also discuss possible modifications for the computation of reproducible, correctly rounded, and multiple precision floating-point approximations. The computational overhead for any of these modifications is kept comparably small. Numerical tests demonstrate that aaaSum performs well for very small to large problem sizes, independent of the condition number of the problem. We compare our algorithm with other accurate and high-precision summation approaches.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "accurate summation", } @Article{Hubschle-Schneider:2022:PWR, author = "Lorenz H{\"u}bschle-Schneider and Peter Sanders", title = "Parallel Weighted Random Sampling", journal = j-TOMS, volume = "48", number = "3", pages = "29:1--29:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3549934", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3549934", abstract = "Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps. We give efficient, fast, and practicable parallel and distributed algorithms for building data structures that support sampling single items (alias tables, compressed data structures). This also yields a simplified and more space-efficient sequential algorithm for alias table construction. Our approaches to sampling k out of n items with/without replacement and to subset (Poisson) sampling are output-sensitive, i.e., the sampling algorithms use work linear in the number of different samples. This is also interesting in the sequential case. Weighted random permutation can be done by sorting appropriate random deviates. We show that this is possible with linear work. Finally, we give a communication-efficient, highly scalable approach to (weighted and unweighted) reservoir sampling. This algorithm is based on a fully distributed model of streaming algorithms that might be of independent interest. Experiments for alias tables and sampling with replacement show near linear speedups using up to 158 threads of shared-memory machines. An experimental evaluation of distributed weighted reservoir sampling on up to 5,120 cores also shows good speedups.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Klinkovsky:2022:COS, author = "Jakub Klinkovsk{\'y} and Tom{\'a}s Oberhuber and Radek Fuc{\'\i}k and V{\'\i}tezslav Zabka", title = "Configurable Open-source Data Structure for Distributed Conforming Unstructured Homogeneous Meshes with {GPU} Support", journal = j-TOMS, volume = "48", number = "3", pages = "30:1--30:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3536164", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3536164", abstract = "A general multi-purpose data structure for an efficient representation of conforming unstructured homogeneous meshes for scientific computations on CPU and GPU-based systems is presented. The data structure is provided as open-source software as part of the TNL library (https://tnl-project.org/). The abstract representation supports almost any cell shape and common 2D quadrilateral, 3D hexahedron and arbitrarily dimensional simplex shapes are currently built into the library. The implementation is highly configurable via templates of the C++ language, which allows avoiding the storage of unnecessary dynamic data. The internal memory layout is based on state-of-the-art sparse matrix storage formats, which are optimized for different hardware architectures in order to provide high-performance computations. The proposed data structure is also suitable for meshes decomposed into several subdomains and distributed computing using the Message Passing Interface (MPI). The efficiency of the implemented data structure on CPU and GPU hardware architectures is demonstrated on several benchmark problems and a comparison with another library. Its applicability to advanced numerical methods is demonstrated with an example problem of two-phase flow in porous media using a numerical scheme based on the mixed-hybrid finite element method (MHFEM). We show GPU speed-ups that rise above 20 in 2D and 50 in 3D when compared to sequential CPU computations, and above 2 in 2D and 9 in 3D when compared to 12-threaded CPU computations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gardner:2022:ENF, author = "David J. Gardner and Daniel R. Reynolds and Carol S. Woodward and Cody J. Balos", title = "Enabling New Flexibility in the {SUNDIALS} Suite of Nonlinear and Differential\slash Algebraic Equation Solvers", journal = j-TOMS, volume = "48", number = "3", pages = "31:1--31:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3539801", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3539801", abstract = "In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed ``behind-the-scenes,'' with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chen:2022:HHI, author = "Qiao Chen and Xiangmin Jiao", title = "{HIFIR}: Hybrid Incomplete Factorization with Iterative Refinement for Preconditioning Ill-Conditioned and Singular Systems", journal = j-TOMS, volume = "48", number = "3", pages = "32:1--32:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3536165", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3536165", abstract = "We introduce a software package called Hybrid Incomplete Factorization with Iterative Refinement (HIFIR) for preconditioning sparse, unsymmetric, ill-conditioned, and potentially singular systems. HIFIR computes a hybrid incomplete factorization (HIF), which combines multilevel incomplete LU factorization with a truncated, rank-revealing QR (RRQR) factorization on the final Schur complement. This novel hybridization is based on the new theory of $ \epsilon $-accurate approximate generalized inverse (AGI). It enables near-optimal preconditioners for consistent systems and enables flexible GMRES to solve inconsistent systems when coupled with iterative refinement. In this article, we focus on some practical algorithmic and software issues of HIFIR. In particular, we introduce a new inverse-based rook pivoting (IBRP) into ILU, which improves the robustness and the overall efficiency for some ill-conditioned systems by significantly reducing the size of the final Schur complement for some systems. We also describe the software design of HIFIR in terms of its efficient data structures for supporting rook pivoting in a multilevel setting, its template-based generic programming interfaces for mixed-precision real and complex values in C++, and its user-friendly high-level interfaces in MATLAB and Python. We demonstrate the effectiveness of HIFIR for ill-conditioned or singular systems arising from several applications, including the Helmholtz equation, linear elasticity, stationary incompressible Navier--Stokes (INS) equations, and time-dependent advection-diffusion equation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Liang:2022:QTP, author = "Ling Liang and Xudong Li and Defeng Sun and Kim-Chuan Toh", title = "{QPPAL}: a Two-phase Proximal Augmented {Lagrangian} Method for High-dimensional Convex Quadratic Programming Problems", journal = j-TOMS, volume = "48", number = "3", pages = "33:1--33:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3476571", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3476571", abstract = "In this article, we aim to solve high-dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality, and inequality constraints. To solve the targeted QP problem to a desired accuracy efficiently, we consider the restricted-Wolfe dual problem and develop a two-phase Proximal Augmented Lagrangian method (QPPAL), with Phase I to generate a reasonably good initial point to warm start Phase II to obtain an accurate solution efficiently. More specifically, in Phase I, based on the recently developed symmetric Gauss-Seidel (sGS) decomposition technique, we design a novel sGS-based semi-proximal augmented Lagrangian method for the purpose of finding a solution of low to medium accuracy. Then, in Phase II, a proximal augmented Lagrangian algorithm is proposed to obtain a more accurate solution efficiently. Extensive numerical results evaluating the performance of QPPAL against existing state-of-the-art solvers Gurobi, OSQP, and QPALM are presented to demonstrate the high efficiency and robustness of our proposed algorithm for solving various classes of large-scale convex QP problems. The MATLAB implementation of the software package QPPAL is available at \url{https://blog.nus.edu.sg/mattohkc/softwares/qppal/}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Psarras:2022:ACA, author = "Christos Psarras and Lars Karlsson and Rasmus Bro and Paolo Bientinesi", title = "{Algorithm 1026}: Concurrent Alternating Least Squares for Multiple Simultaneous Canonical Polyadic Decompositions", journal = j-TOMS, volume = "48", number = "3", pages = "34:1--34:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3519383", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3519383", abstract = "Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the Alternating Least Squares (ALS) algorithm. When the number of components is small, regardless of its implementation, ALS exhibits low arithmetic intensity, which severely hinders its performance and makes GPU offloading ineffective. We observe that, in practice, experts often have to compute multiple decompositions of the same tensor, each with a small number of components (typically fewer than 20), to ultimately find the best ones to use for the application at hand. In this article, we illustrate how multiple decompositions of the same tensor can be fused together at the algorithmic level to increase the arithmetic intensity. Therefore, it becomes possible to make efficient use of GPUs for further speedups; at the same time, the technique is compatible with many enhancements typically used in ALS, such as line search, extrapolation, and non-negativity constraints. We introduce the Concurrent ALS algorithm and library, which offers an interface to MATLAB, and a mechanism to effectively deal with the issue that decompositions complete at different times. Experimental results on artificial and real datasets demonstrate a shorter time to completion due to increased arithmetic intensity.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Audet:2022:ANV, author = "Charles Audet and S{\'e}bastien {Le Digabel} and Viviane Rochon Montplaisir and Christophe Tribes", title = "{Algorithm 1027}: \pkg{NOMAD} Version 4: Nonlinear Optimization with the {MADS} Algorithm", journal = j-TOMS, volume = "48", number = "3", pages = "35:1--35:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3544489", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3544489", abstract = "NOMADis a state-of-the-art software package for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic features published in scientific publications. These features are motivated by real applications encountered by industrial partners. The latest major release of NOMAD, version 3, dates to 2008. Minor releases are produced as new features are incorporated. The present work describes NOMAD 4, a complete redesign of the previous version, with a new architecture providing more flexible code, added functionalities, and reusable code. We introduce algorithmic components, which are building blocks for more complex algorithms and can initiate other components, launch nested algorithms, or perform specialized tasks. They facilitate the implementation of new ideas, including the MegaSearchPoll component, warm and hot restarts, and a revised version of the PsdMads algorithm. Another main improvement of NOMAD 4 is the usage of parallelism, to simultaneously compute multiple blackbox evaluations and to maximize usage of available cores. Running different algorithms, tuning their parameters, and comparing their performance for optimization are simpler than before, while overall optimization performance is maintained between versions 3 and 4. NOMAD is freely available at www.gerad.ca/nomad and the whole project is visible at github.com/bbopt/nomad.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chang:2022:AVS, author = "Tyler H. Chang and Layne T. Watson and Jeffrey Larson and Nicole Neveu and William I. Thacker and Shubhangi Deshpande and Thomas C. H. Lux", title = "{Algorithm 1028}: {VTMOP}: Solver for Blackbox Multiobjective Optimization Problems", journal = j-TOMS, volume = "48", number = "3", pages = "36:1--36:??", month = sep, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3529258", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Oct 29 08:26:38 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3529258", abstract = "VTMOP is a Fortran 2008 software package containing two Fortran modules for solving computationally expensive bound-constrained blackbox multiobjective optimization problems. VTMOP implements the algorithm of [32], which handles two or more objectives, does not require any derivatives, and produces well-distributed points over the Pareto front. The first module contains a general framework for solving multiobjective optimization problems by combining response surface methodology, trust region methodology, and an adaptive weighting scheme. The second module features a driver subroutine that implements this framework when the objective functions can be wrapped as a Fortran subroutine. Support is provided for both serial and parallel execution paradigms, and VTMOP is demonstrated on several test problems as well as one real-world problem in the area of particle accelerator optimization.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alves:2022:COH, author = "Jo{\~a}o Nuno Ferreira Alves and Lu{\'\i}s Manuel Silveira Russo and Alexandre Francisco", title = "Cache-oblivious {Hilbert} Curve-based Blocking Scheme for Matrix Transposition", journal = j-TOMS, volume = "48", number = "4", pages = "37:1--37:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3555353", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3555353", abstract = "This article presents a fast SIMD Hilbert space-filling curve generator, which supports a new cache-oblivious blocking-scheme technique applied to the out-of-place transposition of general matrices. Matrix operations found in high performance computing \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Telen:2022:NFA, author = "Simon Telen and Nick Vannieuwenhoven", title = "A Normal Form Algorithm for Tensor Rank Decomposition", journal = j-TOMS, volume = "48", number = "4", pages = "38:1--38:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3555369", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3555369", abstract = "We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system of polynomial \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Jarlebring:2022:CGM, author = "Elias Jarlebring and Massimiliano Fasi and Emil Ringh", title = "Computational Graphs for Matrix Functions", journal = j-TOMS, volume = "48", number = "4", pages = "39:1--39:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3568991", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3568991", abstract = "Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve them, and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mai:2022:ECT, author = "Ngoc Hoang Anh Mai and J. B. Lasserre and Victor Magron and Jie Wang", title = "Exploiting Constant Trace Property in Large-scale Polynomial Optimization", journal = j-TOMS, volume = "48", number = "4", pages = "40:1--40:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3555309", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3555309", abstract = "We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result, such moment relaxations \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "40", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Stripinis:2022:DND, author = "Linas Stripinis and Remigijus Paulavicius", title = "{DIRECTGO}: a New {DIRECT}-Type {MATLAB} Toolbox for Derivative-Free Global Optimization", journal = j-TOMS, volume = "48", number = "4", pages = "41:1--41:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3559755", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3559755", abstract = "In this work, we introduce DIRECTGO, a new MATLAB toolbox for derivative-free global optimization. DIRECTGO collects various deterministic derivative-free DIRECT-type algorithms for box-constrained, generally constrained, and problems with hidden constraints. Each sequential algorithm is implemented in two ways: using static and dynamic data structures for more efficient information storage and organization. Furthermore, parallel schemes are applied to some promising algorithms within DIRECTGO. The toolbox is equipped with a graphical user interface (GUI), ensuring the user-friendly use of all functionalities available in DIRECTGO. Available features are demonstrated in detailed computational studies using a comprehensive DIRECTGOLib v1.0 library of global optimization test problems. Additionally, 11 classical engineering design problems illustrate the potential of DIRECTGO to solve challenging real-world problems. Finally, the appendix gives examples of accompanying MATLAB programs and provides a synopsis of its use on the test problems with box and general constraints.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "41", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Wang:2022:CTC, author = "Jie Wang and Victor Magron and J. B. Lasserre and Ngoc Hoang Anh Mai", title = "{CS-TSSOS}: Correlative and Term Sparsity for Large-Scale Polynomial Optimization", journal = j-TOMS, volume = "48", number = "4", pages = "42:1--42:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3569709", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3569709", abstract = "This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two existing \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "42", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Phipps:2022:ADC, author = "Eric Phipps and Roger Pawlowski and Christian Trott", title = "Automatic Differentiation of {C++} Codes on Emerging Manycore Architectures with {Sacado}", journal = j-TOMS, volume = "48", number = "4", pages = "43:1--43:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3560262", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3560262", abstract = "Automatic differentiation (AD) is a well-known technique for evaluating analytic derivatives of calculations implemented on a computer, with numerous software tools available for incorporating AD technology into complex applications. However, a growing \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "43", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Sobczyk:2022:PPA, author = "Aleksandros Sobczyk and Efstratios Gallopoulos", title = "\pkg{pylspack}: Parallel Algorithms and Data Structures for Sketching, Column Subset Selection, Regression, and Leverage Scores", journal = j-TOMS, volume = "48", number = "4", pages = "44:1--44:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3555370", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3555370", abstract = "We present parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra: (i) Gaussian and CountSketch random projections and their combination, (ii) computation of the Gram matrix, and (iii) computation of the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "44", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Meisrimel:2022:WRA, author = "Peter Meisrimel and Philipp Birken", title = "Waveform Relaxation with Asynchronous Time-integration", journal = j-TOMS, volume = "48", number = "4", pages = "45:1--45:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3569578", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3569578", abstract = "We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "45", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{DeMichele:2022:RAB, author = "Cristiano {De Michele}", title = "Remark on {Algorithm 1010}: Boosting Efficiency in Solving Quartic Equations with No Compromise in Accuracy", journal = j-TOMS, volume = "48", number = "4", pages = "46:1--46:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3564270", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Orellana:2020:ABE}.", URL = "https://dl.acm.org/doi/10.1145/3564270", abstract = "We present a correction and an improvement to Algorithm 1010 [A. Orellana and C. De Michele 2020]", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "46", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Demeure:2022:AEE, author = "Nestor Demeure and C{\'e}dric Chevalier and Christophe Denis and Pierre Dossantos-Uzarralde", title = "{Algorithm 1029}: Encapsulated Error, a Direct Approach to Evaluate Floating-Point Accuracy", journal = j-TOMS, volume = "48", number = "4", pages = "47:1--47:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3549205", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3549205", abstract = "Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce encapsulated error, a new way to estimate the numerical error of an application and provide a reference implementation, the Shaman library. Our method uses dedicated arithmetic over a type that encapsulates both the result the user would have had with the original computation and an approximation of its numerical error. We thus can measure the number of significant digits of any result or intermediate result in a simulation. We show that this approach, although simple, gives results competitive with state-of-the-art methods. It has a smaller overhead, and it is compatible with parallelism, making it suitable for the study of large-scale applications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "47", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brust:2022:ASS, author = "Johannes Brust and Oleg Burdakov and Jennifer Erway and Roummel Marcia", title = "{Algorithm 1030}: {SC-SR1}: {MATLAB} Software for Limited-memory {SR1} Trust-region Methods", journal = j-TOMS, volume = "48", number = "4", pages = "48:1--48:??", month = dec, year = "2022", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3550269", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3550269", abstract = "We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix, which can be used for large-scale optimization. The method takes advantage of two shape-changing norms [Burdakov and Yuan 2002; Burdakov et al. 2017] to decompose the trust-region subproblem into two separate problems. Using one of the proposed norms, the resulting subproblems have closed-form solutions. Meanwhile, using the other proposed norm, one of the resulting subproblems has a closed-form solution while the other is easily solvable using techniques that exploit the structure of L-SR1 matrices. Numerical results suggest that the SC-SR1 method is able to solve trust-region subproblems to high accuracy even in the so-called ``hard case.'' When integrated into a trust-region algorithm, extensive numerical experiments suggest that the proposed algorithms perform well, when compared with widely used solvers, such as truncated conjugate-gradients.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "48", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lefevre:2023:ACE, author = "Vincent Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller and Joris Picot and Laurence Rideau", title = "Accurate Calculation of {Euclidean} Norms Using Double-word Arithmetic", journal = j-TOMS, volume = "49", number = "1", pages = "1:1--1:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3568672", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3568672", abstract = "We consider the computation of the Euclidean (or $ L^2$) norm of an $n$-dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and\slash or to obtain very accurate results. We modify a recently published algorithm (that uses double-word arithmetic) to allow for a very accurate solution, free of spurious overflows and underflows. To that purpose, we use a double-word square-root algorithm of which we provide a tight error analysis. The returned $ L^2$ norm will be within very slightly more than 0.5 ulp from the exact result, which means that we will almost always provide correct rounding", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reberol:2023:RTC, author = "Maxence Reberol and Kilian Verhetsel and Fran{\c{c}}ois Henrotte and David Bommes and Jean-Fran{\c{c}}ois Remacle", title = "Robust Topological Construction of All-hexahedral Boundary Layer Meshes", journal = j-TOMS, volume = "49", number = "1", pages = "2:1--2:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3577196", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3577196", abstract = "We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bluhdorn:2023:EBA, author = "Johannes Bl{\"u}hdorn and Max Sagebaum and Nicolas Gauger", title = "Event-Based Automatic Differentiation of {OpenMP} with {OpDiLib}", journal = j-TOMS, volume = "49", number = "1", pages = "3:1--3:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3570159", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3570159", abstract = "We present the new software OpDiLib, a universal add-on for classical operator overloading AD tools that enables the automatic differentiation (AD) of OpenMP parallelized code. With it, we establish support for OpenMP features in a reverse mode operator \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Amestoy:2023:CSA, author = "Patrick Amestoy and Alfredo Buttari and Nicholas J. Higham and Jean-Yves L'Excellent and Theo Mary and Bastien Vieubl{\'e}", title = "Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement", journal = j-TOMS, volume = "49", number = "1", pages = "4:1--4:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3582493", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3582493", abstract = "The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Anselmann:2023:GMM, author = "Mathias Anselmann and Markus Bause", title = "A Geometric Multigrid Method for Space-Time Finite Element Discretizations of the {Navier--Stokes} Equations and its Application to {$3$D} Flow Simulation", journal = j-TOMS, volume = "49", number = "1", pages = "5:1--5:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3582492", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3582492", abstract = "We present a parallelized geometric multigrid (GMG) method, based on the cell-based Vanka smoother, for higher order space-time finite element methods (STFEM) to the incompressible Navier--Stokes equations. The STFEM is implemented as a time marching \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lux:2023:AMM, author = "Thomas Lux and Layne T. Watson and Tyler Chang and William Thacker", title = "{Algorithm 1031}: {MQSI}-Monotone Quintic Spline Interpolation", journal = j-TOMS, volume = "49", number = "1", pages = "6:1--6:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3570157", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3570157", abstract = "MQSI is a Fortran 2003 subroutine for constructing monotone quintic spline interpolants to univariate monotone data. Using sharp theoretical monotonicity constraints, first and second derivative estimates at data provided by a quadratic facet model are \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Peters:2023:ABC, author = "J{\"o}rg Peters and Kyle Lo and K{\k{e}}stutis Karciauskas", title = "{Algorithm 1032}: Bi-cubic Splines for Polyhedral Control Nets", journal = j-TOMS, volume = "49", number = "1", pages = "7:1--7:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3570158", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/peters-jorg.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3570158", abstract = "For control nets outlining a large class of topological polyhedra, not just tensor-product grids, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Akin to tensor-. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Quintana-Orti:2023:API, author = "Gregorio Quintana-Ort{\'\i} and Fernando Hernando and Francisco D. Igual", title = "{Algorithm 1033}: Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Distributed-memory Architectures", journal = j-TOMS, volume = "49", number = "1", pages = "8:1--8:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3573383", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3573383", abstract = "The minimum distance of a linear code is a key concept in information theory. Therefore, the time required by its computation is very important to many problems in this area. In this article, we introduce a family of implementations of the Brouwer-\ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fahmy:2023:AAA, author = "Thierry Fahmy", title = "{Algorithm 1034}: an Accelerated Algorithm to Compute the {$ Q_n $} Robust Statistic, with Corrections to Constants", journal = j-TOMS, volume = "49", number = "1", pages = "9:1--9:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3576920", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3576920", abstract = "The robust scale estimator Q$_n$ developed by Croux and Rousseeuw [ 3 ], for the computation of which they provided a deterministic algorithm, has proven to be very useful in several domains including in quality management and time series analysis. It has \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Li:2023:NRC, author = "Xiaoye S. Li and Paul Lin and Yang Liu and Piyush Sao", title = "Newly Released Capabilities in the Distributed-Memory {SuperLU} Sparse Direct Solver", journal = j-TOMS, volume = "49", number = "1", pages = "10:1--10:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3577197", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3577197", abstract = "We present the new features available in the recent release of SuperLU\_DIST, Version 8.1.1. SuperLU\_DIST is a distributed-memory parallel sparse direct solver. The new features include (1) a 3D communication-avoiding algorithm framework that trades off \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Breiding:2023:CZP, author = "Paul Breiding and Kemal Rose and Sascha Timme", title = "Certifying Zeros of Polynomial Systems Using Interval Arithmetic", journal = j-TOMS, volume = "49", number = "1", pages = "11:1--11:??", month = mar, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3580277", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Mar 23 11:34:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3580277", abstract = "We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk's method. We demonstrate that it dramatically outperforms earlier approaches to certification. We see this contribution as a powerful new tool in numerical algebraic geometry, which can make certification the default and not just an option.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Horacsek:2023:FAG, author = "Joshua Horacsek and Usman Alim", title = "{FastSpline}: Automatic Generation of Interpolants for Lattice Samplings", journal = j-TOMS, volume = "49", number = "2", pages = "12:1--12:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3577194", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3577194", abstract = "Interpolation is a foundational concept in scientific computing and is at the heart of many scientific visualization techniques. There is usually a tradeoff between the approximation capabilities of an interpolation scheme and its evaluation efficiency. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ketcheson:2023:CBS, author = "David I. Ketcheson and Hendrik Ranocha", title = "Computing with {B}-series", journal = j-TOMS, volume = "49", number = "2", pages = "13:1--13:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3573384", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3573384", abstract = "We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the theory of B-series and associated concepts and provide examples of their use, including method composition and backward error analysis. The associated software is highly performant and makes it possible to work with B-series of high order.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Borm:2023:DHM, author = "Steffen B{\"o}rm", title = "Distributed {$ \mathcal {H}_2 $}-Matrices for Boundary Element Methods", journal = j-TOMS, volume = "49", number = "2", pages = "14:1--14:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3582494", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3582494", abstract = "Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method or hierarchical matrices. If the underlying mesh is very large, running the corresponding algorithms on a distributed computer is attractive, e.g., since distributed computers frequently are cost-effective and offer a high accumulated memory bandwidth.\par Compared to the closely related particle methods, for which distributed algorithms are well-established, the Galerkin discretization poses a challenge, since the supports of the basis functions influence the block structure of the matrix and therefore the flow of data in the corresponding algorithms. This article introduces distributed $ \mathcal {H}_2$-matrices, a class of hierarchical matrices that is closely related to fast multipole methods and particularly well-suited for distributed computing. While earlier efforts required the global tree structure of the $ \mathcal {H}_2$-matrix to be stored in every node of the distributed system, the new approach needs only local multilevel information that can be obtained via a simple distributed algorithm, allowing us to scale to significantly larger systems. Experiments show that this approach can handle very large meshes with more than 130 million triangles efficiently.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Agullo:2023:TBP, author = "Emmanuel Agullo and Alfredo Buttari and Abdou Guermouche and Julien Herrmann and Antoine Jego", title = "Task-based Parallel Programming for Scalable Matrix Product Algorithms", journal = j-TOMS, volume = "49", number = "2", pages = "15:1--15:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3583560", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3583560", abstract = "Task-based programming models have succeeded in gaining the interest of the high-performance mathematical software community because they relieve part of the burden of developing and implementing distributed-memory parallel algorithms in an efficient and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chalkis:2023:TLC, author = "Apostolos Chalkis and Vissarion Fisikopoulos and Marios Papachristou and Elias Tsigaridas", title = "Truncated Log-concave Sampling for Convex Bodies with Reflective {Hamiltonian Monte Carlo}", journal = j-TOMS, volume = "49", number = "2", pages = "16:1--16:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3589505", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3589505", abstract = "We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm to sample from a log-concave distribution restricted to a convex body. The random walk is based on incorporating reflections to the Hamiltonian dynamics such that the support \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kim:2023:HMB, author = "Ki-Tae Kim and Umberto Villa and Matthew Parno and Youssef Marzouk and Omar Ghattas and Noemi Petra", title = "{hIPPYlib-MUQ}: a {Bayesian} Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty", journal = j-TOMS, volume = "49", number = "2", pages = "17:1--17:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3580278", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3580278", abstract = "Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fasi:2023:CCL, author = "Massimiliano Fasi and Mantas Mikaitis", title = "{CPFloat}: a {C} Library for Simulating Low-precision Arithmetic", journal = j-TOMS, volume = "49", number = "2", pages = "18:1--18:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3585515", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3585515", abstract = "One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing implementations are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of rounding algorithms. CPFloat is a C library for simulating low-precision arithmetics. It offers efficient routines for rounding, performing mathematical computations, and querying properties of the simulated low-precision format. The software exploits the bit-level floating-point representation of the format in which the numbers are stored and replaces costly library calls with low-level bit manipulations and integer arithmetic. In numerical experiments, the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Reynolds:2023:AFI, author = "Daniel R. Reynolds and David J. Gardner and Carol S. Woodward and Rujeko Chinomona", title = "{ARKODE}: a Flexible {IVP} Solver Infrastructure for One-step Methods", journal = j-TOMS, volume = "49", number = "2", pages = "19:1--19:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3594632", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3594632", abstract = "We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE supports one-step \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hager:2023:AGB, author = "William W. Hager and Hongchao Zhang", title = "{Algorithm 1035}: a Gradient-based Implementation of the Polyhedral Active Set Algorithm", journal = j-TOMS, volume = "49", number = "2", pages = "20:1--20:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3583559", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3583559", abstract = "The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over a polyhedron. Phase one of the algorithm is a nonmonotone gradient projection algorithm, while phase two is an active set algorithm that explores faces of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Baert:2023:AAA, author = "Wouter Baert and Nick Vannieuwenhoven", title = "{Algorithm 1036}: {ATC}, An Advanced {Tucker} Compression Library for Multidimensional Data", journal = j-TOMS, volume = "49", number = "2", pages = "21:1--21:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3585514", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3585514", abstract = "We present ATC, a C++ library for advanced Tucker-based lossy compression of dense multidimensional numerical data in a shared-memory parallel setting, based on the sequentially truncated higher-order singular value decomposition (ST-HOSVD) and bit plane \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bestuzheva:2023:ERT, author = "Ksenia Bestuzheva and Mathieu Besan{\c{c}}on and Wei-Kun Chen and Antonia Chmiela and Tim Donkiewicz and Jasper van Doornmalen and Leon Eifler and Oliver Gaul and Gerald Gamrath and Ambros Gleixner and Leona Gottwald and Christoph Graczyk and Katrin Halbig and Alexander Hoen and Christopher Hojny and Rolf van der Hulst and Thorsten Koch and Marco L{\"u}bbecke and Stephen J. Maher and Frederic Matter and Erik M{\"u}hmer and Benjamin M{\"u}ller and Marc E. Pfetsch and Daniel Rehfeldt and Steffan Schlein and Franziska Schl{\"o}sser and Felipe Serrano and Yuji Shinano and Boro Sofranac and Mark Turner and Stefan Vigerske and Fabian Wegscheider and Philipp Wellner and Dieter Weninger and Jakob Witzig", title = "Enabling Research through the {SCIP Optimization Suite 8.0}", journal = j-TOMS, volume = "49", number = "2", pages = "22:1--22:??", month = jun, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3585516", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Jun 29 07:01:00 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3585516", abstract = "The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Deshmukh:2023:COP, author = "Sameer Deshmukh and Rio Yokota and George Bosilca", title = "Cache Optimization and Performance Modeling of Batched, Small, and Rectangular Matrix Multiplication on {Intel}, {AMD}, and {Fujitsu} Processors", journal = j-TOMS, volume = "49", number = "3", pages = "23:1--23:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3595178", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3595178", abstract = "Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of these operations. In addition to a lower arithmetic complexity, such methods can, by their structure, be designed to efficiently exploit modern hardware architectures. The majority of existing work relies on batched BLAS libraries to handle the computation of many small dense matrices. We show that through careful analysis of the cache utilization, register accumulation using SIMD registers and a redesign of the implementation, one can achieve significantly higher throughput for these types of batched low-rank matrices across a large range of block and batch sizes. We test our algorithm on three CPUs using diverse ISAs --- the Fujitsu A64FX using ARM SVE, the Intel Xeon 6148 using AVX-512, and AMD EPYC 7502 using AVX-2, and show that our new batching methodology is able to obtain more than twice the throughput of vendor optimized libraries for all CPU architectures and problem sizes.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Claus:2023:SAM, author = "Lisa Claus and Pieter Ghysels and Yang Liu and Th{\'a}i Anh Nhan and Ramakrishnan Thirumalaisamy and Amneet Pal Singh Bhalla and Sherry Li", title = "Sparse Approximate Multifrontal Factorization with Composite Compression Methods", journal = j-TOMS, volume = "49", number = "3", pages = "24:1--24:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3611662", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3611662", abstract = "This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to $ 2.7 \times $ larger than before and leads to a memory consumption that is reduced by 70\% while ensuring the same execution time. The code is made publicly available in GitHub.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fehling:2023:APG, author = "Marc Fehling and Wolfgang Bangerth", title = "Algorithms for Parallel Generic {\em hp\/}-Adaptive Finite Element Software", journal = j-TOMS, volume = "49", number = "3", pages = "25:1--25:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3603372", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3603372", abstract = "The {\em hp\/}-adaptive finite element method --- where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell --- has long been known to have better theoretical convergence properties than either h- or p-adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements.\par Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation of {\em hp\/}-adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multistage algorithm for the unique enumeration of degrees of freedom suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples and demonstrate that they scale reasonably up to at least 16,384 message passage interface processes.\par We provide a reference implementation of our algorithms as part of the open source library deal.II.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Giles:2023:AIC, author = "Michael Giles and Oliver Sheridan-Methven", title = "Approximating Inverse Cumulative Distribution Functions to Produce Approximate Random Variables", journal = j-TOMS, volume = "49", number = "3", pages = "26:1--26:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3604935", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3604935", abstract = "For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced using approximations to a distribution's inverse cumulative distribution function. These approximations are designed to be computationally inexpensive and much cheaper than library functions, which are exact to within machine precision and, thus, highly suitable for use in Monte Carlo simulations. The approximation errors they introduce can then be eliminated through use of the multilevel Monte Carlo method. Two approximations are presented for the Gaussian distribution: a piecewise constant on equally spaced intervals and a piecewise linear using geometrically decaying intervals. The errors of the approximations are bounded and the convergence demonstrated, and the computational savings are measured for C and C++ implementations. Implementations tailored for Intel and Arm hardware are inspected alongside hardware agnostic implementations built using OpenMP. The savings are incorporated into a nested multilevel Monte Carlo framework with the Euler-Maruyama scheme to exploit the speedups without losing accuracy, offering speed ups by a factor of 5--7. These ideas are empirically extended to the Milstein scheme and the non-central $ \chi^2 $ distribution for the Cox--Ingersoll--Ross process, offering speedups of a factor of 250 or more.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fioravanti:2023:AAM, author = "Massimo Fioravanti and Daniele Cattaneo and Federico Terraneo and Silvano Seva and Stefano Cherubin and Giovanni Agosta and Francesco Casella and Alberto Leva", title = "Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models", journal = j-TOMS, volume = "49", number = "3", pages = "27:1--27:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3611661", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3611661", abstract = "Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays' problems, however, well assessed model translation techniques exhibit scalability issues that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is nontrivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Davis:2023:ASG, author = "Timothy A. Davis", title = "{Algorithm 1037: SuiteSparse:GraphBLAS}: Parallel Graph Algorithms in the Language of Sparse Linear Algebra", journal = j-TOMS, volume = "49", number = "3", pages = "28:1--28:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3577195", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3577195", abstract = "SuiteSparse:GraphBLAS is a full parallel implementation of the GraphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. A description of the parallel implementation of SuiteSparse:GraphBLAS is given, including its novel parallel algorithms for sparse matrix multiply, addition, element-wise multiply, submatrix extraction and assignment, and the GraphBLAS mask/accumulator operation. Its performance is illustrated by solving the graph problems in the GAP Benchmark and by comparing it with other sparse matrix libraries", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Roman:2023:ISR, author = "Jose E. Roman and Fernando Alvarruiz and Carmen Campos and Lisandro Dalcin and Pierre Jolivet and Alejandro Lamas Davi{\~n}a", title = "Improvements to \pkg{SLEPc} in Releases 3.14--3.18", journal = j-TOMS, volume = "49", number = "3", pages = "29:1--29:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3603373", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3603373", abstract = "This short article describes the main new features added to SLEPc, the Scalable Library for Eigenvalue Problem Computations, in the past two and a half years, corresponding to five release versions. The main novelty is the extension of the SVD module with new problem types, such as the generalized SVD or the hyperbolic SVD. Additionally, many improvements have been incorporated in different parts of the library, including contour integral eigensolvers, preconditioning, and GPU support.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Papanikos:2023:ICL, author = "Georgios Papanikos and Catherine E. Powell and David J. Silvester", title = "\pkg{IFISS$3$D}: a Computational Laboratory for Investigating Finite Element Approximation in Three Dimensions", journal = j-TOMS, volume = "49", number = "3", pages = "30:1--30:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3604934", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3604934", abstract = "IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three space dimensions. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error estimation, as well as iterative solvers. The package is designed to be useful as a teaching tool for instructors and students who want to learn about state-of-the-art finite element methodology. It will also be useful for researchers as a source of reproducible test matrices of arbitrarily large dimension.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Himpe:2023:EEG, author = "Christian Himpe", title = "\pkg{emgr} --- {EMpirical GRamian} Framework Version 5.99", journal = j-TOMS, volume = "49", number = "3", pages = "31:1--31:??", month = sep, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3609860", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 29 08:05:09 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3609860", abstract = "Version 5.99 of the empirical Gramian framework --- emgr --- completes a development cycle which focused on parametric model order reduction of gas network models while preserving compatibility to the previous development for the application of combined state and parameter reduction for neuroscience network models. Second, new features concerning empirical Gramian types, perturbation design, and trajectory post-processing, as well as a Python version in addition to the default MATLAB / Octave implementation, have been added. This work summarizes these changes, particularly since emgr version 5.4, see Himpe, 2018 [Algorithms 11(7): 91], and gives recent as well as future applications, such as parameter identification in systems biology, based on the current feature set.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "31", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rump:2023:IPP, author = "Siegfried M. Rump", title = "{IEEE-754} Precision-$p$ base-$ \beta $ Arithmetic Implemented in Binary", journal = j-TOMS, volume = "49", number = "4", pages = "32:1--32:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3596218", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3596218; https://www.tuhh.de/ti3/paper/rump/Ru23b.pdf", abstract = "We show how an IEEE-754 conformant precision-$p$ base-$ \beta $ arithmetic can be implemented based on some binary floating-point and/or integer arithmetic. This includes the four basic operations and square root subject to the five IEEE-754 rounding modes, namely he nearest roundings with roundTiesToEven and roundTiesToAway, the directed roundings downwards and upwards, as well as rounding towards zero. Exceptional values like $ \infty $ or NaN are covered according to the IEEE-754 arithmetic standard. The results of the precision-$p$ base-$ \beta $ operations are computed using some underlying precision-$q$ binary arithmetic. We distinguish two cases. When using a precision-$q$ binary integer arithmetic, the base-$ \beta $ precision $p$ is limited for all operations by $ \beta^{2 p} \leq 2^q$, whereas using a precision-$q$ binary floating-point arithmetic imposes stronger limits on the base-$ \beta $ precision, namely $ \beta^{2p} \leq 2^q$ for addition and multiplication, $ \beta^{2p} \leq 2^{q - 1}$ for division and $ \beta^{2p} \leq 2^{q - 3}$ for the square root. Those limitations cannot be improved. The algorithms are implemented in a Matlab/Octave flbeta-toolbox with the choice of using uint64 or binary64 as underlying arithmetic. The former allows larger precisions, the latter is advantageous for the square root, whereas computing times are similar. The flbeta-toolbox offers precision-$p$ base-$ \beta $ scalar, vector and matrix operations including sparse matrices as well as corresponding interval operations. The base $ \beta $ can be chosen in the range $ \beta $ [2,64]. The flbeta-toolbox will be part of Version 13 of INTLAB [18], the Matlab/Octave toolbox for reliable computing.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "32", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", remark = "Received 6 December 2021; revised 10 October 2022; accepted 30 March 2023.", } @Article{Axen:2023:MJE, author = "Seth D. Axen and Mateusz Baran and Ronny Bergmann and Krzysztof Rzecki", title = "\pkg{Manifolds.jl}: an Extensible {Julia} Framework for Data Analysis on Manifolds", journal = j-TOMS, volume = "49", number = "4", pages = "33:1--33:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3618296", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3618296", abstract = "We present the Julia package Manifolds.jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in \pkg{ManifoldsBase.jl}, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of \pkg{Manifolds.jl} using B{\'e}zier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, \pkg{Manifolds.jl} outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "33", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{LeBrigant:2023:PIG, author = "Alice {Le Brigant} and Jules Deschamps and Antoine Collas and Nina Miolane", title = "Parametric Information Geometry with the Package \pkg{Geomstats}", journal = j-TOMS, volume = "49", number = "4", pages = "34:1--34:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3627538", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3627538", abstract = "We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher--Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized probability density function as input. The implemented Riemannian geometry tools allow users to compare, average, interpolate between distributions inside a given family. Importantly, such capabilities open the door to statistics and machine learning on probability distributions. We present the object-oriented implementation of the module along with illustrative examples and show how it can be used to perform learning on manifolds of parametric probability distributions.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "34", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Villar-Sepulveda:2023:CTB, author = "Edgardo Villar-Sep{\'u}lveda and Alan Champneys", title = "Computation of {Turing} Bifurcation Normal Form for $n$-Component Reaction--Diffusion Systems", journal = j-TOMS, volume = "49", number = "4", pages = "35:1--35:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3625560", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3625560", abstract = "General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction--diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth order, which \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "35", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Budisa:2023:HSC, author = "Ana Budisa and Xiaozhe Hu and Miroslav Kuchta and Kent-Andr{\'e} Mardal and Ludmil T. Zikatanov", title = "{HAZniCS} --- Software Components for Multiphysics Problems", journal = j-TOMS, volume = "49", number = "4", pages = "36:1--36:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3625561", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3625561", abstract = "We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "36", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ranocha:2023:EIM, author = "Hendrik Ranocha and Michael Schlottke-Lakemper and Jesse Chan and Andr{\'e}s M. Rueda-Ram{\'\i}rez and Andrew R. Winters and Florian Hindenlang and Gregor J. Gassner", title = "Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous {Galerkin} Methods for Conservation Laws", journal = j-TOMS, volume = "49", number = "4", pages = "37:1--37:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3625559", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3625559", abstract = "Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "37", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kusch:2023:KRE, author = "Jonas Kusch and Steffen Schotth{\"o}fer and Pia Stammer and Jannick Wolters and Tianbai Xiao", title = "\pkg{KiT-RT}: an Extendable Framework for Radiative Transfer and Therapy", journal = j-TOMS, volume = "49", number = "4", pages = "38:1--38:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3630001", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3630001", abstract = "In this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open source C++-based framework for solving kinetic equations in therapy applications available at \url{https://github.com/CSMMLab/KiT-RT}. This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "38", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kimiaei:2023:NSM, author = "Morteza Kimiaei and Arnold Neumaier and Parvaneh Faramarzi", title = "New Subspace Method for Unconstrained Derivative-Free Optimization", journal = j-TOMS, volume = "49", number = "4", pages = "39:1--39:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3618297", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3618297", abstract = "This article defines an efficient subspace method, called SSDFO, for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available. SSDFO employs \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "39", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lin:2023:AKM, author = "Hao Lin and Hongfu Liu and Junjie Wu and Hong Li and Stephan G{\"u}nnemann", title = "Algorithm 1038: {KCC}: a {MATLAB} Package for $k$-Means-based Consensus Clustering", journal = j-TOMS, volume = "49", number = "4", pages = "40:1--40:??", month = dec, year = "2023", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3616011", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 23 05:40:24 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3616011", abstract = "Consensus clustering is gaining increasing attention for its high quality and robustness. In particular, $k$-means-based Consensus Clustering (KCC) converts the usual computationally expensive problem to a classic $k$-means clustering with generalized utility functions, bringing potentials for large-scale data clustering on different types of data. Despite KCC s applicability and generalizability, implementing this method such as representing the binary dataset in the k-means heuristic is challenging and has seldom been discussed in prior work. To fill this gap, we present a MATLAB package, KCC, that completely implements the KCC framework and utilizes a sparse representation technique to achieve a low space complexity. Compared to alternative consensus clustering packages, the KCC package is of high flexibility, efficiency, and effectiveness. Extensive numerical experiments are also included to show its usability on real-world datasets.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "40", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drmac:2024:LID, author = "Zlatko Drmac", title = "A {LAPACK} Implementation of the Dynamic Mode Decomposition", journal = j-TOMS, volume = "50", number = "1", pages = "1:1--1:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3640012", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3640012", abstract = "The Dynamic Mode Decomposition (DMD) is a method for computational analysis of nonlinear dynamical systems in data driven scenarios. Based on high fidelity numerical simulations or experimental data, the DMD can be used to reveal the latent structures in \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Drmac:2024:HDM, author = "Zlatko Drmac", title = "{Hermitian} Dynamic Mode Decomposition --- Numerical Analysis and Software Solution", journal = j-TOMS, volume = "50", number = "1", pages = "2:1--2:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3641884", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3641884", abstract = "The Dynamic Mode Decomposition (DMD) is a versatile and increasingly popular method for data driven analysis of dynamical systems that arise in a variety of applications in, e.g., computational fluid dynamics, robotics or machine learning. In the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hascoet:2024:DFR, author = "Laurent Hasco{\"e}t", title = "Data-flow Reversal and Garbage Collection", journal = j-TOMS, volume = "50", number = "1", pages = "3:1--3:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3627537", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3627537", abstract = "Data-flow reversal is at the heart of source-transformation reverse algorithmic differentiation (reverse ST-AD), arguably the most efficient way to obtain gradients of numerical models. However, when the model implementation language uses garbage \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brehard:2024:EVN, author = "Florent Br{\'e}hard and Nicolas Brisebarre and Mioara Joldes and Warwick Tucker", title = "Efficient and Validated Numerical Evaluation of {Abelian} Integrals", journal = j-TOMS, volume = "50", number = "1", pages = "4:1--4:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3637550", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3637550", abstract = "Abelian integrals play a key role in the infinitesimal version of Hilbert's 16th problem. Being able to evaluate such integrals-with guaranteed error bounds-is a fundamental step in computer-aided proofs aimed at this problem. Using interpolation by \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alkamper:2024:IPM, author = "Maria Alk{\"a}mper and Jim Magiera and Christian Rohde", title = "An Interface-Preserving Moving Mesh in Multiple Space Dimensions", journal = j-TOMS, volume = "50", number = "1", pages = "5:1--5:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3630000", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3630000", abstract = "An interface-preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving ( d -1)-dimensional manifold directly within the d -dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Alaejos:2024:AAG, author = "Guillermo Alaejos and Adri{\'a}n Castell{\'o} and Pedro Alonso-Jord{\'a} and Francisco D. Igual and H{\'e}ctor Mart{\'\i}nez and Enrique S. Quintana-Ort{\'\i}", title = "{Algorithm 1039}: Automatic Generators for a Family of Matrix Multiplication Routines with {Apache TVM}", journal = j-TOMS, volume = "50", number = "1", pages = "6:1--6:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3638532", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3638532", abstract = "We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS, and OpenBLAS, to obtain high-performance \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Piazzola:2024:ASG, author = "Chiara Piazzola and Lorenzo Tamellini", title = "{Algorithm 1040}: The {Sparse Grids Matlab Kit} --- a {Matlab} implementation of sparse grids for high-dimensional function approximation and uncertainty quantification", journal = j-TOMS, volume = "50", number = "1", pages = "7:1--7:22", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3630023", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3630023", abstract = "The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be used for approximating high-dimensional functions and, in particular, for surrogate-model-based uncertainty quantification. It is lightweight, high-level and easy to se also in realistic applications. The goal of this paper is to provide an overview of the data structure and of the mathematical aspects forming the basis of the software, as well as comparing the current release of our package to similar available software.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ouermi:2024:AHH, author = "Timbwoga A. J. Ouermi and Robert M. Kirby and Martin Berzins", title = "{Algorithm 1041}: {HiPPIS} --- A High-order Positivity-preserving Mapping Software for Structured Meshes", journal = j-TOMS, volume = "50", number = "1", pages = "8:1--8:??", month = mar, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3632291", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Mar 23 16:17:51 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3632291", abstract = "Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead to negative \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Scott:2024:ABI, author = "Jennifer Scott and Miroslav Tuma", title = "Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic", journal = j-TOMS, volume = "50", number = "2", pages = "9:1--9:25", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3651155", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3651155", abstract = "The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for mixed precision variants of iterative refinement. We consider the iterative solution of large sparse systems using incomplete factorization preconditioners. The focus is on the robust computation of such preconditioners in half precision arithmetic and employing them to solve symmetric positive definite systems to higher precision accuracy; however, the proposed ideas can be applied more generally. Even for well-conditioned problems, incomplete factorizations can break down when small entries occur on the diagonal during the factorization. When using half precision arithmetic, overflows are an additional possible source of breakdown. We examine how breakdowns can be avoided and implement our strategies within new half precision Fortran sparse incomplete Cholesky factorization software. Results are reported for a range of problems from practical applications. These demonstrate that, even for highly ill-conditioned problems, half precision preconditioners can potentially replace double precision preconditioners, although unsurprisingly this may be at the cost of additional iterations of a Krylov solver.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Beaumont:2024:ORM, author = "Olivier Beaumont and Lionel Eyraud-Dubois and Julien Herrmann and Alexis Joly and Alena Shilova", title = "Optimal Re-Materialization Strategies for Heterogeneous Chains: How to Train Deep Neural Networks with Limited Memory", journal = j-TOMS, volume = "50", number = "2", pages = "10:1--10:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3648633", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3648633", abstract = "Training in Feed Forward Deep Neural Networks is a memory-intensive operation which is usually performed on GPUs with limited memory capacities. This may force data scientists to limit the depth of the models or the resolution of the input data if data \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chowdhary:2024:PES, author = "Abhijit Chowdhary and Shady E. Ahmed and Ahmed Attia", title = "{PyOED}: an Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments", journal = j-TOMS, volume = "50", number = "2", pages = "11:1--11:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3653071", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3653071", abstract = "This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Chang:2024:RAC, author = "Tyler H. Chang and Layne T. Watson and Sven Leyffer and Thomas C. H. Lux and Hussain M. J. Almohri", title = "Remark on {Algorithm 1012}: Computing Projections with Large Datasets", journal = j-TOMS, volume = "50", number = "2", pages = "12:1--12:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3656581", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Chang:2020:ADI}.", URL = "https://dl.acm.org/doi/10.1145/3656581", abstract = "In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum-of-squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD. This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world datasets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE, due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Eftekhari:2024:ASP, author = "Aryan Eftekhari and Lisa Gaedke-Merzh{\"a}user and Dimosthenis Pasadakis and Matthias Bollh{\"o}fer and Simon Scheidegger and Olaf Schenk", title = "{Algorithm 1042}: Sparse Precision Matrix Estimation with {SQUIC}", journal = j-TOMS, volume = "50", number = "2", pages = "13:1--13:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3650108", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3650108", abstract = "We present SQUIC, a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the $ \ell_1$-regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Feng:2024:AFR, author = "Xu Feng and Wenjian Yu and Yuyang Xie and Jie Tang", title = "{Algorithm 1043}: Faster Randomized {SVD} with Dynamic Shifts", journal = j-TOMS, volume = "50", number = "2", pages = "14:1--14:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3660629", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3660629", abstract = "Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e., for computing a few of the largest singular values and the corresponding singular vectors), a dynamically shifted power iteration \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Arnaudon:2024:APM, author = "Alexis Arnaudon and Dominik J. Schindler and Robert L. Peach and Adam Gosztolai and Maxwell Hodges and Michael T. Schaub and Mauricio Barahona", title = "{Algorithm 1044: {PyGenStability}}, a Multiscale Community Detection with Generalized {Markov} Stability", journal = j-TOMS, volume = "50", number = "2", pages = "15:1--15:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3651225", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/python.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3651225", abstract = "We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualization tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Helwig:2024:ACD, author = "Jacob Helwig and Sutanoy Dasgupta and Peng Zhao and Bani K. Mallick and Debdeep Pati", title = "{Algorithm 1045}: a Covariate-Dependent Approach to {Gaussian} Graphical Modeling in {R}", journal = j-TOMS, volume = "50", number = "2", pages = "16:1--16:??", month = jun, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3659206", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jul 2 07:51:57 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3659206", abstract = "Graphical models are used to capture complex multivariate relationships and have applications in diverse disciplines such as biology, physics, and economics. Within this field, Gaussian graphical models aim to identify the pairs of variables whose dependence is maintained even after conditioning on the remaining variables in the data, known as the conditional dependence structure of the data. There are many existing software packages for Gaussian graphical modeling, however, they often make restrictive assumptions that reduce their flexibility for modeling data that are not identically distributed. Conversely, \pkg{covdepGE} is an R implementation of a variational weighted pseudo-likelihood algorithm for modeling the conditional dependence structure as a continuous function of an extraneous covariate. To build on the efficiency of this algorithm, \pkg{covdepGE} leverages parallelism and C++ integration with R. Additionally, \pkg{covdepGE} provides fully-automated and data-driven hyperparameter specification while maintaining flexibility for the user to decide key components of the estimation procedure. Through an extensive simulation study spanning diverse settings, \pkg{covdepGE} is demonstrated to be top of its class in recovering the ground truth conditional dependence structure while efficiently managing computational overhead.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Rozanski:2024:EGA, author = "Piotr T. R{\'o}za{\'n}ski", title = "\pkg{empi}: {GPU}-Accelerated Matching Pursuit with Continuous Dictionaries", journal = j-TOMS, volume = "50", number = "3", pages = "17:1--17:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3674832", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3674832", abstract = "This article introduces an effective approach to performing matching pursuit calculations with continuous (quasi-infinite) dictionaries. Simulating continuous parameter space is accomplished by combining optimal dictionary construction as introduced \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Marzorati:2024:EML, author = "Denise Marzorati and Joaqu{\'\i}n Fern{\'a}ndez and Ernesto Kofman", title = "Efficient Matching in Large {DAE} Models", journal = j-TOMS, volume = "50", number = "3", pages = "18:1--18:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3674831", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3674831", abstract = "This article presents a matching algorithm for bipartite graphs containing repetitive structures and represented by intension as Set-Based Graphs. Under certain conditions on the structure of the graphs, the computational cost of this novel algorithm is \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Hou:2024:SSN, author = "Di Hou and Ling Liang and Kim-Chuan Toh", title = "A Sparse Smoothing {Newton} Method for Solving Discrete Optimal Transport Problems", journal = j-TOMS, volume = "50", number = "3", pages = "19:1--19:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3688800", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3688800", abstract = "The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications. This paper \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Thompson:2024:AIR, author = "Ian Thompson", title = "{Algorithm 1046}: an Improved Recurrence Method for the Scaled Complex Error Function", journal = j-TOMS, volume = "50", number = "3", pages = "20:1--20:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3688799", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3688799", abstract = "Calculation of the scaled complex error function $ w(z) $ by recurrence is discussed, and a new method for determining the number of steps required to achieve a given accuracy is introduced. This method is found to work throughout the complex plane, except for a short section of the real line, centred at the origin. An algorithm based on this analysis is implemented; Taylor series with stored coefficients are used to compute $ w(z) $ in a small region where recurrence is not efficient. The new algorithm is tested extensively and found to outperform earlier recurrence-based codes. It also performs favourably against recent codes based on other methods.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Michele:2024:RAB, author = "Cristiano De Michele", title = "Remark on {Algorithm 1010}: {Boosting} Efficiency in Solving Quartic Equations with No Compromise in Accuracy", journal = j-TOMS, volume = "50", number = "3", pages = "21:1--21:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3674833", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3674833", abstract = "In this second remark, we present a revised correction to Algorithm 1010 [A. Orellana and C. De Michele 2020] with respect to the one already proposed in the remark on Algorithm 1010 [C. De Michele 2022].", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Khalighi:2024:AFJ, author = "Moein Khalighi and Giulio Benedetti and Leo Lahti", title = "{Algorithm 1047}: {FdeSolver}, a {Julia} Package for Solving Fractional Differential Equations", journal = j-TOMS, volume = "50", number = "3", pages = "22:1--22:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3680280", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3680280", abstract = "We introduce FdeSolver, an open-source Julia package designed to solve fractional-order differential equations efficiently. The available solutions are based on product-integration rules, predictor--corrector algorithms, and the Newton-Raphson method. The package covers solutions for one-dimensional equations with orders of positive real numbers. For higher-dimensional systems, it supports orders up to one. Incommensurate derivatives are allowed and defined in the Caputo sense. Here, we summarize the implementation for a representative class of problems and compare it with available alternatives in Julia and MATLAB. Moreover, FdeSolver leverages the power and flexibility of the Julia environment to offer enhanced computational performance, and our development emphasizes adherence to the best practices of open research software. To highlight its practical utility, we demonstrate its capability in simulating microbial community dynamics and modeling the spread of COVID-19. This latter application involves fitting the order of derivatives grounded on real-world epidemiological data. Overall, these results highlight the efficiency, reliability, and practicality of the FdeSolver Julia package.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fuda:2024:ACC, author = "Chiara Fuda and Kai Hormann", title = "{Algorithm 1048}: a {C++} Class for Robust Linear Barycentric Rational Interpolation", journal = j-TOMS, volume = "50", number = "3", pages = "23:1--23:??", month = sep, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3681781", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 28 09:16:22 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3681781", abstract = "Barycentric rational interpolation is a recent interpolation method with several favourable properties. In this article, we present the BRI class, which features a new C++ class template that contains all variables and functions related to linear \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gillette:2024:ADD, author = "Andrew Gillette and Eugene Kur", title = "{Algorithm 1049}: The {Delaunay} Density Diagnostic", journal = j-TOMS, volume = "50", number = "4", pages = "24:1--24:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3700134", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3700134", abstract = "Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs --- i.e., the ``geometric scale'' of the function --- despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2--10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input--output pairs. We include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mejia-Domenzain:2024:ASC, author = "Lorena Mejia-Domenzain and Jinhao Chen and Christopher Lourenco and Erick Moreno-Centeno and Timothy A. Davis", title = "{Algorithm 1050}: {SPEX} {Cholesky}, {LDL}, and {Backslash} for Exactly Solving Sparse Linear Systems", journal = j-TOMS, volume = "50", number = "4", pages = "25:1--25:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3700592", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3700592", abstract = "SPEX Cholesky, SPEX LDL, and SPEX Backslash are software packages for exactly solving sparse linear systems, $ A \mathbf {x} = \mathbf {b} $. SPEX Cholesky, used for symmetric positive definite (SPD) systems, computes an integral Cholesky factorization to solve the system in time proportional to arithmetic work --- to date the only algorithm for SPD linear systems with this property. SPEX LDL extends SPEX Cholesky for symmetric negative definite and symmetric indefinite matrices with exclusively non-zero leading principal minors. SPEX Backslash is a general-purpose exact solver that automatically determines the best ordering and factorization to exactly solve the system. Computationally, we test the accuracy of MATLAB sparse backslash, the state-of-the-art collection of sparse matrix solvers, revealing it is near perfect for 87\% of the tested instances. In addition, we show that SPEX Cholesky outperforms alternate exact solvers in runtime; specifically, SPEX Cholesky outperforms the exact solver Linbox and exact LU factorization on 70\% and 92\% of tested instances, respectively. Each of SPEX Cholesky, SPEX LDL, and SPEX Backslash is implemented in C and is accompanied by easy-to-use Python and MATLAB interfaces. They are distributed via GitHub, as a component of the SPEX software package, and as component of SuiteSparse.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Lindquist:2024:GRB, author = "Neil Lindquist and Piotr Luszczek and Jack Dongarra", title = "Generalizing Random Butterfly Transforms to Arbitrary Matrix Sizes", journal = j-TOMS, volume = "50", number = "4", pages = "26:1--26:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3699714", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3699714", abstract = "Parker and L{\^e} introduced random butterfly transforms (RBTs) as a preprocessing technique to replace pivoting in dense LU factorization. Unfortunately, their FFT-like recursive structure restricts the dimensions of the matrix. Furthermore, on multinode systems, efficient management of the communication overheads restricts the matrix's distribution even more. To remove these limitations, we have generalized the RBT to arbitrary matrix sizes by truncating the dimensions of each layer in the transform. We expanded Parker's theoretical analysis to generalized RBT, specifically that in exact arithmetic, Gaussian elimination with no pivoting will succeed with probability 1 after transforming a matrix with full-depth RBTs. Furthermore, we experimentally show that these generalized transforms improve performance over Parker's formulation by up to 62\% while retaining the ability to replace pivoting. This generalized RBT is available in the SLATE numerical software library.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Toledo:2024:AUF, author = "Sivan Toledo", title = "{Algorithm 1051}: {UltimateKalman}, Flexible {Kalman} Filtering and Smoothing Using Orthogonal Transformations", journal = j-TOMS, volume = "50", number = "4", pages = "27:1--27:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3699958", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3699958", abstract = "UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying numbers of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-track smoothers, and combinations. The article describes the algorithm and its implementation as well as a test suite of examples and tests.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bouillaguet:2024:AEB, author = "Charles Bouillaguet", title = "{Algorithm 1052}: Evaluating a {Boolean} Polynomial on All Possible Inputs", journal = j-TOMS, volume = "50", number = "4", pages = "28:1--28:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3699957", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3699957", abstract = "Evaluating a Boolean polynomial on all possible inputs (i.e., building the truth table of the corresponding Boolean function) is a simple computational problem that sometimes appears inside broader applications, for instance in cryptanalysis or in the implementation of more sophisticated algorithms to solve Boolean polynomial systems.\par Two techniques share the crown to perform this task: the Fast Exhaustive Search (FES) algorithm from 2010 (which is based on Gray Codes) and the space-efficient Moebius transform from 2021 (which is reminiscent of the FFT). Both require operations for a degree-$d$ Boolean polynomial on variables and operate mostly in-place, but have other slightly different characteristics. They both provide an efficient iterator over the full truth table.\par This article describes BoolEAN POLynomial Evaluation (BeanPolE), a concise and flexible C library that implements both algorithms, as well as many other functions to deal with Boolean multivariate polynomials in dense representation.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Ge:2024:ASD, author = "Dongdong Ge and Jinsong Liu and Tianhao Liu and Jiyuan Tan and Yinyu Ye", title = "{Algorithm 1053}: {SOLNP+}: a Derivative-Free Solver for Constrained Nonlinear Optimization", journal = j-TOMS, volume = "50", number = "4", pages = "29:1--29:??", month = dec, year = "2024", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3699956", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Dec 14 17:48:45 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "https://dl.acm.org/doi/10.1145/3699956", abstract = "SOLNP+ is a derivative-free solver for constrained nonlinear optimization. It starts from SOLve Nonlinear Programming (SOLNP) proposed in 1989 by Ye. The main ideas are to use finite difference to approximate the gradient of the objective function and constraints, and use augmented Lagrangian method and sequential quadratic programming to deal with nonlinear constraints. We incorporate the techniques of implicit filtering, a new restart mechanism, and a modern quadratic programming solver into this new version with an ANSI C implementation. The algorithm exhibits a great advantage in running time and robustness under noise compared with the old version implemented in MATLAB. The numerical experiments show that SOLNP is comparable with two widely used solvers, COBYLA and NOMAD. SOLNP is available at \url{https://github.com/COPT-Public/SOLNP_plus}.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Suzuki:2025:IAB, author = "Kengo Suzuki and Takeshi Fukaya and Takeshi Iwashita", title = "An Integer Arithmetic-Based {AMG} Preconditioned {FGMRES} Solver", journal = j-TOMS, volume = "51", number = "1", pages = "1:1--1:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3704726", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We consider solving a sparse linear system using integer (fixed-point) arithmetic. Integer arithmetic has attracted attention in scientific computing because of its high computational efficiency. Furthermore, considering the current circumstances of hardware development, integer arithmetic is expected to become increasingly important. Nevertheless, integer arithmetic has not been widely used for solving linear systems because it lacks robustness against overflow and underflow, making it hard to solve practical problems. Thus, we propose a new integer-based implementation framework for the Flexible GMRES (FGMRES) method, which enables integer-based solvers to solve linear systems with the same accuracy as conventional floating-point solvers. In addition, we propose an integer-only algebraic multigrid preconditioner. Combining it with the integer-based FGMRES framework, we develop an integer-based solver. Numerical experiments on CPUs showed that the developed integer-based solver has a comparable convergence rate to floating-point solvers. We also found the test cases where the integer-based solver runs faster than the floating-point solvers.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Walczyk:2025:OAX, author = "Cezary J. Walczyk and Leonid V. Moroz and Volodymyr Samotyy and Jan L. Cie{\'s}li{\'n}ski", title = "Optimal Approximation of the $ 1 / x $ Function using {Chebyshev} Polynomials and Magic Constants", journal = j-TOMS, volume = "51", number = "1", pages = "2:1--2:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3708472", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In this article we analyze low-cost accurate approximation of the function $ 1 / x $ using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so-called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new optimal iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.", accepted = "4 December 2024", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", received = "3 September 2022", revised = "25 September 2024", } @Article{Antonietti:2025:LDP, author = "Paola F. Antonietti and Stefano Bonetti and Michele Botti and Mattia Corti and Ivan Fumagalli and Ilario Mazzieri", title = "\pkg{lymph}: Discontinuous Polytopal Methods for Multi-Physics Differential Problems", journal = j-TOMS, volume = "51", number = "1", pages = "3:1--3:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3716310", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a MATLAB library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the article is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting --- when necessary --- key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the article, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, the elastodynamics system, and a multi-physics problem coupling poroelasticity and acoustic equations. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e., geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", keywords = "MATLAB", } @Article{Hu:2025:SSL, author = "Tianchen Hu and Mark C. Messner", title = "A Simple, Scalable Large Deformation Solid Mechanics Implementation in the {MOOSE} Framework", journal = j-TOMS, volume = "51", number = "1", pages = "4:1--4:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3716308", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article describes a large deformation solid mechanics solver implemented as part of the freely available and open source MOOSE finite element simulation framework. The article documents the choices made in developing the solid mechanics framework and describes novel formulations for the gradient operator and constitutive modeling framework made to simplify implementations of different coordinate systems, stabilized gradient operators, and different constitutive model inputs and outputs. In the process, the article describes a new formulation that casts objective integration of the Cauchy stress as a linear transformation of the small stress rate. Finally, the article presents key implementation details and examines the parallel efficiency of the solid mechanics solver implemented in MOOSE. The implementation retains a good weak scaling efficiency beyond 1,000 parallel processes. The article includes a discussion of the factors limiting the parallel efficiency of implicit, large deformation solid mechanics codes on current high-performance computers, with the main current limitation being the scalability of the algebraic multigrid methods used to solve the linearized equilibrium equations.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gao:2025:MPJ, author = "Weiguo Gao and Yuxin Ma and Meiyue Shao", title = "A Mixed Precision {Jacobi} {SVD} Algorithm", journal = j-TOMS, volume = "51", number = "1", pages = "5:1--5:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3721124", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "5", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Trim:2025:AEF, author = "Sean J. Trim and Raymond J. Spiteri", title = "Algorithm 1054: \pkg{ellipFor}, a {Fortran} Software Library for {Legendre} Elliptic Integrals and {Jacobi} Elliptic Functions with Generalized Input Arguments", journal = j-TOMS, volume = "51", number = "1", pages = "6:1--6:??", month = mar, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3709136", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Apr 10 08:03:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1--3, arbitrary real Jacobi amplitudes for points 1--2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "6", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Aehle:2025:FMA, author = "Max Aehle and Johannes Bl{\"u}hdorn and Max Sagebaum and Nicolas R. Gauger", title = "Forward-Mode Automatic Differentiation of Compiled Programs", journal = j-TOMS, volume = "51", number = "2", pages = "7:1--7:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3716309", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Algorithmic differentiation (AD) is a set of techniques that provide partial derivatives of computer-implemented functions. Such functions can be supplied to state-of-the-art AD tools via their source code, or via intermediate representations produced while compiling their source code.\par We present the novel AD tool Derivgrind, which augments the machine code of compiled programs with forward-mode AD logic. Derivgrind leverages the Valgrind instrumentation framework for structured access to the machine code, and a shadow memory tool to store dot values. Access to the source code is required at most for the files in which input and output variables are defined.\par Derivgrind's versatility mainly comes at the price of reduced run-time performance. According to our extensive regression test suite, Derivgrind produces correct results on GCC- and Clang-compiled programs, including a Python interpreter, with a small number of exceptions. We provide a list of ``bit-tricks'' that Derivgrind does not handle correctly, some of which actually appear in highly optimized math libraries. As long as differentiating those is avoided, Derivgrind enables black-box forward-mode AD for an unprecedentedly wide range of cross-language software with little integration efforts.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McCoid:2025:IT, author = "Conor McCoid and Martin J. Gander", title = "Intersection of Tetrahedra", journal = j-TOMS, volume = "51", number = "2", pages = "8:1--8:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3729532", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "When intersecting non-matching three-dimensional lattices, one needs to calculate the intersections of tetrahedra. The authors' previously published two-dimensional triangle--triangle intersection algorithm suggests a novel approach in three dimensions based on parsimony. The algorithm presented here expands on this two-dimensional algorithm and introduces new strategies necessitated by the increase in dimension. An extensive proof is given for the consistency of the algorithm. Thus, the algorithm is shown to be robust to numerical error arising from floating-point arithmetic. Example problems demonstrate its use and effectiveness.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Fowkes:2025:ALS, author = "Jaroslav M. Fowkes and Nicholas I. M. Gould and Jennifer A. Scott", title = "Approximating Large-Scale {Hessian} Matrices Using Secant Equations", journal = j-TOMS, volume = "51", number = "2", pages = "9:1--9:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3728460", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Large-scale optimization algorithms frequently require sparse Hessian matrices that are not readily available. Existing methods for approximating large sparse Hessian matrices either do not impose sparsity or are computationally prohibitive. To try and overcome these limitations, we propose a novel approach that seeks to satisfy as many componentwise secant equations as necessary to define each row of the Hessian matrix. A naive application of this approach is too expensive for Hessian matrices that have some relatively dense rows but, by carefully taking into account the symmetry and connectivity of the Hessian matrix, we are able devise an approximation algorithm that is fast and efficient with scope for parallelism. Example sparse Hessian matrices from the CUTEst test collection for optimization illustrate the effectiveness and robustness of our proposed method.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "9", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Molu:2025:LGA, author = "Lekan Molu", title = "{LevelSetPy}: a {GPU}-Accelerated Package for Hyperbolic {Hamilton--Jacobi} Partial Differential Equations", journal = j-TOMS, volume = "51", number = "2", pages = "10:1--10:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3730407", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "This article introduces a software package release for geometrically reasoning about the safety desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with the Hamilton--Jacobi equations. In scope, we provide implementations of numerical algorithms for the resolution of Hamilton--Jacobi--Isaacs equations: the spatial derivatives of the associated value function via upwinding, the Hamiltonian via Lax--Friedrichs schemes, and the integration of the Hamilton--Jacobi equation altogether via total variation diminishing Runge--Kutta schemes. Since computational speed and interoperability with other modern scientific computing libraries (typically written in the Python language) are of essence, we capitalize on modern computational frameworks such as CUPY and NUMPY and move heavy computations to GPU devices to aid parallelization and improve bring-up time in safety analysis. We hope that this package can aid users to quickly iterate on ideas and evaluate all possible safety desiderata of a system via geometrical simulation in modern engineering problems", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "10", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Velasco:2025:SUF, author = "Manel Velasco and Isiah Zaplana and Arnau D{\`o}ria-Cerezo and Pau Mart{\'\i}", title = "Symbolic and User-friendly Geometric Algebra Routines {(SUGAR)} for Computations in {Matlab}", journal = j-TOMS, volume = "51", number = "2", pages = "11:1--11:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3734693", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Geometric Algebra (GA) provides a unified, compact mathematical framework for geometric computing, simplifying relations typically handled with more complex tools like matrix multiplication. In fields like robotics, GA replaces conventional coordinate-based approaches with the multiplication of special elements called rotors, offering greater efficiency. Despite its advantages, GA's complexity and the lack of symbolic tools hinder its broader adoption among applied mathematicians and engineers. To address this, this article introduces Symbolic and User-friendly Geometric Algebra Routines (SUGAR), an open source Matlab toolbox. SUGAR streamlines GA usage in Matlab through a collection of user-friendly functions that support both numeric and symbolic computations, even in high-dimensional algebras. Designed for applied mathematics and engineering, it enables intuitive manipulation of geometric elements and transformations in two- and three-dimensional projective and conformal GAs, consistent with established computational methods. Moreover, SUGAR manages multivector functions such as exponential, logarithmic, sinusoidal, and cosine operations, enhancing its applicability in domains like robotics, control systems, and power electronics. Finally, this article also presents three validation examples across these fields, showcasing SUGAR's practical utility in solving real-world engineering and applied mathematics problems.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "11", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Gao:2025:AHS, author = "Wenzhi Gao and Dongdong Ge and Yinyu Ye", title = "Algorithm 1055: {HDSDP}: Software for Semidefinite Programming", journal = j-TOMS, volume = "51", number = "2", pages = "12:1--12:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3721123", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "HDSDP is a numerical software solving semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP and several new features, including a dual method based on the simplified homogeneous self-dual embedding, have been implemented. The embedding technique enhances the stability of the dual method, and several new heuristics and computational techniques are designed to accelerate its convergence. HDSDP aims to show how the dual-scaling algorithm benefits from the self-dual embedding, and it is developed in parallel to DSDP5.8. Numerical experiments over several classical benchmark datasets exhibit their robustness and efficiency, particularly their advantages on SDP instances featuring low-rank structure and sparsity. HDSDP is open sourced under an MIT license and available at https://github.com/Gwzwpxz/HDSDP.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Koprowski:2025:AQM, author = "Przemys{\l}aw Koprowski", title = "Algorithm 1056: {qPoly} --- a {Magma} Package for Working with Quaternionic Polynomials", journal = j-TOMS, volume = "51", number = "2", pages = "13:1--13:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3731677", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The article presents the package for the computer algebra system Magma. It is a collection of functions for manipulating quaternionic polynomials over number fields. It provides nearly the same functionality for quaternionic polynomials as the ones provided by Magma for polynomials over fields.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "13", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McAdam:2025:AFM, author = "Shawn S. C. McAdam and Raymond J. Spiteri", title = "Algorithm 1057: {FunC}: a Minimally Invasive {C++} Library for the Generation and Analysis of Univariate Lookup Tables", journal = j-TOMS, volume = "51", number = "2", pages = "14:1--14:??", month = jun, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3734692", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Jul 12 10:36:07 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A Lookup Table (LUT) is a computationally inexpensive piecewise function used to approximate computationally expensive mathematical functions. Evaluating a LUT can be as quick as using Horner's method to evaluate a polynomial after looking up its coefficients. A common choice of LUT is a piecewise constant or piecewise linear function; however, high-degree interpolating polynomials can also be valuable.\par Here, we describe the functionality of FunC 2.0, a C++ library designed to streamline the process of building, comparing, and implementing univariate LUTs in practical applications. In particular, FunC 2.0 can build relatively small LUTs satisfying user-provided absolute and relative tolerances for error. Furthermore, FunC 2.0 can build nonuniform LUTs, it provides utilities to quickly determine reasonable LUT bounds and tolerances for error, and it provides a way to quickly profile a set of LUTs. We demonstrate FunC's utility in application by reducing the total runtime of a simulation performed by the Canadian Hydrological Model (CHM). This simulation modeled the snow mass distribution across Western Canada over 1 month. Now, the CHM can evaluate the mathematical function of interest about 28 times faster, allowing the necessary algorithm to finish two times faster, and the overall simulation is about 9\% faster.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "14", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Mayani:2025:MPP, author = "Sonali Mayani and Veronica Montanaro and Antoine Cerfon and Matthias Frey and Sriramkrishnan Muralikrishnan and Andreas Adelmann", title = "A Massively Parallel Performance Portable Free-Space Spectral {Poisson} Solver", journal = j-TOMS, volume = "51", number = "3", pages = "15:1--15:23", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3748815", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Vico et al. suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the algorithm of Hockney and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "15", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Smith:2025:TSI, author = "Barry Smith and Marsha Berger and Junchao Zhang and Hui Zhou", title = "Towards Seamless Interoperability of {MPI--OpenMP} Applications", journal = j-TOMS, volume = "51", number = "3", pages = "16:1--16:13", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3757913", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "A chasm exists between mathematical software libraries written for MPI-based applications and those written for OpenMP applications. Recently, however, PETSc enables the simple use of its MPI-based linear solvers from OpenMP applications. Separately, the MPICH MPI development team has started a new project to allow almost seamless MPI use in OpenMP applications. Both proposed approaches would result in a similar user experience. We discuss the reasons for these projects and their potential for providing more numerical library choices for OpenMP applications, including the unlimited assortment of linear solvers available in PETSc. In addition, we present the performance of an application using the first approach, demonstrating its efficacy.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "16", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kirby:2025:EII, author = "Robert C. Kirby and Scott P. MacLachlan", title = "Extending {Irksome}: Improvements in Automated {Runge--Kutta} Time Stepping for Finite Element Methods", journal = j-TOMS, volume = "51", number = "3", pages = "17:1--17:27", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3759245", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of Partial Differential Equations (PDEs). Allowing users to express \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "17", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cyr:2025:THP, author = "Eric C. Cyr and Jens Hahne and Nicholas S. Moore and Jacob B. Schroder and Ben S. Southworth and David A. Vargas", title = "{TorchBraid}: High-Performance Layer-Parallel Training of Deep Neural Networks with {MPI} and {GPU} Acceleration", journal = j-TOMS, volume = "51", number = "3", pages = "18:1--18:30", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3759244", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "TorchBraid is a high-performance implementation of layer-parallel training for deep neural networks (DNNs) supporting MPI-based parallelism and GPU acceleration. Layer-parallel training has been developed to overcome the serialization inherent in forward and backward propagation of DNNs that limits utilization of computational resources in the strong scaling limit. To achieve this, TorchBraid integrates the PyTorch neural network framework with the state-of-the-art XBraid time-parallel library. This article presents the use and performance of TorchBraid, in addition to solutions for overcoming the algorithmic challenges inherent in combining automatic differentiation with layer-parallel. Results are presented with and without GPU acceleration for the Tiny ImageNet and MNIST image classification data sets, as well as recurrent neural networks. Overall, TorchBraid enables fast training of DNNs, both in a strong and weak scaling context.\par In addition to the TorchBraid software, several new advances in applying layer-parallel algorithms are detailed. Integration of layer-parallel with data-parallel algorithms is presented for the first time, showing the computational advantages of the combination. Standard deep learning techniques, like batch-normalization, are developed for layer-parallel training. Finally, a new approach combining layer-parallel with spatial coarsening in order to accelerate training for 3D image classification shows roughly a $ 10 \times $ speedup over serial execution.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "18", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Cui:2025:MIP, author = "Cu Cui and Guido Kanschat", title = "Multilevel Interior Penalty Methods on {GPUs}", journal = j-TOMS, volume = "51", number = "3", pages = "19:1--19:27", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3765616", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We present a matrix-free multigrid method for high-order Discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are optimized \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "19", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Koprowski:2025:ACG, author = "Przemys{\l}aw Koprowski", title = "{Algorithm 1058}: Computing the Group of Local Dyadic Square-Classes the Easy Way", journal = j-TOMS, volume = "51", number = "3", pages = "20:1--20:14", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3759246", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We propose a novel method for constructing a basis of the group of local square-classes of a dyadic completion of a number field. The described method has been implemented by the author in the computer algebra systems Magma and SageMath. It turned out to \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "20", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Brubeck:2025:FIP, author = "Pablo D. Brubeck and Robert C. Kirby and Fabian Laakmann and Lawrence Mitchell", title = "{FIAT}: Improving Performance and Accuracy for High-Order Finite Elements", journal = j-TOMS, volume = "51", number = "3", pages = "21:1--21:17", month = sep, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3748816", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Oct 6 06:57:23 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This release paper describes recent improvements to FIAT aimed at improving its \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "21", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kinnewig:2025:CDI, author = "Sebastian Kinnewig and Alexander Heinlein and Thomas Wick", title = "Coupling {deal.II} and {FROSch}: a Sustainable and Accessible {(O)RAS} Preconditioner", journal = j-TOMS, volume = "51", number = "4", pages = "22:1--22:29", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3766906", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "22", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Kinnewig:2025:ARS, author = "Sebastian Kinnewig and Thomas Wick and Sven Beuchler", title = "Algorithmic Realization of the Solution to the Sign Conflict Problem for Hanging Nodes on Hp-Hexahedral {N{\'e}d{\'e}lec} Elements", journal = j-TOMS, volume = "51", number = "4", pages = "23:1--23:20", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3766903", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "23", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{McCoid:2025:PSI, author = "Conor McCoid", title = "Parsimonious Simplicial Intersection Algorithm", journal = j-TOMS, volume = "51", number = "4", pages = "24:1--24:25", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3766904", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "24", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Arzelier:2025:EAO, author = "Denis Arzelier and Florent Brehard and Tom Hubrecht and Mioara Joldes", title = "An Exchange Algorithm for Optimizing Both Approximation and Finite-Precision Evaluation Errors in Polynomial Approximations", journal = j-TOMS, volume = "51", number = "4", pages = "25:1--25:32", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3770066", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "The finite precision implementation of mathematical functions frequently depends on polynomial approximations. A key characteristic of this approach is that rounding errors occur both when representing the coefficients of the polynomial on a finite number of bits, and when evaluating it in finite precision arithmetic. Hence, to find a best polynomial, for a given fixed degree, norm, and interval, it is necessary to account for both the approximation error and the floating-point evaluation error. While efficient algorithms were already developed for taking into account the approximation error, the evaluation part is usually a posteriori handled, in an ad hoc manner. Here, we formulate a semi-infinite linear optimization problem whose solution is a best polynomial with respect to the supremum norm of the sum of both errors. This problem is then solved with an iterative exchange algorithm, which can be seen as an extension of the well-known Remez exchange algorithm. An open source C implementation using the Sollya library is presented and tested on several examples, which are then analyzed and compared against state-of-the-art Sollya routines.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "25", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{San-Jose:2025:ACG, author = "Rodrigo San-Jos{\'e}", title = "An Algorithm for Computing Generalized {Hamming} Weights and the {Sage} Package {GHWs}", journal = j-TOMS, volume = "51", number = "4", pages = "26:1--26:20", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3773284", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "26", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pashinska-Gadzheva:2025:ALL, author = "Maria Pashinska-Gadzheva and Iliya Bouyukliev", title = "Algorithm 1059: {LinCodeWeightInv-Library} for Computing the Weight Distribution of Linear Codes over Finite Fields", journal = j-TOMS, volume = "51", number = "4", pages = "27:1--27:22", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3777479", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "27", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Bucelli:2025:LLV, author = "Michele Bucelli", title = "The {\tt lifex} Library Version 2.0", journal = j-TOMS, volume = "51", number = "4", pages = "28:1--28:10", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3748817", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "28", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Besancon:2025:IAN, author = "Mathieu Besan{\c{c}}on and S{\'e}bastien Designolle and Jannis Halbey and Deborah Hendrych and Dominik Kuzinowicz and Sebastian Pokutta and Hannah Troppens and Daniel Viladrich Herrmannsdoerfer and Elias Wirth", title = "Improved Algorithms and Novel Applications of the {FrankWolfe.jl} Library", journal = j-TOMS, volume = "51", number = "4", pages = "29:1--29:33", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3765626", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "29", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Prokopenko:2025:ALV, author = "Andrey Prokopenko and Daniel Arndt and Damien Lebrun-Grandi{\'e} and Bruno Turcksin", title = "The {ArborX Library}: Version 2.0", journal = j-TOMS, volume = "51", number = "4", pages = "30:1--30:10", month = dec, year = "2025", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3772288", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Dec 23 05:39:42 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "30", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pal:2026:NJH, author = "Avik Pal and Flemming Holtorf and Axel Larsson and Torkel Loman and Utkarsh and Frank Sch{\"a}fer and Qingyu Qu and Edelman Alan and Chris Rackauckas", title = "{NonlinearSolve.jl}: High-Performance and Robust Solvers for Systems of Nonlinear Equations in {Julia}", journal = j-TOMS, volume = "52", number = "1", pages = "1:1--1:26", month = mar, year = "2026", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3779117", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 20 14:40:27 MDT 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This article presents NonlinearSolve.jl --- a suite of high-performance open source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for static array kernels for improved GPU computation on smaller problems, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as PETSc SNES, Sundials KINSOL, and MINPACK, NonlinearSolve.jl demonstrates robustness and efficiency, achieving significant advancements in solving nonlinear equations while being implemented in a high-level programming language. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "1", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Heldens:2026:KFU, author = "Stijn Heldens and Ben van Werkhoven", title = "Kernel Float: Unlocking Mixed-Precision {GPU} Programming", journal = j-TOMS, volume = "52", number = "1", pages = "2:1--2:36", month = mar, year = "2026", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3779120", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 20 14:40:27 MDT 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Modern GPUs feature specialized hardware for low-precision floating-point arithmetic to accelerate compute-intensive workloads that do not require high numerical accuracy, such as those from artificial intelligence. However, despite the significant gains n computational throughput, memory bandwidth utilization, and energy efficiency, integrating low-precision formats into scientific applications remains difficult. We introduce Kernel Float, a header-only C++ library that simplifies the development of portable mixed-precision GPU kernels. Kernel Float provides a generic vector type, a unified interface for common mathematical operations, and fast approximations for low-precision transcendental functions that lack native hardware support. To demonstrate the potential of mixed-precision computing unlocked by our library, we integrated Kernel Float into nine GPU kernels from various domains. Our evaluation on Nvidia A100 and AMD MI250X GPUs shows performance improvements of up to over double precision, while reducing source code length by up to 50\% compared to handwritten kernels and having negligible runtime overhead. Our results further show that mixed-precision performance depends not only on choosing appropriate data types but also on tuning traditional optimization parameters (e.g., block size and vector width) and, when relevant, even domain-specific parameters.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "2", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Pereira:2026:LLC, author = "Lu{\'\i}s F. Pereira and Alice {Le Brigant} and Adele Myers and Emmanuel Hartman and Amil Khan and Malik Tuerkoen and Trey Dold and Mengyang Gu and Pablo Su{\'a}rez-Serrato and Nina Miolane", title = "Learning from Landmarks, Curves, Surfaces, and Shapes in Geomstats", journal = j-TOMS, volume = "52", number = "1", pages = "3:1--3:31", month = mar, year = "2026", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3779118", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 20 14:40:27 MDT 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves, and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces, and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "3", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } @Article{Peng:2026:AEP, author = "Mai Peng and Delaram Yazdani and Danial Yazdani and Zeneng She and Wenjian Luo and Changhe Li and Juergen Branke and Trung Thanh Nguyen and Amir H. Gandomi and Shengxiang Yang and Yaochu Jin and Xin Yao", title = "{Algorithm 1060}: {EDOLAB}, a Platform for Research and Education in Evolutionary Dynamic Optimization", journal = j-TOMS, volume = "52", number = "1", pages = "4:1--4:30", month = mar, year = "2026", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/3785134", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Mar 20 14:40:27 MDT 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization methods. Evolutionary Dynamic Optimization Algorithms (EDOAs) have been developed to address these challenges by adapting to changing environments over time. However, the reproducibility and consistency of experimental results in the literature remain limited due to the lack of publicly available source codes and the complexity of accurately re-implementing algorithms and performance evaluation protocols. To support the community, we introduce Evolutionary Dynamic Optimization LABoratory (EDOLAB), an open source MATLAB platform designed for both research and educational purposes. EDOLAB includes 27 EDOAs, four highly configurable benchmark generators, and a growing suite of performance indicators. The platform supports full parameter tuning, batch experiment management, parallel execution, and automated statistical comparisons --- including rankings, significance testing, box plots, and performance trend visualizations over time. An educational application allows users to observe: (a) dynamic changes in a 2D problem landscape, (b) the movement of individuals in response to these changes, and (c) the ability of an algorithm to track moving optima. By providing an integrated environment for experimentation, benchmarking, and instructional use, EDOLAB promotes reproducibility, comparative analysis, and a deeper understanding of EDOAs in dynamic environments.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Math. Softw.", articleno = "4", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "https://dl.acm.org/loi/toms", } %%% ==================================================================== %%% Cross-referenced bibliography entries must come last: @TechReport{Learmonth:1973:NPS, author = "G. P. Learmonth and P. A. W. Lewis", title = "{Naval Postgraduate School} Random Number Generator Package {LLRANDOM}", type = "Report", number = "NP555LW73061A", institution = "Naval Postgraduate School", address = "Monterey, CA, USA", year = "1973", bibdate = "Thu Jan 05 14:33:09 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "The shuffling algorithm proposed in this report does {\em not\/} lengthen the period, and only marginally reduces the lattice structure of linear congruential generators, despite the apparently tiny difference with the \cite{Bays:1976:IPR} algorithm: see \cite{Bays:1990:CIR} for a comparison, both mathematical, and graphical.", acknowledgement = ack-nhfb, } @Article{Hanson:1981:APE, author = "David R. Hanson", title = "{Algorithm 568}: {PDS}\emdash a Portable Directory System", journal = j-TOPLAS, volume = "3", number = "2", pages = "162--167", month = apr, year = "1981", CODEN = "ATPSDT", DOI = "https://doi.org/10.1145/357133.357137", ISSN = "0164-0925 (print), 1558-4593 (electronic)", ISSN-L = "0164-0925", bibdate = "Fri Sep 9 14:11:06 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Programming Languages and Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783", } @Article{Bays:1990:CIR, author = "Carter Bays", title = "{C364}. {Improving} a random number generator: a comparison between two shuffling methods", journal = j-J-STAT-COMPUT-SIMUL, volume = "36", number = "1", pages = "57--59", month = may, year = "1990", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949659008811264", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Tue Feb 7 06:50:18 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Learmonth:1973:NPS,Bays:1976:IPR} for the two nearly-identical shuffling algorithms. This paper explains why the first does not lengthen the generator period, or much reduce the lattice structure of linear congruential generators, but the second improves both dramatically.", URL = "http://www.tandfonline.com/doi/abs/10.1080/00949659008811264", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", keywords = "random number; shuffling", onlinedate = "20 Mar 2007", } @Misc{ACM:2002:CSE, author = "ACM", title = "{CALGO} Special Edition {CD}", howpublished = "CD-ROM organized as a Web site.", year = "2002", ISBN = "1-58113-333-2", ISBN-13 = "978-1-58113-333-2", bibdate = "Thu Jan 31 05:49:15 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "ACM order number 201001.", price = "US\$99.95 (member), US\$159.95 (nonmember), US\$199.95 (library)", acknowledgement = ack-nhfb, } @Article{Brent:2008:SCC, author = "Richard P. Brent", title = "Some Comments on {C. S. Wallace}'s Random Number Generators", journal = j-COMP-J, volume = "51", number = "5", pages = "579--584", month = feb, year = "2008", CODEN = "CMPJA6", DOI = "https://doi.org/10.1093/comjnl/bxm122", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Sun Apr 26 12:52:31 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Wallace:1996:FPG}.", abstract = "We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his recent idea for generating normally distributed variates without relying on a source of uniform random numbers and compare it with more conventional methods for generating normal random numbers. Implementations of Wallace's idea can be very fast (approximately as fast as good uniform generators). We discuss the statistical quality of the output, and mention how certain pitfalls can be avoided.", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "Gaussian distribution; maximum-entropy distributions; normal distribution; orthogonal transformations; random number generation; Wallace algorithm", remark = "Wallace's generators produce normal and exponential distributions directly, without first generation numbers from a uniform distribution.", } @Article{Nakatsukasa:2013:SES, author = "Yuji Nakatsukasa and Nicholas J. Higham", title = "Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the {SVD}", journal = j-SIAM-J-SCI-COMP, volume = "35", number = "3", pages = "A1325--A1349", month = "????", year = "2013", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/120876605", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15", MRnumber = "3054594", MRreviewer = "Fatemeh Panjeh Ali Beik", bibdate = "Fri Jul 19 07:43:53 MDT 2013", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Sukkari:2019:QBS}.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2013", } @Article{Dumas:2014:NRI, author = "Jean-Guillaume Dumas", title = "On {Newton--Raphson} Iteration for Multiplicative Inverses Modulo Prime Powers", journal = j-IEEE-TRANS-COMPUT, volume = "63", number = "8", pages = "2106--2109", month = aug, year = "2014", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/TC.2013.94", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Mon Aug 25 08:24:32 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrections \cite{Walther:2019:VNR}.", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @InProceedings{Jeannerod:2017:REC, author = "Claude-Pierre Jeannerod and Jean-Michel Muller", editor = "Michael B. Matthews", booktitle = "{2017 51st Asilomar Conference on Signals, Systems, and Computers. October 29--November 1, 2017. Pacific Grove, California}", title = "On the relative error of computing complex square roots in floating-point arithmetic", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "737--740", year = "2017", DOI = "https://doi.org/10.1109/ACSSC.2017.8335442", ISBN = "1-5386-1823-0", ISBN-13 = "978-1-5386-1823-3", bibdate = "Fri Sep 29 10:59:32 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We study the accuracy of a classical approach to computing complex square-roots in floating-point arithmetic. Our analyses are done in binary floating-point arithmetic in precision p, and we assume that the (real) arithmetic operations $+$, $-$, $ \times $, $ \div $, $ \sqrt {} $ are rounded to nearest, so the unit roundoff is $ u = 2^{-p} $. We show that in the absence of underflow and overflow, the componentwise and normwise relative errors of this approach are at most $ 7 / 2 u $ and $ \sqrt {37} / 2 u $, respectively, and this without having to neglect terms of higher order in $u$. We then provide some input examples showing that these bounds are reasonably sharp for the three basic binary interchange formats (binary32, binary64, and binary128) of the IEEE 754 standard for floating-point arithmetic.", acknowledgement = ack-nhfb, } @Article{Du:2021:IES, author = "Yusong Du and Baoying Fan and Baodian Wei", title = "An improved exact sampling algorithm for the standard normal distribution", journal = j-COMP-STAT, volume = "37", number = "??", pages = "721--737", month = jul, year = "2021", CODEN = "CSTAEB", DOI = "https://doi.org/10.1007/s00180-021-01136-w", ISSN = "0943-4062 (print), 1613-9658 (electronic)", ISSN-L = "0943-4062", bibdate = "Mon Jan 24 15:06:17 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/compstat.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Karney:2016:SEN}.", abstract = "In 2016, Karney [\cite{Karney:2016:SEN}] proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the access to an infinite sequence of independently and uniformly random deviates over the range $ (0, 1) $. We give a theoretical estimate of the expected number of uniform deviates used by this algorithm until it completes, and present an improved algorithm with lower uniform deviate consumption. The experimental results also shows that our improved algorithm has better performance than Karney's algorithm.", acknowledgement = ack-nhfb, fjournal = "Computational Statistics", journal-URL = "https://www.springer.com/journal/180", }