%%% -*-BibTeX-*- %%% /u/sy/beebe/tex/bib/gvl.bib, Mon Oct 15 18:20:08 1990 %%% Edit by Nelson H. F. Beebe %%% %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.10", %%% date = "07 May 1999", %%% time = "14:01:42 MDT", %%% filename = "gvl.bib", %%% address = "Center for Scientific Computing %%% University of Utah %%% Department of Mathematics, 322 INSCC %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 585 1640, +1 801 581 4148", %%% checksum = "47561 8776 30547 253701", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at ieee.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "BibTeX, bibliography, matrix computations", %%% supported = "yes", %%% docstring = "This is the Golub/Van Loan Matrix %%% Computations bibliography. %%% %%% At version 1.10, the year coverage looked %%% like this: %%% %%% 1846 ( 1) 1894 ( 0) 1942 ( 0) %%% 1851 ( 0) 1899 ( 0) 1947 ( 1) %%% 1853 ( 0) 1901 ( 1) 1949 ( 0) %%% 1854 ( 0) 1902 ( 0) 1950 ( 1) %%% 1855 ( 0) 1903 ( 0) 1951 ( 1) %%% 1856 ( 0) 1904 ( 0) 1952 ( 2) %%% 1859 ( 0) 1907 ( 0) 1955 ( 4) %%% 1860 ( 0) 1908 ( 0) 1956 ( 1) %%% 1861 ( 0) 1909 ( 1) 1957 ( 2) %%% 1862 ( 0) 1910 ( 0) 1958 ( 6) %%% 1863 ( 0) 1911 ( 0) 1959 ( 5) %%% 1864 ( 0) 1912 ( 0) 1960 ( 7) %%% 1865 ( 0) 1913 ( 0) 1961 ( 7) %%% 1866 ( 0) 1914 ( 0) 1962 ( 5) %%% 1867 ( 0) 1915 ( 0) 1963 ( 6) %%% 1868 ( 0) 1916 ( 0) 1964 ( 9) %%% 1869 ( 0) 1917 ( 0) 1965 ( 14) %%% 1870 ( 0) 1918 ( 0) 1966 ( 15) %%% 1871 ( 0) 1919 ( 0) 1967 ( 13) %%% 1872 ( 0) 1920 ( 0) 1968 ( 28) %%% 1873 ( 1) 1921 ( 0) 1969 ( 21) %%% 1874 ( 0) 1922 ( 0) 1970 ( 34) %%% 1875 ( 0) 1923 ( 0) 1971 ( 32) %%% 1876 ( 0) 1924 ( 0) 1972 ( 20) %%% 1877 ( 0) 1925 ( 0) 1973 ( 38) %%% 1878 ( 0) 1926 ( 0) 1974 ( 33) %%% 1879 ( 0) 1927 ( 0) 1975 ( 36) %%% 1880 ( 0) 1928 ( 0) 1976 ( 40) %%% 1881 ( 0) 1929 ( 0) 1977 ( 37) %%% 1882 ( 0) 1930 ( 0) 1978 ( 28) %%% 1883 ( 0) 1931 ( 1) 1979 ( 36) %%% 1884 ( 0) 1932 ( 0) 1980 ( 26) %%% 1885 ( 0) 1933 ( 0) 1981 ( 29) %%% 1886 ( 0) 1934 ( 0) 1982 ( 25) %%% 1887 ( 0) 1935 ( 0) 1983 ( 34) %%% 1888 ( 0) 1936 ( 0) 1984 ( 43) %%% 1889 ( 0) 1937 ( 0) 1985 ( 35) %%% 1890 ( 0) 1938 ( 0) 1986 ( 55) %%% 1891 ( 0) 1939 ( 1) 1987 ( 59) %%% 1892 ( 0) 1940 ( 0) 1988 ( 62) %%% 1893 ( 0) 1941 ( 0) 1989 ( 5) %%% %%% Article: 673 %%% Book: 68 %%% InCollection: 37 %%% InProceedings: 16 %%% Manual: 3 %%% PhdThesis: 13 %%% Proceedings: 5 %%% TechReport: 46 %%% %%% Total entries: 861 %%% %%% 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.", %%% } %%% ==================================================================== % From cs.cornell.edu!cv Fri Oct 5 10:00:53 PDT 1990 % % Bibliography of the book "Matrix Computations", 2nd Edn., % by Gene H. Golub & Charles F. Van Loan, % The Joh ns Hopkins University Press, Baltimore, Maryland 21218, 1989. % The original bibliography prepared by Charles Van Loan % (Computer Science, Cornell University, Ithaca, NY 14583) % was corrected, edited and put in Bibtex format (September 1990) % by Chris Paige and Clement Pellerin % (Computer Science, McGill University, Montreal, PQ, Canada H3A 2A7). % email any corrections to Charlie Van Loan at cv'AT SIGN'cs.cornell.edu % % This is the BibTeX file, store it as, for example, gvl.bib % % USE: suppose you want the first reference only to appear, without % citing it. Store in a file called say egcite.tex (without the %s): % % \documentstyle[art12,fullpage]{article} % \begin{document} % \nocite{Aas71} % \bibliographystyle{unsrt} % \bibliography{gvl} % \end{document} % % Then run % latex egcite % bibtex egcite % latex egcite % latex egcite % and use the resulting egcite.dvi to give the required output. % Using \nocite{*} should give you all entries, but you may have to % \nocite half of them, then the rest, to do this. % % Some entries have a \cite in the Note field because they appear % both in a journal and in a book, Calling % latex; bibtex; latex; latex % fails if you cite one of these entries. % If this happens you should either call: % latex; bibtex; latex; bibtex; latex; latex % or else you should \nocite{WilR71} at the beginning of your document % but don't use \bibliographystyle{unsrt} because WilR71 will come first % Journals % First the Full Name is given, then the abbreviation used in the AMS Math % Reviews, with an indication if it could not be found there. % Note the 2nd overwrites the 1st, so swap them if you want the full name. %{AMS} @String{AMSTrans = "American Mathematical Society Translations" } @String{AMSTrans = "Amer. Math. Soc. Transl." } @String{BullAMS = "Bulletin of the American Mathematical Society" } @String{BullAMS = "Bull. Amer. Math. Soc." } @String{ProcAMS = "Proceedings of the American Mathematical Society" } @String{ProcAMS = "Proc. Amer. Math. Soc." } @String{TransAMS = "Transactions of the American Mathematical Society" } @String{TransAMS = "Trans. Amer. Math. Soc." } %ACM @String{CACM = "Communications of the {ACM}" } @String{CACM = "Comm. {ACM}" } @String{CompServ = "{ACM} Computing Surveys" } @String{CompServ = "Comput. Surveys" } @String{JACM = "Journal of the {ACM}" } @String{JACM = "J. Assoc. Comput. Mach." } @String{ACMMathSoft = "{ACM} Transactions on Mathematical Software" } @String{ACMMathSoft = "{ACM} Trans. Math. Software" } @String{SIGNUM = "{ACM} {SIGNUM} Newsletter" } @String{SIGNUM = "{ACM} {SIGNUM} Newslett." } @String{AmerSocio = "American Journal of Sociology" } @String{AmerSocio = "Amer. J. Sociology" } % didn't find in AMS MR @String{AmerStatAssoc = "Journal of the American Statistical Association" } @String{AmerStatAssoc = "J. Amer. Statist. Assoc." } @String{ApplMathComp = "Applied Mathematics and Computation" } @String{ApplMathComp = "Appl. Math. Comput." } @String{AmerMathMonthly = "American Mathematical Monthly" } @String{AmerMathMonthly = "Amer. Math. Monthly" } @String{BIT = "{BIT}" } @String{BIT = "{BIT}" } @String{BritStatPsych = "British Journal of Mathematical and Statistical Psychology" } @String{BritStatPsych = "Brit. J. Math. Statist. Psych." } @String{CanMathBull = "Canadian Mathematical Bulletin" } @String{CanMathBull = "Canad. Math. Bull." } @String{CompApplMath = "Journal of Computational and Applied Mathematics" } @String{CompApplMath = "J. Comput. Appl. Math." } @String{CompPhys = "Journal of Computational Physics" } @String{CompPhys = "J. Comput. Phys." } @String{CompStruct = "Computers and Structures" } @String{CompStruct = "Comput. \& Structures" } @String{CompJour = "The Computer Journal" } @String{CompJour = "Comput. J." } @String{CompSysSci = "Journal of Computer and System Sciences" } @String{CompSysSci = "J. Comput. System Sci." } @String{Computing = "Computing" } @String{Computing = "Computing" } @String{ContempMath = "Contemporary Mathematics" } @String{ContempMath = "Contemp. Math." } @String{Crelle = "Crelle's Journal" } @String{Crelle = "Crelle's J." } % didn't find in AMS MR. %% When will they get up to date? @String{GiornaleMath = "Giornale di Mathematiche" } @String{GiornaleMath = "Giorn. Mat." } % didn't find in AMS MR., ibid. %IEEE @String{Computer = "{IEEE} Computer" } @String{Computer = "{IEEE} Computer" } @String{IEEETransComp = "{IEEE} Transactions on Computers" } @String{IEEETransComp = "{IEEE} Trans. Comput." } @String{IEEETransAC = "{IEEE} Transactions on Automatic Control" } @String{IEEETransAC = "{IEEE} Trans. Automat. Control" } @String{IEEESpec = "{IEEE} Spectrum" } @String{IEEESpec = "{IEEE} Spectrum" } % didn't find in AMS MR @String{ProcIEEE = "Proceedings of the {IEEE}" } @String{ProcIEEE = "Proc. {IEEE}" } % didn't find in AMS MR @String{IEEETransAeroElec = "{IEEE} Transactions on Aerospace and Electronic Systems" } @String{IEEETransAeroElec = "{IEEE} Trans. Aerospace Electron. Systems" } @String{IMANumerAna = "{IMA} Journal of Numerical Analysis" } @String{IMANumerAna = "{IMA} J. Numer. Anal." } @String{InfProcLet = "Information Processing Letters" } @String{InfProcLet = "Inform. Process. Lett." } @String{InstMathApp = "Journal of the Institute of Mathematics and its Applications" } @String{InstMathApp = "J. Inst. Math. Appl." } @String{IntControl = "International Journal of Control" } @String{IntControl = "Internat. J. Control" } @String{IntNumerEng = "International Journal for Numerical Methods in Engineering" } @String{IntNumerEng = "Internat. J. Numer. Methods Engrg." } @String{IntSuper = "International Journal of Supercomputing Applications" } @String{IntSuper = "Internat. J. Supercomputing Applic." } % didn't find %% in AMS MR @String{Kibernetika = "Kibernetika" } @String{Kibernetika = "Kibernetika" } @String{JResNatBurStand = "Journal of Research of the National Bureau of Standards" } @String{JResNatBurStand = "J. Res. Nat. Bur. Standards" } @String{LinAlgApp = "Linear Algebra and its Applications" } @String{LinAlgApp = "Linear Algebra Appl." } @String{MathAnaAppl = "Journal of Mathematical Analysis and Applications" } @String{MathAnaAppl = "J. Math. Anal. Appl." } @String{MathAnnalen = "Mathematische Annalen" } @String{MathAnnalen = "Math. Ann." } @String{MathPhys = "Journal of Mathematical Physics" } @String{MathPhys = "J. Math. Phys." } @String{MathComp = "Mathematics of Computation" } @String{MathComp = "Math. Comp." } @String{MathScand = "Mathematica Scandinavica" } @String{MathScand = "Math. Scand." } @String{TablesAidsComp = "Mathematical Tables and Other Aids to Computation" } @String{TablesAidsComp = "Math. Tables Aids Comput." } @String{NumerMath = "Numerische Mathematik" } @String{NumerMath = "Numer. Math." } @String{PacificMath = "Pacific Journal of Mathematics" } @String{PacificMath = "Pacific J. Math." } @String{ParDistComp = "Journal of Parallel and Distributed Computing" } @String{ParDistComp = "J. Parallel and Distrib. Comput." } % didn't find %% in AMS MR @String{ParComputing = "Parallel Computing" } @String{ParComputing = "Parallel Comput." } @String{PhilMag = "Philosophical Magazine" } @String{PhilMag = "Philos. Mag." } @String{ProcNAS = "Proceedings of the National Academy of Sciences of the USA" } @String{ProcNAS = "Proc. Nat. Acad. Sci. U. S. A." } @String{Psychometrika = "Psychometrika" } @String{Psychometrika = "Psychometrika" } @String{QuartMath = "Quarterly Journal of Mathematics, Oxford, Series (2)" } @String{QuartMath = "Quart. J. Math. Oxford Ser. (2)" } @String{QuartApplMath = "Quarterly of Applied Mathematics" } @String{QuartApplMath = "Quart. Appl. Math." } @String{RevueInstStat = "Review of the International Statisical Institute" } @String{RevueInstStat = "Rev. Inst. Internat. Statist." } %SIAM @String{JSIAM = "Journal of the Society for Industrial and Applied Mathematics" } @String{JSIAM = "J. Soc. Indust. Appl. Math." } @String{JSIAMB = "Journal of the Society for Industrial and Applied Mathematics, Series B, Numerical Analysis" } @String{JSIAMB = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal." } @String{SIAMAlgMeth = "{SIAM} Journal on Algebraic and Discrete Methods" } @String{SIAMAlgMeth = "{SIAM} J. Algebraic Discrete Methods" } @String{SIAMAppMath = "{SIAM} Journal on Applied Mathematics" } @String{SIAMAppMath = "{SIAM} J. Appl. Math." } @String{SIAMComp = "{SIAM} Journal on Computing" } @String{SIAMComp = "{SIAM} J. Comput." } @String{SIAMMatrix = "{SIAM} Journal on Matrix Analysis and Applications" } @String{SIAMMatrix = "{SIAM} J. Matrix Anal. Appl." } @String{SIAMNumAnal = "{SIAM} Journal on Numerical Analysis" } @String{SIAMNumAnal = "{SIAM} J. Numer. Anal." } @String{SIAMReview = "{SIAM} Review" } @String{SIAMReview = "{SIAM} Rev." } @String{SIAMSciStat = "{SIAM} Journal on Scientific and Statistical Computing" } @String{SIAMSciStat = "{SIAM} J. Sci. Statist. Comput." } @String{SoftPracExp = "Software Practice and Experience" } @String{SoftPracExp = "Software Prac. Experience" } % didn't find in AMS MR @String{StatScience = "Statistical Science" } @String{StatScience = "Statist. Sci." } @String{Techno = "Technometrics" } @String{Techno = "Technometrics" } @String{USSRCompMathPhys = "{USSR} Computational Mathematics and Mathematical Physics" } @String{USSRCompMathPhys = "{U. S. S. R.} Comput. Math. and Math. Phys." } @String{VLSICompSys = "Journal of {VLSI} and Computer Systems" } @String{VLSICompSys = "J. {VLSI} Comput. Syst." } @String{ZAngewMathMech = "Zeitschrift fur Angewandte Mathematik und Mechanik" } @String{ZAngewMathMech = "Z. Angew. Math. Mech." } @String{ZAngewMathPhys = "Zeitschrift fur Angewandte Mathematik und Physik" } @String{ZAngewMathPhys = "Z. Angew. Math. Phys." } % Publishers @String{Academic = "Academic Press" } @String{ACMPress = "{ACM} Press" } @String{AdamHilger = "Adam Hilger" } @String{AddisonWesley = "Addison-Wesley" } @String{AllynBacon = "Allyn and Bacon" } @String{AMS = "American Mathematical Society" } @String{Birkhauser = "Birkha{\"u}ser" } @String{CambridgePress = "Cambridge University Press" } @String{Chelsea = "Chelsea" } @String{ClaredonPress = "Claredon Press" } @String{DoverPub = "Dover Publications" } @String{Eyolles = "Eyolles" } @String{HoltRinehartWinston = "Holt, Rinehart and Winston" } @String{Interscience = "Interscience" } @String{JohnsHopkinsPress = "The Johns Hopkins University Press" } @String{JohnWileySons = "John Wiley and Sons" } @String{Macmillan = "Macmillan" } @String{MathWorks = "The Math Works Inc." } @String{McGrawHill = "McGraw-Hill" } @String{NatBurStd = "National Bureau of Standards" } @String{NorthHolland = "North-Holland" } @String{OxfordPress = "Oxford University Press" } %address Oxford or London? @String{PergamonPress = "Pergamon Press" } @String{PlenumPress = "Plenum Press" } @String{PrenticeHall = "Prentice-Hall" } @String{SIAMPub = "{SIAM} Publications" } @String{Springer = "Springer-Verlag" } @String{TexasPress = "University of Texas Press" } @String{VanNostrand = "Van Nostrand" } @String{WHFreeman = "W. H. Freeman and Co." } %Entries @Article{Aas71, author = "J. O. Aasen", year = "1971", title = "On the Reduction of a Symmetric Matrix to Tridiagonal Form", journal = BIT, volume = "11", pages = "233--242", } @Article{Abd71, author = "N. N. Abdelmalek", year = "1971", title = "Roundoff Error Analysis for {Gram}-{Schmidt} Method and Solution of Linear Least Squares Problems", journal = BIT, volume = "11", pages = "1345--1368", } @Article{Ada85, author = "L. Adams", year = "1985", title = "{m}-step Preconditioned Conjugate Gradient Methods", journal = SIAMSciStat, volume = "6", pages = "452--463", } @Article{AdaC84, author = "L. Adams and T. Crockett", year = "1984", title = "Modelling Algorithm Execution Time on Processor Arrays", journal = Computer, volume = "17", pages = "38--43", } @Article{AlePP88, author = "S. T. Alexander and C. T. Pan and R. J. Plemmons", year = "1988", title = "Analysis of a Recursive Least Squares Hyperbolic Rotation Algorithm for Signal Processing", journal = LinAlgApp, volume = "98", pages = "3--40", } @Article{All73, author = "E. L. Allgower", year = "1973", title = "Exact Inverses of Certain Band Matrices", journal = NumerMath, volume = "21", pages = "279--284", } @Techreport{AmiM65, author = "A. R. Amir-Moez", year = "1965", title = "Extremal Properties of Linear Transformations and Geometry of Unitary Spaces", institution = "Texas Tech University", type = "Mathematics Series", number = "243", address = "Lubbock, TX, USA", } @Article{AndK75, author = "N. Anderson and I. Karasalo", year = "1975", title = "On Computing Bounds for the Least Singular Value of a Triangular Matrix", journal = BIT, volume = "15", pages = "1--4", } @Article{AndL73, author = "P. Anderson and G. Loizou", year = "1973", title = "On the Quadratic Convergence of an Algorithm that Diagonalizes a Complex Symmetric Matrix", journal = InstMathApp, volume = "12", pages = "261--271", } @Article{AndL76, author = "P. Anderson and G. Loizou", year = "1976", title = "A {Jacobi}-Type Method for Complex Symmetric Matrices ({Handbook})", journal = NumerMath, volume = "25", pages = "347--363", } @Article{AndOU87, author = "T. W. Anderson and I. Olkin and L. G. Underhill", year = "1987", title = "Generation of Random Orthogonal Matrices", journal = SIAMSciStat, volume = "8", pages = "625--629", } @Article{AndS83, author = "G. Andrews and F. B. Schneider", year = "1983", title = "Concepts and Notations for Concurrent Programming", journal = CompServ, volume = "15", pages = "1--43", } @Article{Arn51, author = "W. E. Arnoldi", year = "1951", title = "The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem", journal = QuartApplMath, volume = "9", pages = "17--29", } @Techreport{ArbG87, author = "P. Arbenz and G. H. Golub", year = "1987", title = "On the Spectral Decomposition of {Hermitian} Matrices Subject to Indefinite Low Rank Perturbations with Applications", number = "NA 87-07", institution = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{ArbGG88, author = "P. Arbenz and W. Gander and G. H. Golub", year = "1988", title = "Restricted Rank Modification of the Symmetric Eigenvalue Problem: Theoretical Considerations", journal = LinAlgApp, volume = "104", pages = "75--95", } @Article{ArbG88, author = "P. Arbenz and G. H. Golub", year = "1988", title = "On the Spectral Decomposition of {Hermitian} Matrices Subject to Indefinite Low Rank Perturbations with Applications", journal = SIAMMatrix, volume = "9", pages = "40--58", } @Techreport{AriDD88, author = "M. Arioli and J. W. Demmel and I. S. Duff", year = "1988", title = "Solving Sparse Linear Systems with Sparse Backward Error", number = "CSS 214", institution = "Computer Science and Systems Division, AERE Harwell", address = "Didcot, UK", } @Article{AriR85, author = "M. Arioli and F. Romani", year = "1985", title = "Relations Between Condition Numbers and the Convergence of the {Jacobi} Method for Real Positive Definite Matrices", journal = NumerMath, volume = "46", pages = "31--42", } @Article{AriL85, author = "M. Arioli and A. Laratta", year = "1985", title = "Error Analysis of an Algorithm for Solving an Underdetermined System", journal = NumerMath, volume = "46", pages = "255--268", } @Techreport{ArmC76, author = "E. S. Armstrong and A. K. Caglayan", year = "1976", title = "An Algorithm for the Weighting Matrices in the Sample-Data Optimal Linear Regulator Problem", number = "TN D-8372", institution = "NASA", } @Article{ArnL84, author = "W. F. Arnold and A. J. Laub", year = "1984", title = "Generalized Eigenproblem Algorithms and Software for Algebraic {Riccati} Equations", journal = ProcIEEE, volume = "72", pages = "1746--1754", } @Phdthesis{Ash87, author = "S. F. Ashby", year = "1987", title = "Polynomial Preconditioning for Conjugate Gradient Methods", school = "Computer Science, University of Illinois", address = "ILL", } @Techreport{AshMS88, author = "S. Ashby and T. A. Manteuffel and P. E. Saylor", year = "1988", title = "A Taxonomy for Conjugate Gradient Methods", number = "UCRL-98508", institution = "Lawrence Livermore National Laboratory", address = "Livermore, CA, USA", } @Article{Asp59, author = "E. Asplund", year = "1959", title = "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy {$a_{ij} = 0$, $j > i+p$}", journal = MathScand, volume = "7", pages = "57--60", } @Incollection{Axe77, author = "O. Axelsson", year = "1977", title = "Solution of Linear Systems of Equations: Iterative Methods", booktitle = "Sparse Matrix Techniques: {Copenhagen}, 1976", editor = "V. A. Barker", publisher = Springer, address = "Berlin, Germany", } @Article{Axe80, author = "O. Axelsson", year = "1980", title = "Conjugate Gradient Type Methods for Unsymmetric and Inconsistent Systems of Linear Equations", journal = LinAlgApp, volume = "29", pages = "1--66", } @Article{Axe85, author = "O. Axelsson", year = "1985", title = "A Survey of Preconditioned Iterative Methods for Linear Systems of Equations", journal = BIT, volume = "25", pages = "166--187", } @Article{AxeP86, author = "O. Axelsson and B. Polman", year = "1986", title = "On Approximate Factorization Methods for Block Matrices Suitable for Vector and Parallel Processors", journal = LinAlgApp, volume = "77", pages = "3--26", } @Article{Bai88a, author = "Z. Bai", year = "1988", title = "Note on the Quadratic Convergence of {Kogbetliantz}'s Algorithm for Computing the Singular Value Decomposition", journal = LinAlgApp, volume = "104", pages = "131--140", } @Article{Bai88b, author = "D. Bailey", year = "1988", title = "Extra High Speed Matrix Multiplication on the {Cray}-2", journal = SIAMSciStat, volume = "9", pages = "603--607", } @Article{BarI75, author = "I. Y. Bar-Itzhack", year = "1975", title = "Iterative Optimal Orthogonalization of the Strapdown Matrix", journal = IEEETransAeroElec, volume = "11", pages = "30--37", } @Article{Bar87, author = "J. L. Barlow", year = "1987", title = "On the Smallest Positive Singular Value of an {$M$}-Matrix with Applications to Ergodic {Markov} Chains", journal = SIAMAlgMeth, volume = "7", pages = "414--424", } @Article{BarNP88, author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons", year = "1988", title = "Iterative Methods for Equality Constrained Least Squares Problems", journal = SIAMSciStat, volume = "9", pages = "892--906", } @Article{BarS68, author = "S. Barnett and C. Storey", year = "1968", title = "Some Applications of the {Lyapunov} Matrix Equation", journal = InstMathApp, volume = "4", pages = "33--42", } @Article{BarP75a, author = "I. Barrodale and C. Phillips", year = "1975", title = "Algorithm~495: Solution of an Overdetermined System of Linear Equations in the {Chebychev} Norm", journal = ACMMathSoft, volume = "1", pages = "264--270", } @Article{BarR73, author = "I. Barrodale and F. D. K. Roberts", year = "1973", title = "An Improved Algorithm for Discrete {$L_{1}$} Linear Approximation", journal = SIAMNumAnal, volume = "10", pages = "839--848", } @Article{Bar71, author = "R. H. Bartels", year = "1971", title = "A Stabilization of the Simplex Method", journal = NumerMath, volume = "16", pages = "414--434", } @Article{BarCC78, author = "R. H. Bartels and A. R. Conn and C. Charalambous", year = "1978", title = "On {Cline}'s Direct Method for Solving Overdetermined Linear Systems in the {$L_{\infty}$} Sense", journal = SIAMNumAnal, volume = "15", pages = "255--270", } @Article{BarCS78, author = "R. H. Bartels and A. R. Conn and J. W. Sinclair", year = "1978", title = "Minimization Techniques for Piecewise Differentiable Functions: The {$L_{1}$} Solution to an Overdetermined Linear System", journal = SIAMNumAnal, volume = "15", pages = "224--241", } @Article{BarS72, author = "R. H. Bartels and G. W. Stewart", year = "1972", title = "Solution of the Equation {$AX + XB = C$}", journal = CACM, volume = "15", pages = "820--826", } @Article{BarMW67, author = "W. Barth and R. S. Martin and J. H. Wilkinson", year = "1967", title = "Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection", journal = NumerMath, volume = "9", pages = "386--393", note = "Also in \cite[pages 249--256]{WilR71}", } @Article{BarG76, author = "V. Barwell and J. A. George", year = "1976", title = "A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations", journal = ACMMathSoft, volume = "2", pages = "242--251", } @Article{BatW73, author = "K. J. Bathe and E. L. Wilson", year = "1973", title = "Solution Methods for Eigenvalue Problems in Structural Mechanics", journal = IntNumerEng, volume = "6", pages = "213--226", } @Article{BauF60a, author = "F. L. Bauer and C. T. Fike", year = "1960", title = "Norms and Exclusion Theorems", journal = NumerMath, volume = "2", pages = "137--144", } @Article{Bau63, author = "F. L. Bauer", year = "1963", title = "Optimally Scaled Matrices", journal = NumerMath, volume = "5", pages = "73--87", } @Article{Bau65, author = "F. L. Bauer", year = "1965", title = "Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems", journal = NumerMath, volume = "7", pages = "338--352", note = "Also in \cite[pages 119--133]{WilR71}", } @Article{BauF60b, author = "F. L. Bauer and C. T. Fike", year = "1960", title = "Norms and Exclusion Theorems", journal = NumerMath, volume = "2", pages = "137--144", } @Article{BauR68, author = "F. L. Bauer and C. Reinsch", year = "1968", title = "Rational {QR} Transformation with {Newton} Shift for Symmetric Tridiagonal Matrices", journal = NumerMath, volume = "11", pages = "264--272", note = "Also in \cite[pages 257--265]{WilR71}", } @Incollection{BauR70, author = "F. L. Bauer and C. Reinsch", year = "1970", title = "Inversion of Positive Definite Matrices by the {Gauss}-{Jordan} Methods", booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", editor = "J. H. Wilkinson and C. Reinsch", publisher = Springer, address = "New York, NY, USA", pages = "45--49", } @Article{BavS79, author = "C. Bavely and G. W. Stewart", year = "1979", title = "An Algorithm for Computing Reducing Subspaces by Block Diagonalization", journal = SIAMNumAnal, volume = "16", pages = "359--367", } @Book{Bel70, author = "R. Bellman", year = "1970", title = "Introduction to Matrix Analysis", edition = "second", publisher = McGrawHill, address = "New York, NY, USA", } @Article{Bel73, author = "E. Beltrami", year = "1873", title = "Sulle Funzioni Bilineari", journal = GiornaleMath, volume = "11", pages = "98--106", } @Article{BenS70, author = "C. F. Bender and I. Shavitt", year = "1970", title = "An Iterative Procedure for the Calculation of the Lowest Real Eigenvalue and Eigenvector of a Non-Symmetric Matrix", journal = CompPhys, volume = "6", pages = "146--149", } @Article{BerBI71, author = "A. Berman and A. Ben-Israel", year = "1971", title = "A Note on Pencils of {Hermitian} of Symmetric Matrices", journal = SIAMAppMath, volume = "21", pages = "51--54", } @Article{BerV68, author = "M. J. M. Bernal and J. H. Verner", year = "1968", title = "On Generalizations of the Theory of Consistent Orderings for Successive Over-Relaxation Methods", journal = NumerMath, volume = "12", pages = "215--222", } @Inproceedings{BerS86, author = "M. Berry and A. Sameh", year = "1986", title = "Multiprocessor {Jacobi} Algorithms for Dense Symmetric Eigenvalue and Singular Value Decompositions", booktitle = "Proceedings International Conference on Parallel Processing", pages = "433--440", } @Incollection{Bis87, author = "C. H. Bischof", year = "1987", title = "The Two-Sided Block {Jacobi} Method on Hypercube Architectures", booktitle = "Hypercube Multiprocessors", editor = "M. T. Heath", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Techreport{Bis88a, author = "C. H. Bischof", year = "1988", title = "Computing the Singular Value Decomposition on a Distributed System of Vector Processors", number = "87 869", institution = "Computer Science, Cornell University", address = "Ithaca, NY, USA", } @Phdthesis{Bis88b, author = "C. H. Bischof", year = "1988", title = "{QR} Factorization Algorithms for Coarse Grain Distributed Systems", school = "Computer Science, Cornell University", address = "Ithaca, NY, USA", } @Incollection{BisL86, author = "C. H. Bischof and C. Van Loan", year = "1986", title = "Computing the {SVD} on a Ring of Array Processors", booktitle = "Large Scale Eigenvalue Problems", editor = "J. Cullum and R. Willoughby", publisher = NorthHolland, pages = "51--66", } @Article{BisL87, author = "C. H. Bischof and C. Van Loan", year = "1987", title = "The {WY} Representation for Products of {Householder} Matrices", journal = SIAMSciStat, volume = "8", pages = "s2--s13", } @Article{Bjo67a, author = "{\AA}. Bj{\"o}rck", year = "1967", title = "Iterative Refinement of Linear Least Squares Solution~{I}", journal = BIT, volume = "7", pages = "257--278", } @Article{Bjo67b, author = "{\AA}. Bj{\"o}rck", year = "1967", title = "Solving Linear Least Squares Problems by {Gram}-{Schmidt} Orthogonalization", journal = BIT, volume = "7", pages = "1--21", } @Article{Bjo68, author = "{\AA}. Bj{\"o}rck", year = "1968", title = "Iterative Refinement of Linear Least Squares Solution {II}", journal = BIT, volume = "8", pages = "8--30", } @Article{Bjo84, author = "{\AA}. Bj{\"o}rck", year = "1984", title = "A General Updating Algorithm for Constrained Linear Least Squares Problems", journal = SIAMSciStat, volume = "5", pages = "394--402", } @Article{Bjo87, author = "{\AA}. Bj{\"o}rck", year = "1987", title = "Stability Analysis of the Method of Seminormal Equations", journal = LinAlgApp, volume = "88/89", pages = "31--48", } @Book{Bjo88, author = "{\AA}. Bj{\"o}rck", year = "1988", title = "Solution of Equations in {$R^N$}", series = "Least Squares Methods: Handbook of Numerical Analysis", volume = "1", publisher = NorthHolland, } @Article{BjoB71, author = "{\AA}. Bj{\"o}rck and C. Bowie", year = "1971", title = "An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix", journal = SIAMNumAnal, volume = "8", pages = "358--364", } @Article{BjoE73, author = "{\AA}. Bj{\"o}rck and T. Elfving", year = "1973", title = "Algorithms for Confluent {Vandermonde} Systems", journal = NumerMath, volume = "21", pages = "130--137", } @Article{BjoG67, author = "{\AA}. Bj{\"o}rck and G. H. Golub", year = "1967", title = "Iterative Refinement of Linear Least Squares Solutions by {Householder} Transformation", journal = BIT, volume = "7", pages = "322--337", } @Article{BjoG73, author = "{\AA}. Bj{\"o}rck and G. H. Golub", year = "1973", title = "Numerical Methods for Computing Angles Between Linear Subspaces", journal = MathComp, volume = "27", pages = "579--594", } @Article{BjoP70, author = "{\AA}. Bj{\"o}rck and V. Pereyra", year = "1970", title = "Solution of {Vandermonde} Systems of Equations", journal = MathComp, volume = "24", pages = "893--903", } @Book{BjoPS81, author = "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider", year = "1981", title = "Large-Scale Matrix Problems", publisher = NorthHolland, address = "New York, NY, USA", } @Article{BjoH83, author = "{\AA}. Bj{\"o}rck and S. Hammarling", year = "1983", title = "A {Schur} Method for the Square Root of a Matrix", journal = LinAlgApp, volume = "52/53", pages = "127--140", } @Article{Blu78, author = "J. M. Blue", year = "1978", title = "A Portable {Fortran} Program to Find the {Euclidean} Norm of a Vector", journal = ACMMathSoft, volume = "4", pages = "15--23", } @Article{Boh75, author = "Z. Bohte", year = "1975", title = "Bounds for Rounding Errors in the {Gaussian} Elimination for Band Systems", journal = InstMathApp, volume = "16", pages = "133--142", } @Article{BojBdH86, author = "A. W. Bojanczyk and R. P. Brent and F. R. de Hoog", year = "1986", title = "{QR} Factorization of {Toeplitz} Matrices", journal = NumerMath, volume = "49", pages = "81--94", } @Article{BojBDdH87, author = "A. W. Bojanczyk and R. P. Brent and P. Van Dooren and F. R. de Hoog", year = "1987", title = "A Note on Downdating the {Cholesky} Factorization", journal = SIAMSciStat, volume = "8", pages = "210--221", } @Inproceedings{BolG78, author = "D. L. Boley and G. H. Golub", year = "1978", title = "The Matrix Inverse Eigenvalue Problem for Periodic {Jacobi} Matrices", booktitle = "Proceedings Fourth Symposium on Basic Problems of Numerical Mathematics, {Prague}", pages = "63--76", } @Article{BolG84a, author = "D. Boley and G. H. Golub", year = "1984", title = "A Modified Method for Restructuring Periodic {Jacobi} Matrices", journal = MathComp, volume = "42", pages = "143--150", } @Article{BooE68, author = "J. Boothroyd and P. J. Eberlein", year = "1968", title = "Solution to the Eigenproblem by a Norm-Reducing {Jacobi}-Type Method (Handbook)", journal = NumerMath, volume = "11", pages = "1--12", note = "Also in \cite[pages 327--338]{WilR71}", } @Article{BowMPW66, author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H. Wilkinson", year = "1966", title = "Solution of Real and Complex Systems of Linear Equations", journal = NumerMath, volume = "8", pages = "217--234", note = "Also in \cite[pages 93--110]{WilR71}", } @Article{BowMRW68, author = "H. Bowdler and R. S. Martin and C. Reinsch and J. H. Wilkinson", year = "1968", title = "The {QR} and {QL} Algorithms for Symmetric Matrices", journal = NumerMath, volume = "11", pages = "293--306", note = "Also in \cite[pages 227--240]{WilR71}", } @Book{BoyBD+87, author = "J. Boyle and R. Butler and T. Disz and B. Glickfield and E. Lusk and R. Overbeek and J. Patterson and R. Stevens", year = "1987", title = "Portable Programs for Parallel Processors", publisher = HoltRinehartWinston, } @Article{BraPS86a, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", year = "1986", title = "The construction of Preconditioners for Elliptic Problems by Substructuring {I}", journal = MathComp, volume = "47", pages = "103--134", } @Article{BraPS86b, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", year = "1986", title = "The construction of Preconditioners for Elliptic Problems by Substructuring {II}", journal = MathComp, volume = "49", pages = "1--17", } @Article{Bre70, author = "R. P. Brent", year = "1970", title = "Error Analysis of Algorithms for Matrix Multiplication and Triangular Decomposition Using {Winograd}'s Identity", journal = NumerMath, volume = "16", pages = "145--156", } @Article{BreL85, author = "R. P. Brent and F. T. Luk", year = "1985", title = "The Solution of Singular Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays", journal = SIAMSciStat, volume = "6", pages = "69--84", } @Article{BreLL85, author = "R. P. Brent and F. T. Luk and C. Van Loan", year = "1985", title = "Computation of the Singular Value Decomposition Using Mesh Connected Processors", journal = VLSICompSys, volume = "1", pages = "242--270", } @Article{BroP75b, author = "K. W. Brodlie and M. J. D. Powell", year = "1975", title = "On the Convergence of Cyclic {Jacobi} Methods", journal = InstMathApp, volume = "15", pages = "279--287", } @Article{Bro73, author = "C. G. Broyden", year = "1973", title = "Some Condition Number Bounds for the {Gaussian} Elimination Process", journal = InstMathApp, volume = "12", pages = "273--286", } @Article{Buc74, author = "A. Buckley", year = "1974", title = "A Note on Matrices {$A = 1 + H$}, {$H$} Skew-Symmetric", journal = ZAngewMathMech, volume = "54", pages = "125--126", } @Article{Buc77, author = "A. Buckley", year = "1977", title = "On the Solution of Certain Skew-Symmetric Linear Systems", journal = SIAMNumAnal, volume = "14", pages = "566--570", } @Article{Bun71a, author = "J. R. Bunch", year = "1971", title = "Analysis of the Diagonal Pivoting Method", journal = SIAMNumAnal, volume = "8", pages = "656--680", } @Article{Bun71b, author = "J. R. Bunch", year = "1971", title = "Equilibration of Symmetric Matrices in the Max-Norm", journal = JACM, volume = "18", pages = "566--572", } @Article{Bun74, author = "J. R. Bunch", year = "1974", title = "Partial Pivoting Strategies for Symmetric Matrices", journal = SIAMNumAnal, volume = "11", pages = "521--528", } @Incollection{Bun76, author = "J. R. Bunch", year = "1976", title = "Block Methods for Solving Sparse Linear Systems", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = Academic, address = "New York, NY, USA", } @Article{BunK77, author = "J. R. Bunch and K. Kaufman", year = "1977", title = "Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems", journal = MathComp, volume = "31", pages = "162--179", } @Article{BunKP76, author = "J. R. Bunch and K. Kaufman and B. N. Parlett", year = "1976", title = "Decomposition of a Symmetric Matrix", journal = NumerMath, volume = "27", pages = "95--109", } @Article{BunNS78, author = "J. R. Bunch and C. P. Nielsen and D. C. Sorensen", year = "1978", title = "Rank-One Modification of the Symmetric Eigenproblem", journal = NumerMath, volume = "31", pages = "31--48", } @Article{BunP71, author = "J. R. Bunch and B. N. Parlett", year = "1971", title = "Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations", journal = SIAMNumAnal, volume = "8", pages = "639--655", } @Book{BunR76, editor = "J. R. Bunch and D. J. Rose", year = "1976", title = "Sparse Matrix Computations", publisher = Academic, address = "New York, NY, USA", } @Article{Bun82, author = "J. R. Bunch", year = "1982", title = "A Note on the Stable Decomposition of Skew Symmetric Matrices", journal = MathComp, volume = "158", pages = "475--480", } @Article{Bun85, author = "J. R. Bunch", year = "1985", title = "Stability of Methods for Solving {Toeplitz} Systems of Equations", journal = SIAMSciStat, volume = "6", pages = "349--364", } @Article{Bun87, author = "J. R. Bunch", year = "1987", title = "The Weak and Strong Stability of Algorithms in Numerical Linear Algebra", journal = LinAlgApp, volume = "88/89", pages = "49--66", } @Techreport{Bun69, author = "O. Buneman", year = "1969", title = "A Compact Non-Iterative {Poisson} Solver", institution = "Institute for Plasma Research", address = "Stanford University, Stanford, CA, USA", number = "294", } @Article{BunG84b, author = "A. Bunse-Gerstner", year = "1984", title = "An Algorithm for the Symmetric Generalized Eigenvalue Problem", journal = LinAlgApp, volume = "58", pages = "43--68", } @Article{BunGG88, author = "A. Bunse-Gerstner and W. B. Gragg", year = "1988", title = "Singular Value Decompositions of Complex Symmetric Matrices", journal = CompApplMath, volume = "21", pages = "41--54", } @Article{Bus68, author = "P. A. Businger", year = "1968", title = "Matrices Which Can be Optimally Scaled", journal = NumerMath, volume = "12", pages = "346--348", } @Article{Bus69, author = "P. A. Businger", year = "1969", title = "Reducing a Matrix to {Hessenberg} Form", journal = MathComp, volume = "23", pages = "819--821", } @Article{Bus71a, author = "P. A. Businger", year = "1971", title = "Monitoring the Numerical Stability of {Gaussian} Elimination", journal = NumerMath, volume = "16", pages = "360--361", } @Article{Bus71b, author = "P. A. Businger", year = "1971", title = "Numerically Stable Deflation of {Hessenberg} and Symmetric Tridiagonal Matrices", journal = BIT, volume = "11", pages = "262--270", } @Article{BusG65, author = "P. A. Businger and G. H. Golub", year = "1965", title = "Linear Least Squares Solutions by {Householder} Transformations", journal = NumerMath, volume = "7", pages = "269--276", note = "Also in \cite[pages 111--118]{WilR71}", } @Article{BusG69, author = "P. A. Businger and G. H. Golub", year = "1969", title = "Algorithm~358: Singular Value Decomposition of a Complex Matrix", journal = CACM, volume = "12", pages = "564--565", } @Article{BuzD74, author = "B. L. Buzbee and F. W. Dorr", year = "1974", title = "The Direct Solution of the Biharmonic Equation on Rectangular Regions and the {Poisson} Equation on Irregular Regions", journal = SIAMNumAnal, volume = "11", pages = "753--763", } @Article{BuzDGG71, author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub", year = "1971", title = "The Direct Solution of the Discrete {Poisson} Equation on Irregular Regions", journal = SIAMNumAnal, volume = "8", pages = "722--736", } @Article{BuzGN70, author = "B. L. Buzbee and G. H. Golub and C. W. Nielson", year = "1970", title = "On Direct Methods for Solving {Poisson}'s Equations", journal = SIAMNumAnal, volume = "7", pages = "627--656", } @Article{Buz86, author = "B. L. Buzbee", year = "1986", title = "A Strategy for Vectorization", journal = ParComputing, volume = "3", pages = "187--192", } @Phdthesis{Bye83, author = "R. Byers", year = "1983", title = "{Hamiltonian} and Symplectic Algorithms for the Algebraic {Riccati} Equation", school = "Center for Applied Mathematics, Cornell University", address = "Ithaca, NY, USA", } @Article{Bye84, author = "R. Byers", year = "1984", title = "A {Linpack}-Style Condition Estimator for the Equation {$AX - XB^{T} = C$}", journal = IEEETransAC, volume = "AC-29", pages = "926--928", } @Article{Bye86, author = "R. Byers", year = "1986", title = "A {Hamiltonian} {QR} Algorithm", journal = SIAMSciStat, volume = "7", pages = "212--229", } @Article{ByeN87, author = "R. Byers and S. G. Nash", year = "1987", title = "On the Singular Vectors of the {Lyapunov} Operator", journal = SIAMAlgMeth, volume = "8", pages = "59--66", } @Inproceedings{Cal86, author = "D. A. Calihan", year = "1986", title = "Block-Oriented, Local-Memory-Based Linear Equation Solution on the {Cray}-2: Uniprocessor Algorithms", booktitle = "Proceedings of the 1986 Conference on Parallel Processing", pages = "375--378", } @Article{ChaP77, author = "S. P. Chan and B. N. Parlett", year = "1977", title = "Algorithm~517: A Program for Computing the Condition Numbers of Matrix Eigenvalues without Computing Eigenvectors", journal = ACMMathSoft, volume = "3", pages = "186--203", } @Article{Cha82b, author = "T. F. Chan", year = "1982", title = "An Improved Algorithm for Computing the Singular Value Decomposition", journal = ACMMathSoft, volume = "8", pages = "72--83", } @Article{Cha82a, author = "T. F. Chan", year = "1982", title = "Algorithm~581: An Improved Algorithm for Computing the Singular Value Decomposition", journal = ACMMathSoft, volume = "8", pages = "84--88", } @Article{Cha84, author = "T. F. Chan", year = "1984", title = "Deflated Decomposition Solutions of Nearly Singular Systems", journal = SIAMNumAnal, volume = "21", pages = "738--754", } @Article{Cha85, author = "T. F. Chan", year = "1985", title = "On the Existence and Computation of {LU} Factorizations with small pivots", journal = MathComp, volume = "42", pages = "535--548", } @Article{Cha87, author = "T. F. Chan", year = "1987", title = "Rank-Revealing {QR} Factorizations", journal = LinAlgApp, volume = "88/89", pages = "67--82", } @Article{Cha88, author = "T. F. Chan", year = "1988", title = "An Optimal Circulant Preconditioner for {Toeplitz} Systems", journal = SIAMSciStat, volume = "9", pages = "766--771", } @Article{ChaJZ83, author = "T. F. Chan and K. R. Jackson and B. Zhu", year = "1983", title = "Alternating Direction Incomplete Factorizations", journal = SIAMNumAnal, volume = "20", pages = "239--257", } @Article{ChaM88, author = "H. Y. Chang and M.Salama", year = "1988", title = "A Parallel {Householder} Tridiagonalization Stratagem Using Scattered Square Decomposition", journal = ParComputing, volume = "6", pages = "297--312", } @Article{ChaVD88, author = "J. P. Charlier and M. Vanbegin and P. Van Dooren", year = "1988", title = "On Efficient Implementation of {Kogbetliantz}'s Algorithm for Computing the Singular Value Decomposition", journal = NumerMath, volume = "52", pages = "279--300", } @Article{ChaD87, author = "J. P. Charlier and P. Van Dooren", year = "1987", title = "On {Kogbetliantz}'s {SVD} Algorithm in the Presence of Clusters", journal = LinAlgApp, volume = "95", pages = "135--160", } @Article{CheDH84, author = "S. Chen and J. Dongarra and C. Hsuing", title = "Multiprocessing Linear Algebra Algorithms on the {Cray X-MP-2}: Experiences with Small Granularity", year = "1984", journal = ParDistComp, volume = "1", pages = "22--31", } @Article{CheKS78, author = "S. Chen and D. Kuck and A. Sameh", year = "1978", title = "Practical Parallel Band Triangular Systems Solvers", journal = ACMMathSoft, volume = "4", pages = "270--277", } @Article{CheS87, author = "K. H. Cheng and S. Sahni", year = "1987", title = "{VLSI} Systems for Band Matrix Multiplication", journal = ParComputing, volume = "4", pages = "239--258", } @Article{ChiMdP84, author = " R. C. Chin and T. A. Manteuffel and J. de Pillis", year = "1984", title = "{ADI} as a Preconditioning for Solving the Convection-Diffusion Equation", journal = SIAMSciStat, volume = "5", pages = "281--299", } @Article{Cli73, author = "A. K. Cline", year = "1973", title = "An Elimination Method for the Solution of Linear Least Squares Problems", journal = SIAMNumAnal, volume = "10", pages = "283--289", } @Article{Cli76a, author = "A. K. Cline", year = "1976", title = "A Descent Method for the Uniform Solution to Overdetermined Systems of Equations", journal = SIAMNumAnal, volume = "13", pages = "293--309", } @Techreport{Cli76b, author = "A. K. Cline", year = "1976", title = "Several observations on the Use of Conjugate Gradient Methods", type = "report", number = "76-22", institution = "ICASE, NASA Langley Research Center", address = "Hampton, VA, USA", } @Article{CliR83, author = "A. K. Cline and R. K. Rew", year = "1983", title = "A Set of Counter examples to Three Condition Number Estimators", journal = SIAMSciStat, volume = "4", pages = "602--611", } @Incollection{CliCL82, author = "A. K. Cline and A. R. Conn and C. Van Loan", year = "1982", title = "Generalizing the {LINPACK} Condition Estimator", booktitle = "Numerical Analysis", editor = "J. P. Hennart", series = "Lecture Notes in Mathematics 909", publisher = Springer, address = "New York, NY, USA", } @Incollection{CliGP76, author = "A. K. Cline and G. H. Golub and G. W. Platzman", year = "1976", title = "Calculation of Normal Modes of Oceans Using a {Lanczos} Method", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = Academic, address = "New York, NY, USA", pages = "409--426", } @Article{CliMSW79, author = "A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson", year = "1979", title = "An Estimate for the Condition Number of a Matrix", journal = SIAMNumAnal, volume = "16", pages = "368--375", } @Article{CliP76, author = "R. E. Cline and R. J. Plemmons", year = "1976", title = "{$L_{1}$}-Solutions to Underdetermined Linear Systems", journal = SIAMReview, volume = "18", pages = "92--106", } @Article{CliJ70, author = "M. Clint and A. Jennings", year = "1970", title = "The Evaluation of Eigenvalues and Eigenvectors of Real Symmetric Matrix by Simultaneous Iteration", journal = CompJour, volume = "13", pages = "76--80", } @Article{CliJ71, author = "M. Clint and A. Jennings", year = "1971", title = "A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem", journal = InstMathApp, volume = "8", pages = "111--121", } @Article{Coc68, author = "W. G. Cochrane", year = "1968", title = "Errors of Measurement in Statistics", journal = Techno, volume = "10", pages = "637--666", } @Article{Coh74, author = "A. M. Cohen", year = "1974", title = "A Note on Pivot Size in {Gaussian} Elimination", journal = LinAlgApp, volume = "8", pages = "361--368", } @Book{ColL88, author = "T. Coleman and C. Van Loan", year = "1988", title = "Handbook for Matrix Computations", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Article{ConG73, author = "P. Concus and G. H. Golub", year = "1973", title = "Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations", journal = SIAMNumAnal, volume = "10", pages = "1103--1120", } @Article{ConGM85, author = "P. Concus and G. H. Golub and G. Meurant", year = "1985", title = "Block Preconditioning for the Conjugate Gradient Method", journal = SIAMSciStat, volume = "6", pages = "220--252", } @Incollection{ConGO76, author = "P. Concus and G. H. Golub and D. P. O'Leary", year = "1976", title = "A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = Academic, address = "New York, NY, USA", } @Book{CdB80, author = "S. D. Conte and C. de Boor", year = "1980", title = "Elementary Numerical Analysis: An Algorithmic Approach", publisher = McGrawHill, address = "New York, NY, USA", edition = "third", } @Article{CopR79, author = "J. E. Cope and B. W. Rust", year = "1979", title = "Bounds on Solutions of Systems with Inaccurate Data", journal = SIAMNumAnal, volume = "16", pages = "950--963", } @Article{CosMR86, author = "M. Costnard and J. M. Muller and Y. Robert", year = "1986", title = "Parallel {QR} Decomposition of a Rectangular Matrix", journal = NumerMath, volume = "48", pages = "239--250", } @Article{CosMR88, author = "M. Costnard and M. Marrakchi and Y. Robert", year = "1988", title = "Parallel {Gaussian} Elimination on an {MIMD} Computer", journal = ParComputing, volume = "6", pages = "275--296", } @Article{Cot74, author = "R. W. Cottle", year = "1974", title = "Manifestations of the {Schur} Complement", journal = LinAlgApp, volume = "8", pages = "189--211", } @Article{Cox81, author = "M. G. Cox", year = "1981", title = "The Least Squares Solution of Overdetermined Linear Equations having Band or Augmented Band Structure", journal = IMANumerAna, volume = "1", pages = "3--22", } @Article{Cra73, author = "C. R. Crawford", year = "1973", title = "Reduction of a Band Symmetric Generalized Eigenvalue Problem", journal = CACM, volume = "16", pages = "41--44", } @Article{Cra76, author = "C. R. Crawford", year = "1976", title = "A Stable Generalized Eigenvalue Problem", journal = SIAMNumAnal, volume = "13", pages = "854--860", } @Article{Cra86, author = "C. R. Crawford", year = "1986", title = "Algorithm~646 {PDFIND}: A Routine to Find a Positive Definite Linear Combination of Two Real Symmetric Matrices", journal = ACMMathSoft, volume = "12", pages = "278--282", } @Article{CraM83, author = "C. R. Crawford and Y. S. Moon", year = "1983", title = "Finding a Positive Definite Linear Combination of Two {Hermitian} Matrices", journal = LinAlgApp, volume = "51", pages = "37--48", } @Article{Cry68, author = "C. W. Cryer", year = "1968", title = "Pivot Size in {Gaussian} Elimination", journal = NumerMath, volume = "12", pages = "335--345", } @Article{Cul78, author = "J. Cullum", year = "1978", title = "The Simultaneous Computation of a Few of the Algebraically Largest and Smallest Eigenvalues of a Large Sparse Symmetric Matrix", journal = BIT, volume = "18", pages = "265--275", } @Inproceedings{CulD74, author = "J. Cullum and W. E. Donath", year = "1974", title = "A Block {Lanczos} Algorithm for Computing the {Q} Algebraically Largest Eigenvalues and a Corresponding Eigenspace of Large, Sparse Real Symmetric Matrices", booktitle = "Proceedings of the 1974 IEEE Conference on Decision and Control, {Phoenix, AZ}", pages = "505--509", } @Techreport{CulW77, author = "J. Cullum and R. A. Willoughby", year = "1977", title = "The Equivalence of the {Lanczos} and the Conjugate Gradient Algorithms", number = "RC-6903", institution = "IBM", address = "Yorktown Heights, NY, USA", } @Inproceedings{CulW79, author = "J. Cullum and R. A. Willoughby", year = "1979", title = "{Lanczos} and the Computation in Specified Intervals of the Spectrum of Large, Sparse Real Symmetric Matrices", booktitle = "Sparse Matrix Proceedings 1978", editor = "I. S. Duff and G. W. Stewart", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Article{CulW80, author = "J. Cullum and R. A. Willoughby", year = "1980", title = "The {Lanczos} Phenomena: An Interpretation Based on Conjugate Gradient Optimization", journal = LinAlgApp, volume = "29", pages = "63--90", } @Book{CulW85b, author = "J. Cullum and R. A. Willoughby", year = "1985", title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue Computations, Volume 1: Theory", publisher = Birkhauser, address = "Boston, MA, USA", } @Book{CulW85a, author = "J. Cullum and R. A. Willoughby", year = "1985", title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue Computations, Volume 2: Programs", publisher = Birkhauser, address = "Boston, MA, USA", } @Book{CulW86, editor = "J. Cullum and R. A. Willoughby", year = "1986", title = "Large Scale Eigenvalue Problems", publisher = NorthHolland, } @Article{CulWL83, author = "J. Cullum and R. A. Willoughby and M. Lake", year = "1983", title = "A {Lanczos} Algorithm for Computing Singular Values and Vectors of Large Matrices", journal = SIAMSciStat, volume = "4", pages = "197--215", } @Article{Cup81, author = "J. J. M. Cuppen", year = "1981", title = "A Divide and Conquer Method for the Symmetric Eigenproblem", journal = NumerMath, volume = "36", pages = "177--195", } @Article{Cup83, author = "J. J. M. Cuppen", year = "1983", title = "The Singular Value Decomposition in Product Form", journal = SIAMSciStat, volume = "4", pages = "216--222", } @Article{Cup84, author = "J. J. M. Cuppen", year = "1984", title = "On Updating Triangular Products of {Householder} Matrices", journal = NumerMath, volume = "45", pages = "403--410", } @Incollection{Cut72, author = "E. Cuthill", year = "1972", title = "Several Strategies for Reducing the Bandwidth of Matrices", booktitle = "Sparse Matrices and Their Applications", editor = "D. J. Rose and R. A. Willoughby", publisher = PlenumPress, address = "New York, NY, USA", } @Phdthesis{Cyb78, author = "G. Cybenko", year = "1978", title = "Error Analysis of Some Signal Processing Algorithms", school = "Princeton University", address = "Princeton, NJ, USA", } @Article{Cyb80, author = "G. Cybenko", year = "1980", title = "The Numerical Stability of the {Levinson}-{Durbin} Algorithm for {Toeplitz} Systems of Equations", journal = SIAMSciStat, volume = "1", pages = "303--310", } @Article{Cyb84, author = "G. Cybenko", year = "1984", title = "The Numerical Stability of the Lattice Algorithm for Least Squares Linear Prediction Problems", journal = BIT, volume = "24", pages = "441--455", } @Article{CybL86, author = "G. Cybenko and C. Van Loan", year = "1986", title = "Computing the Minimum Eigenvalue of a Symmetric Positive Definite {Toeplitz} Matrix", journal = SIAMSciStat, volume = "7", pages = "123--131", } @Article{DanGKS76, author = "J. Daniel and W. B. Gragg and L. Kaufman and G. W. Stewart", year = "1976", title = "Reorthogonalization and Stable Algorithms for Updating the {Gram}-{Schmidt} {QR} Factorization", journal = MathComp, volume = "30", pages = "772--795", } @Article{Dav73, author = "C. Davis", year = "1973", title = "Explicit Functional Calculus", journal = LinAlgApp, volume = "6", pages = "193--199", } @Book{DatJK+88, author = "B. N. Datta and C. R. Johnson and M. A. Kaashoek and R. Plemmons and E. D. Sontag", year = "1988", title = "Linear Algebra in Signals, Systems, and Control", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Article{Dav86, author = "G. J. Davis", year = "1986", title = "Column {LU} Pivoting on a Hypercube Multiprocessor", journal = SIAMAlgMeth, volume = "7", pages = "538--550", } @Article{DavK70, author = "C. Davis and W. M. Kahan", year = "1970", title = "The Rotation of Eigenvectors by a Perturbation {III}", journal = SIAMNumAnal, volume = "7", pages = "1--46", } @Article{DaxK77, author = "A. Dax and S. Kaniel", year = "1977", title = "Pivoting Techniques for Symmetric {Gaussian} Elimination", journal = NumerMath, volume = "28", pages = "221--242", } @Article{DayP88, author = "J. Day and B. Peterson", year = "1988", title = "Growth in {Gaussian} Elimination", journal = AmerMathMonthly, volume = "95", pages = "489--513", } @Techreport{DayD88, author = "M. J. Dayde and I. S. Duff", year = "1988", title = "Use of Level-3 {BLAS} in {LU} Factorization on the {Cray}-2, the {ETA-10P}, and the {IBM 3090-200/VF}", number = "CSS-229", institution = "Computer Science and Systems Division, Harwell Laboratory", address = "Oxon OX11 ORA, UK", } @Article{dBooP77, author = "C. de Boor and A. Pinkus", year = "1977", title = "A Backward Error Analysis for Totally Positive Linear Systems", journal = NumerMath, volume = "27", pages = "485--490", } @Article{DeiNT83, author = "P. Deift and T. Nande and C. Tome", year = "1983", title = "Ordinary Differential Equations and the Symmetric Eigenvalue Problem", journal = SIAMNumAnal, volume = "20", pages = "1--22", } @Article{DekT71, author = "T. J. Dekker and J. F. Traub", year = "1971", title = "The Shifted {QR} Algorithm for {Hermitian} Matrices", journal = LinAlgApp, volume = "4", pages = "137--154", } @Article{DelI86, author = "J. M. Delosme and I. C. F. Ipsen", year = "1986", title = "Parallel Solution of Symmetric Positive Definite Systems with Hyperbolic Rotations", journal = LinAlgApp, volume = "77", pages = "75--112", } @Phdthesis{Dem83b, author = "J. W. Demmel", year = "1983", title = "A Numerical Analyst's {Jordan} Canonical Form", school = "Univ. of California at Berkeley", address = "Berkeley, CA, USA", } @Article{Dem83a, author = "J. W. Demmel", year = "1983", title = "The Condition Number of Equivalence Transformations that Block Diagonalize Matrix Pencils", journal = SIAMNumAnal, volume = "20", pages = "599--610", } @Article{Dem84, author = "J. W. Demmel", year = "1984", title = "Underflow and the Reliability of Numerical Software", journal = SIAMSciStat, volume = "5", pages = "887--919", } @Article{Dem87b, author = "J. W. Demmel", year = "1987", title = "On the Distance to the Nearest Ill-Posed Problem", journal = NumerMath, volume = "51", pages = "251--289", } @Article{Dem87a, author = "J. W. Demmel", year = "1987", title = "A Counterexample for two Conjectures About Stability", journal = IEEETransAC, volume = "AC-32", pages = "340--342", } @Article{Dem87d, author = "J. W. Demmel", year = "1987", title = "Three Methods for Refining Estimates of Invariant Subspaces", journal = Computing, volume = "38", pages = "43--57", } @Article{Dem87c, author = "J. W. Demmel", year = "1987", title = "The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems", journal = SIAMNumAnal, volume = "24", pages = "199--206", } @Article{Dem88, author = "J. W. Demmel", year = "1988", title = "The Probability that a Numerical Analysis Problem is Difficult", journal = MathComp, volume = "50", pages = "449--480", } @Article{DemK87, author = "J. W. Demmel and B. K{\aa}gstr{\"o}m", year = "1987", title = "Computing Stable Eigendecompositions of Matrix Pencils", journal = LinAlgApp, volume = "88/89", pages = "139--186", } @Article{DemK88, author = "J. W. Demmel and B. K{\aa}gstr{\"o}m", year = "1988", title = "Accurate Solutions of Ill-Posed Problems in Control Theory", journal = SIAMMatrix, pages = "126--145", } @Book{DenS83, author = "J. E. Dennis and R. Schnabel", year = "1983", title = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{DenT87, author = "J. E. {Dennis, Jr.} and K. Turner", year = "1987", title = "Generalized Conjugate Directions", journal = LinAlgApp, volume = "88/89", pages = "187--209", } @Article{Des63, author = "J. Descloux", year = "1963", title = "Bounds for the Spectral Norm of Functions of Matrices", journal = NumerMath, volume = "5", pages = "185--190", } @Article{DiaF76, author = "M. A. Diamond and D. L. V. Ferreira", year = "1976", title = "On a Cyclic Reduction Method for the Solution of {Poisson}'s Equation", journal = SIAMNumAnal, volume = "13", pages = "54--70", } @Article{Don83, author = "J. J. Dongarra", year = "1983", title = "Improving the Accuracy of Computed Singular Values", journal = SIAMSciStat, volume = "4", pages = "712--719", } @Manual{DonBMS78, author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", year = "1978", title = "{LINPACK} Users Guide", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Techreport{DonCDH88, author = "J. J. Dongarra and J. Du Croz and I. S. Duff and S. Hammarling", year = "1988", title = "A Set of Level 3 {Basic} {Linear} {Algebra} {Subprograms}", number = "ANL-MCS-TM-88", institution = "Argonne National Laboratory", address = "Argonne, ILL", } @Article{DonCHH88b, author = "J. J. Dongarra and J. Du Croz and S. Hammarling and R. J. Hanson", year = "1988", title = "An Extended Set of {Fortran} {Basic} {Linear} {Algebra} {Subprograms}", journal = ACMMathSoft, volume = "14", pages = "1--17", } @Article{DonCHH88a, author = "J. J. Dongarra and J. Du Croz and S. Hammarling and R. J. Hanson", year = "1988", title = "Algorithm~656: An Extended Set of {Fortran} Basic Linear Algebra Subprograms: Model Implementation and Test Programs", journal = ACMMathSoft, volume = "14", pages = "18--32", } @Article{DonE84, author = "J. J. Dongarra and S. Eisenstat", year = "1984", title = "Squeezing the Most Out of an Algorithm in {Cray} {Fortran}", journal = ACMMathSoft, volume = "10", pages = "221--230", } @Article{DonGK84, author = "J. J. Dongarra and F. G. Gustavson and A. Karp", year = "1984", title = "Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine", journal = SIAMReview, volume = "26", pages = "91--112", } @Techreport{DonHS87, author = "J. J. Dongarra and S. Hammarling and D. C. Sorensen", year = "1987", title = "Block Reduction of Matrices to Condensed form for Eigenvalue Computations", number = "ANL-MCS-TM 99", institution = "Argonne National Laboratory", address = "Argonne, IL, USA", } @Article{DonH86, author = "J. Dongarra and T. Hewitt", year = "1986", title = "Implementing Dense Linear Algebra Algorithms Using Multitasking on the {Cray X-MP-4} (or Approaching the Gigaflop)", journal = SIAMSciStat, volume = "7", pages = "347--350", } @Article{DonH79, author = "J. Dongarra and A. Hinds", year = "1979", title = "Unrolling Loops in {Fortran}", journal = SoftPracExp, volume = "9", pages = "219--229", } @Article{DonH84, author = "J. J. Dongarra and R. E. Hiromoto", year = "1984", title = "A Collection of Parallel Linear Equation Routines for the {Denelcor} {HEP}", journal = ParComputing, volume = "1", pages = "133--142", } @Article{DonKH86, author = "J. J. Dongarra and L. Kaufman and S. Hammarling", year = "1986", title = "Squeezing the Most Out of Eigenvalue Solvers on High Performance Computers", journal = LinAlgApp, volume = "77", pages = "113--136", } @Article{DonMW83, author = "J. J. Dongarra and C. B. Moler and J. H. Wilkinson", year = "1983", title = "Improving the Accuracy of Computed Eigenvalues and Eigenvectors", journal = SIAMNumAnal, volume = "20", pages = "23--46", } @Article{DonS84, author = "J. J. Dongarra and A. H. Sameh", year = "1984", title = "On Some Parallel Banded System Solvers", journal = ParComputing, volume = "1", pages = "223--235", } @Article{DonSS86, author = "J. J. Dongarra and A. Sameh and D. Sorensen", year = "1986", title = "Implementation of Some Concurrent Algorithms for Matrix Factorization", journal = ParComputing, volume = "3", pages = "25--34", } @Article{DonS86, author = "J. J. Dongarra and D. C. Sorensen", year = "1986", title = "Linear Algebra on High Performance Computers", journal = ApplMathComp, volume = "20", pages = "57--88", } @Article{DonS87a, author = "J. J. Dongarra and D. C. Sorensen", year = "1987", title = "A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem", journal = SIAMSciStat, volume = "8", pages = "s139-s154", } @Article{DonS87b, author = "J. J. Dongarra and D. C. Sorensen", year = "1987", title = "A Portable Environment for Developing Parallel Programs", journal = ParComputing, volume = "5", pages = "175--186", } @Article{Dor70, author = "F. W. Dorr", year = "1970", title = "The Direct Solution of the Discrete {Poisson} Equation on a Rectangle", journal = SIAMReview, volume = "12", pages = "248--263", } @Article{Dor73, author = "F. W. Dorr", year = "1973", title = "The Direct Solution of the Discrete {Poisson} Equation in {$O(n^{2})$} Operations", journal = SIAMReview, volume = "15", pages = "412--415", } @Article{DubGR79, author = "P. F. Dubois and A. Greenbaum and G. H. Rodrigue", year = "1979", title = "Approximating the Inverse of a Matrix for Use on Iterative Algorithms on Vector Processors", journal = Computing, volume = "22", pages = "257--268", } @Article{Dub70, author = "A. Dubrulle", year = "1970", title = "A Short Note on the Implicit {QL} Algorithm for Symmetric Tridiagonal Matrices", journal = NumerMath, volume = "15", pages = "450", } @Article{DubMW68, author = "A. Dubrulle and R. S. Martin and J. H. Wilkinson", year = "1968", title = "The Implicit {QL} Algorithm", journal = NumerMath, volume = "12", pages = "377--383", note = "Also in \cite[pages 241--248]{WilR71}", } @Article{Duf74, author = "I. S. Duff", year = "1974", title = "Pivot Selection and Row Ordering in {Givens} Reduction on Sparse Matrices", journal = Computing, volume = "13", pages = "239--248", } @Article{Duf77, author = "I. S. Duff", year = "1977", title = "A Survey of Sparse Matrix Research", journal = ProcIEEE, volume = "65", pages = "500--535", } @Article{DufR75, author = "I. S. Duff and J. K. Reid", year = "1975", title = "On the Reduction of Sparse Matrices to Condensed Forms by Similarity Transformations", journal = InstMathApp, volume = "15", pages = "217--224", } @Article{DufR76, author = "I. S. Duff and J. K. Reid", year = "1976", title = "A Comparison of Some Methods for the Solution of Sparse Over-Determined Systems of Linear Equations", journal = InstMathApp, volume = "17", pages = "267--280", } @Proceedings{DufS78, editor = "I. S. Duff and G. W. Stewart", year = "1978", title = "Sparse Matrix Proceedings", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Book{DufER86, author = "I. S. Duff and A. M. Erisman and J. K. Reid", year = "1986", title = "Direct Methods for Sparse Matrices", publisher = OxfordPress, } @Book{DunS58, author = "N. Dunford and J. Schwartz", year = "1958", title = "Linear Operators, Part {I}", publisher = Interscience, address = "New York, NY, USA", } @Article{Dur60, author = "J. Durbin", year = "1960", title = "The Fitting of Time Series Models", journal = RevueInstStat, volume = "28", pages = "233--243", } @Article{Ebe65, author = "P. J. Eberlein", year = "1965", title = "On Measures of Non-normality for Matrices", journal = AmerMathMonthly, volume = "72", pages = "995--996", } @Article{Ebe70, author = "P. J. Eberlein", year = "1970", title = "Solution to the Complex Eigenproblem by a Norm-Reducing {Jacobi}-Type Method", journal = NumerMath, volume = "14", pages = "232--245", note = "Also in \cite[pages 404--417]{WilR71}", } @Article{Ebe71, author = "P. J. Eberlein", year = "1971", title = "On the Diagonalization of Complex Symmetric Matrices", journal = InstMathApp, volume = "7", pages = "377--383", } @Incollection{Ebe87, author = "P. J. Eberlein", year = "1987", title = "On Using the {Jacobi} Method on a Hypercube", booktitle = "Hypercube Multiprocessors", editor = "M. T. Heath", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Article{EckY39, author = "C. Eckart and G. Young", year = "1939", title = "A Principal Axis Transformation for Non-{Hermitian} Matrices", journal = BullAMS, volume = "45", pages = "118--121", } @Article{EieN83, author = "M. Eiermann and W. Niethammer", year = "1983", title = "On the Construction of Semi-iterative Methods", journal = SIAMNumAnal, volume = "20", pages = "1153--1160", } @Article{Eis84, author = "S. C. Eisenstat", year = "1984", title = "Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods", journal = SIAMSciStat, volume = "2", pages = "1--4", } @Article{EisHHR88, author = "S.C Eisenstat and M. T. Heath and C. S. Henkel and C. H. Romine", year = "1988", title = "Modified Cyclic Algorithms for Solving Triangular Systems on Distributed Memory Multiprocessors", journal = SIAMSciStat, volume = "9", pages = "589--600", } @Article{Eld77a, author = "L. Eld{\`e}n", year = "1977", title = "Algorithms for the Regularization of Ill-Conditioned Least Squares Problems", journal = BIT, volume = "17", pages = "134--145", } @Phdthesis{Eld77b, author = "L. Eld{\`e}n", year = "1977", title = "Numerical Analysis of Regularization and Constrained Least Square Methods", number = "20", school = "Linkoping Studies in Science and Technology", address = "Linkoping, Sweden", } @Article{Eld80, author = "L. Eld{\`e}n", year = "1980", title = "Perturbation Theory for the Least Squares Problem with Linear Equality Constraints", journal = SIAMNumAnal, volume = "17", pages = "338--350", } @Article{Eld83, author = "L. Eld{\`e}n", year = "1983", title = "A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems", journal = BIT, volume = "22", pages = "487--502", } @Article{Eld84, author = "L. Eld{\`e}n", year = "1984", title = "An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems", journal = SIAMSciStat, volume = "5", pages = "237--254", } @Article{Eld85, author = "L. Eld{\`e}n", year = "1985", title = "A Note on the Computation of the Generalized Cross-Validation Function for Ill-Conditioned Least Squares Problems", journal = BIT, volume = "24", pages = "467--472", } @Techreport{Eld88, author = "L. Eld{\`e}n", year = "1988", title = "A Parallel {QR} Decomposition Algorithm", number = "LiTh Mat R 1988-02", institution = "Mathematics, Linkoping University", address = "Sweden", } @Article{EldS86, author = "L. Eld{\`e}n and R. Schreiber", year = "1986", title = "An Application of Systolic Arrays to Linear Discrete Ill-Posed Problems", journal = SIAMSciStat, volume = "7", pages = "892--903", } @Article{Elm86, author = "H. Elman", year = "1986", title = "A Stability Analysis of Incomplete {LU} Factorization", journal = MathComp, volume = "47", pages = "191--218", } @Article{ElsS82, author = "L. Elsner and J. Guang Sun", year = "1982", title = "Perturbation Theorems for the Generalized Eigenvalue Problem", journal = LinAlgApp, volume = "48", pages = "341--357", } @Inproceedings{ElsR88, author = "A. Elster and A. P. Reeves", year = "1988", title = "Block Matrix Operations Using Orthogonal Trees", booktitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", editor = "G. Fox", publisher = ACMPress, address = "New York, NY, USA", pages = "1554--1561", } @Article{Enr79, author = "W. Enright", year = "1979", title = "On the Efficient and Reliable Numerical Solution of Large Linear Systems of {O. D. E.}'s", journal = IEEETransAC, volume = "AC-24", pages = "905--908", } @Article{Erd67, author = "I. Erdelyi", year = "1967", title = "On the Matrix Equation {$Ax = \lambda Bx$}", journal = MathAnaAppl, volume = "17", pages = "119--132", } @Article{EriR80, author = "T. Ericsson and A. Ruhe", year = "1980", title = "The Spectral Transformation {Lanczos} Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems", journal = MathComp, volume = "35", pages = "1251--1268", } @Article{EriR74, author = "A. M. Erisman and J. K. Reid", year = "1974", title = "Monitoring the Stability of the Triangular Factorization of a Sparse Matrix", journal = NumerMath, volume = "22", pages = "183--186", } @Article{Eva84, author = "D. J. Evans", year = "1984", title = "Parallel {SOR} Iterative Methods", journal = ParComputing, volume = "1", pages = "3--18", } @Article{EvaD83, author = "D. J. Evans and R. Dunbar", year = "1983", title = "The Parallel Solution of Triangular Systems of Equations", journal = IEEETransComp, volume = "C-32", pages = "201--204", } @Article{FabM84, author = "V. Faber and T. Manteuffel", year = "1984", title = "Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method", journal = SIAMNumAnal, volume = "21", pages = "352--362", } @Book{FadF63, author = "D. K. Faddeev and V. N. Faddeva", year = "1963", title = "Computational Methods of Linear Algebra", publisher = WHFreeman, address = "San Francisco, CA, USA", } @Article{FadF77, author = "V. N. Fadeeva and D. K. Fadeev", year = "1977", title = "Parallel Calculations in Linear Algebra", journal = Kibernetika, volume = "6", pages = "28--40", } @Article{FaiL70, author = "W. Fair and Y. Luke", year = "1970", title = "{Pad}{\'e} Approximations to the Operator Exponential", journal = NumerMath, volume = "14", pages = "379--382", } @Article{FeiV62, author = "D. G. Feingold and R. S. Varga", year = "1962", title = "Block Diagonally Dominant Matrices and Generalizations of the {Gershgorin} Circle Theorem", journal = "Pacific J. Math.", volume = "12", pages = "1241--1250", } @Article{FenL74, author = "T. Fenner and G. Loizou", year = "1974", title = "Some New Bounds on the Condition Numbers of Optimally Scaled Matrices", journal = JACM, volume = "1", pages = "514--524", } @Article{FisU69, author = "C. Fischer and R. A. Usmani", year = "1969", title = "Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems", journal = SIAMNumAnal, volume = "6", pages = "127--142", } @Article{FixH72, author = "G. Fix and R. Heiberger", year = "1972", title = "An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem", journal = SIAMNumAnal, volume = "9", pages = "78--88", } @Article{Fle76, author = "R. Fletcher", year = "1976", title = "Factorizing Symmetric Indefinite Matrices", journal = LinAlgApp, volume = "14", pages = "257--272", } @Article{For60, author = "G. E. Forsythe", year = "1960", title = "Crout with Pivoting", journal = CACM, volume = "3", pages = "507--508", } @Article{ForG65, author = "G. E. Forsythe and G. H. Golub", year = "1965", title = "On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere", journal = SIAMAppMath, volume = "13", pages = "1050--1068", } @Article{ForH60, author = "G. E. Forsythe and P. Henrici", year = "1960", title = "The Cyclic {Jacobi} Method for Computing the Principal Values of a Complex Matrix", journal = "Trans. Amer. Math. Soc.", volume = "94", pages = "1--23", } @Book{ForMM77, author = "G. E. Forsythe and M. A. Malcolm and C. B. Moler", year = "1977", title = "Computer Methods for Mathematical Computations", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Book{ForM67, author = "G. E. Forsythe and C. B. Moler", year = "1967", title = "Computer Solution of Linear Algebraic Systems", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{Fos86, author = "L. V. Foster", year = "1986", title = "Rank and Null Space Calculations Using Matrix Decomposition without Column Interchanges", journal = LinAlgApp, volume = "74", pages = "47--71", } @Article{Fou84, author = "R. Fourer", year = "1984", title = "Staircase Matrices and Systems", journal = SIAMReview, volume = "26", pages = "1--71", } @Book{Fox64, author = "L. Fox", year = "1964", title = "An Introduction to Numerical Linear Algebra", publisher = OxfordPress, address = "Oxford, UK", } @Proceedings{Fox88, editor = "G. Fox", year = "1988", title = "Applications", series = "The Third Conference on Hypercube Concurrent Computers and Applications", volume = "2", publisher = ACMPress, address = "New York, NY, USA", } @Article{FoxOH87, author = "G. Fox and S. W. Otto and A. J. Hey", year = "1987", title = "Matrix Algorithms on a Hypercube {I}: Matrix Multiplication", journal = ParComputing, volume = "4", pages = "17--31", } @Book{FoxJL+88, author = "G. Fox and M. Johnson and G. Lyzenga and S. Otto and J. Salmon and D. Walker", year = "1988", title = "On Concurrent Processors Vol {I}: General Techniques and Regular Problems", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{Fra64a, author = "J. S. Frame", year = "1964", title = "Matrix Functions and Applications, Part {II}", journal = IEEESpec, volume = "1", month = apr, pages = "102--108", } @Article{Fra64b, author = "J. S. Frame", year = "1964", title = "Matrix Functions and Applications, Part {IV}", journal = IEEESpec, volume = "1", month = jun, pages = "123--131", } @Article{Fra61, author = "J. G. F. Francis", year = "1961", title = "The {QR} Transformation: A Unitary Analogue to the {LR} Transformation, Parts~{I} and~{II}", journal = CompJour, volume = "4", pages = "265--272, 332--345", } @Article{Fri75, author = "S. Friedland", year = "1975", title = "On Inverse Multiplicative Eigenvalue Problems for Matrices", journal = LinAlgApp, volume = "12", pages = "127--138", } @Article{Fri77, author = "S. Friedland", year = "1977", title = "Inverse Eigenvalue Problems", journal = LinAlgApp, volume = "17", pages = "15--52", } @Article{FriNO87, author = "S. Friedland and J. Nocedal and M. L. Overton", year = "1987", title = "The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems", journal = SIAMNumAnal, volume = "24", pages = "634--667", } @Article{Fro65, author = "C. E. Froberg", year = "1965", title = "On Triangularization of Complex Matrices by Two-Dimen\-sional Unitary Transformations", journal = BIT, volume = "5", pages = "230--234", } @Article{FunG86, author = "R. E. Funderlic and A. Geist", year = "1986", title = "Torus Data Flow for Parallel Computation of Missized Matrix Problems", journal = LinAlgApp, volume = "77", pages = "149--164", } @Article{FunNP82, author = "R. E. Funderlic and M. Neuman and R. J. Plemmons", year = "1982", title = "Generalized Diagonally Dominant Matrices", journal = NumerMath, volume = "40", pages = "57--70", } @Article{GalP70, author = "G. Galimberti and V. Pereyra", year = "1970", title = "Numerical Differentiation and the Solution of Multidimensional {Vandermonde} Systems", journal = MathComp, volume = "24", pages = "357--364", } @Article{GalP71, author = "G. Galimberti and V. Pereyra", year = "1971", title = "Solving Confluent {Vandermonde} Systems of {Hermite} Type", journal = NumerMath, volume = "18", pages = "44--60", } @Article{GalJM87, author = "K. Gallivan and W. Jalby and U. Meier", year = "1987", title = "The Use of {BLAS3} in Linear Algebra on a Parallel Processor with a Hierarchical Memory", journal = SIAMSciStat, volume = "8", pages = "1079--1084", } @Article{GalJMS88, author = "K. Gallivan and W. Jalby and U. Meier and A. H. Sameh", year = "1988", title = "Impact of Hierarchical Memory Systems on Linear Algebra Algorithm Design", journal = IntSuper, volume = "2", pages = "12--48", } @Article{Gan81, author = "W. Gander", year = "1981", title = "Least Squares with a Quadratic Constraint", journal = NumerMath, volume = "36", pages = "291--307", } @Article{GanR84, author = "D. Gannon and J. Van Rosendale", year = "1984", title = "On the Impact of Communication Complexity on the Design of Parallel Numerical Algorithms", journal = IEEETransComp, volume = "C-33", pages = "1180--1194", } @Book{Gan59a, author = "F. R. Gantmacher", year = "1959", title = "The Theory of Matrices", publisher = Chelsea, address = "New York, NY, USA", volume = "1", } @Book{Gan59b, author = "F. R. Gantmacher", year = "1959", title = "The Theory of Matrices", publisher = Chelsea, address = "New York, NY, USA", volume = "2", } @Manual{GarBDM72, author = "B. S. Garbow and J. M. Boyle and J. J. Dongarra and C. B. Moler", year = "1972", title = "Matrix Eigensystem Routines: {EISPACK} Guide Extension", publisher = Springer, address = "New York, NY, USA", } @Article{Gau75a, author = "W. Gautschi", year = "1975", title = "Norm Estimates for Inverses of {Vandermonde} Matrices", journal = NumerMath, volume = "23", pages = "337--347", } @Article{Gau75b, author = "W. Gautschi", year = "1975", title = "Optimally Conditioned {Vandermonde} Matrices", journal = NumerMath, volume = "24", pages = "1--12", } @Techreport{GeiH85, author = "G. A. Geist and M. T. Heath", year = "1985", title = "Parallel {Cholesky} Factorization on a Hypercube Multiprocessor", number = "ORNL 6190", institution = "Oak Ridge Laboratory", address = "Oak Ridge, TN, USA", } @Incollection{GeiH86, author = "G. A. Geist and M. T. Heath", year = "1986", title = "Matrix Factorization on a Hypercube", booktitle = "Hypercube Multiprocessors", editor = "M. T. Heath", publisher = SIAMPub, pages = "161--180", } @Inproceedings{GeiWDF88, author = "G. A. Geist and R. C. Ward and G. J. Davis and R. E. Funderlic", year = "1988", title = "Finding Eigenvalues and Eigenvectors of Unsymmetric Matrices Using a Hypercube Multiprocessor", booktitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", editor = "G. Fox", publisher = ACMPress, address = "New York, NY, USA", pages = "1577--1582", } @Article{Gen73a, author = "W. M. Gentleman", year = "1973", title = "Error Analysis of {QR} Decompositions by {Givens} Transformations", journal = LinAlgApp, volume = "10", pages = "189--197", } @Article{Gen73b, author = "W. M. Gentleman", year = "1973", title = "Least Squares Computations by {Givens} Transformations Without Square Roots", journal = InstMathApp, volume = "12", pages = "329--336", } @Inproceedings{GenK82, author = "W. M. Gentleman and H. T. Kung", year = "1982", title = "Matrix Triangularization by Systolic Arrays", booktitle = "{SPIE} Proceedings", volume = "298", pages = "19--26", } @Article{Geo73, author = "J. A. George", year = "1973", title = "Nested Dissection of a Regular Finite Element Mesh", journal = SIAMNumAnal, volume = "10", pages = "345--363", } @Article{Geo74, author = "J. A. George", year = "1974", title = "On Block Elimination for Sparse Linear Systems", journal = SIAMNumAnal, volume = "11", pages = "585--603", } @Article{GeoH80, author = "J. A. George and M. T. Heath", year = "1980", title = "Solution of Sparse Linear Least Squares Problems Using {Givens} Rotations", journal = LinAlgApp, volume = "34", pages = "69--83", } @Article{GeoHL86, author = "J. A. George and M. T. Heath and J. Liu", year = "1986", title = "Parallel {Cholesky} Factorization on a Shared Memory Multiprocessor", journal = LinAlgApp, volume = "77", pages = "165--187", } @Book{GeoL81a, author = "J. A. George and J. W. Liu", year = "1981", title = "Computer Solution of Large Sparse Positive Definite Systems", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{GibWP74, author = "N. E. Gibbs and W. G. {Poole, Jr.}", year = "1974", title = "Tridiagonalization by Permutations", journal = CACM, volume = "17", pages = "20--24", } @Article{GibPS76b, author = "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer", year = "1976", title = "A Comparison of Several Bandwidth and Profile Reduction Algorithms", journal = ACMMathSoft, volume = "2", pages = "322--330", } @Article{GibPS76a, author = "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer", year = "1976", title = "An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix", journal = SIAMNumAnal, volume = "13", pages = "236--250", } @Article{GilGMS74, author = "P. E. Gill and G. H. Golub and W. Murray and M. A. Saunders", year = "1974", title = "Methods for Modifying Matrix Factorizations", journal = MathComp, volume = "28", pages = "505--535", } @Incollection{GilM76, author = "P. E. Gill and W. Murray", year = "1976", title = "The Orthogonal Factorization of a Large Sparse Matrix", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = Academic, address = "New York, NY, USA", pages = "177--200", } @Article{GilMS75, author = "P. E. Gill and W. Murray and M. A. Saunders", year = "1975", title = "Methods for Computing and Modifying the {LDV} Factors of a Matrix", journal = MathComp, volume = "29", pages = "1051--1077", } @Incollection{Gin71, author = "T. Ginsburg", year = "1971", title = "The Conjugate Gradient Method", booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", editor = "J. H. Wilkinson and C. Reinsch", publisher = Springer, address = "New York, NY, USA", pages = "57--69", } @Article{Giv58, author = "W. Givens", year = "1958", title = "Computation of Plane Unitary Rotations Transforming a General Matrix to Triangular Form", journal = SIAMAppMath, volume = "6", pages = "26--50", } @Book{GohK69, author = "I. C. Gohberg and M. G. Krein", year = "1969", title = "Introduction to the Theory of Linear Non-Self-Adjoint Operators", publisher = AMS, address = "Providence, RI, USA", } @Book{GohLR86, author = "I. C. Gohberg and P. Lancaster and L. Rodman", year = "1986", title = "Invariant Subspaces of Matrices With Applications", publisher = JohnWileySons, address = "New York, NY, USA", } @Article{GolH59, author = "H. H. Goldstine and L. P. Horowitz", year = "1959", title = "A Procedure for the Diagonalization of Normal Matrices", journal = JACM, volume = "6", pages = "176--195", } @Article{Gol76, author = "D. Goldfarb", year = "1976", title = "Factorized Variable Metric Methods for Unconstrained Optimization", journal = MathComp, volume = "30", pages = "796--811", } @Article{Gol65, author = "G. H. Golub", year = "1965", title = "Numerical Methods for Solving Linear Least Squares Problems", journal = NumerMath, volume = "7", pages = "206--216", } @Incollection{Gol69, author = "G. H. Golub", year = "1969", title = "Matrix Decompositions and Statistical Computation", booktitle = "Statistical Computation", editor = "R. C. Milton and J. A. Nelder", publisher = Academic, address = "New York, NY, USA", pages = "365--397", } @Article{Gol73, author = "G. H. Golub", year = "1973", title = "Some Modified Matrix Eigenvalue Problems", journal = SIAMReview, volume = "15", pages = "318--344", } @Incollection{Gol74, author = "G. H. Golub", year = "1974", title = "Some Uses of the {Lanczos} Algorithm in Numerical Linear Algebra", booktitle = "Topics in Numerical Analysis", editor = "J. J. H. Miller", publisher = Academic, address = "New York, NY, USA", } @Article{GolHW79, author = "G. H. Golub and M. Heath and G. Wahba", year = "1979", title = "Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter", journal = Techno, volume = "21", pages = "215--223", } @Article{GolHS88, author = "G. H. Golub and A. Hoffman and G. W. Stewart", year = "1988", title = "A Generalization of the {Eckart--Young--Mirsky} Approximation Theorem", journal = LinAlgApp, volume = "88/89", pages = "317--328", } @Article{GolK65, author = "G. H. Golub and W. Kahan", year = "1965", title = "Calculating the Singular Values and Pseudo-Inverse of a Matrix", journal = JSIAMB, volume = "2", pages = "205--224", } @Techreport{GolKS76, author = "G. H. Golub and V. Klema and G. W. Stewart", year = "1976", title = "Rank Degeneracy and Least Squares Problems", number = "TR-456", institution = "Computer Science, University of Maryland", address = "College Park, MD, USA", } @Article{GolLO81, author = "G. H. Golub and F. T. Luk and M. Overton", year = "1981", title = "A Block {Lanczos} Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix", journal = ACMMathSoft, volume = "7", pages = "149--169", } @Book{GolM83, author = "G. H. Golub and G. Meurant", year = "1983", title = "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes Lin{\'e}aires", series = "Collection de la Direction des Etudes et Recherches de l'Electricit\'e de France", volume = "49", publisher = Eyolles, address = "Paris, France", } @Article{GolM86, author = "G. H. Golub and C. D. Meyer", year = "1986", title = "Using the {QR} Factorization and Group Inversion to Compute, Differentiate, and estimate the Sensitivity of Stationary Probabilities for {Markov} Chains", journal = SIAMAlgMeth, volume = "7", pages = "273--281", } @Article{GolNL79, author = "G. H. Golub and S. Nash and C. Van Loan", year = "1979", title = "A {Hessenberg}-{Schur} Method for the Matrix Problem {$AX + XB = C$}", journal = IEEETransAC, volume = "AC-24", pages = "909--913", } @Article{GolO88, author = "G. H. Golub and M. Overton", year = "1988", title = "The Convergence of Inexact {Chebychev} and {Richardson} Iterative Methods for Solving Linear Systems", journal = NumerMath, volume = "53", pages = "571--594", } @Article{GolP73, author = "G. H. Golub and V. Pereyra", year = "1973", title = "The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate", journal = SIAMNumAnal, volume = "10", pages = "413--432", } @Incollection{GolP76, author = "G. H. Golub and V. Pereyra", year = "1976", title = "Differentiation of Pseudo-Inverses, Separable Nonlinear Least Squares Problems and Other Tales", booktitle = "Generalized Inverses and Applications", editor = "M. Z. Nashed", publisher = Academic, address = "New York, NY, USA", pages = "303--324", } @Article{GolR70, author = "G. H. Golub and C. Reinsch", year = "1970", title = "Singular Value Decomposition and Least Squares Solutions", journal = NumerMath, volume = "14", pages = "403--420", note = "Also in \cite[pages 134--151]{WilR71}", } @Article{GolT81, author = "G. H. Golub and W. P. Tang", year = "1981", title = "The Block Decomposition of a {Vandermonde} Matrix and Its Applications", journal = BIT, volume = "21", pages = "505--517", } @Article{GolU70, author = "G. H. Golub and R. Underwood", year = "1970", title = "Stationary Values of the Ratio of Quadratic Forms Subject to Linear Constraints", journal = ZAngewMathPhys, volume = "21", pages = "318--326", } @Incollection{GolU77, author = "G. H. Golub and R. Underwood", year = "1977", title = "The Block {Lanczos} Method for Computing Eigenvalues", booktitle = "Mathematical Software {III}", editor = "J. Rice", publisher = Academic, address = "New York, NY, USA", pages = "364--377", } @Techreport{GolUW72, author = "G. H. Golub and R. Underwood and J. H. Wilkinson", year = "1972", title = "The {Lanczos} Algorithm for the Symmetric {$Ax = \lambda Bx$} Problem", number = "STAN-CS-72-270", institution = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{GolL79, author = "G. H. Golub and C. F. Van Loan", year = "1979", title = "Unsymmetric Positive Definite Linear Systems", journal = LinAlgApp, volume = "28", pages = "85--98", } @Article{GolL80, author = "G. H. Golub and C. F. Van Loan", year = "1980", title = "An Analysis of the Total Least Squares Problem", journal = SIAMNumAnal, volume = "17", pages = "883--893", } @Book{GolL89, author = "G. H. Golub and C. F. Van Loan", year = "1989", title = "Matrix Computations", edition = "second", publisher = JohnsHopkinsPress, address = "Baltimore, MD, USA", } @Article{GolV74, author = "G. H. Golub and J. M. Varah", year = "1974", title = "On a Characterization of the Best {$L_{2}$}-Scaling of a Matrix", journal = SIAMNumAnal, volume = "11", pages = "472--479", } @Article{GolV61, author = "G. H. Golub and R. S. Varga", year = "1961", title = "{Chebychev} Semi-Iterative Methods, Successive Over-Relaxation Iterative Methods, and Second-Order {Richardson} Iterative Methods, Parts {I} and {II}", journal = NumerMath, volume = "3", pages = "147--156, 157--168", } @Article{GolW69, author = "G. H. Golub and J. H. Welsch", year = "1969", title = "Calculation of {Gauss} Quadrature Rules", journal = MathComp, volume = "23", pages = "221--230", } @Article{GolW66, author = "G. H. Golub and J. H. Wilkinson", year = "1966", title = "Note on the Iterative Refinement of Least Squares Solution", journal = NumerMath, volume = "9", pages = "139--148", } @Article{GolW76, author = "G. H. Golub and J. H. Wilkinson", year = "1976", title = "Ill-Conditioned Eigensystems and the Computation of the {Jordan} Canonical Form", journal = SIAMReview, volume = "18", pages = "578--619", } @Article{Gou70, author = "A. R. Gourlay", year = "1970", title = "Generalization of Elementary {Hermitian} Matrices", journal = CompJour, volume = "13", pages = "411--412", } @Article{Gra86, author = "W. B. Gragg", year = "1986", title = "The {QR} Algorithm for Unitary {Hessenberg} Matrices", journal = CompApplMath, volume = "16", pages = "1--8", } @Article{GraH84, author = "W. B. Gragg and W. J. Harrod", year = "1984", title = "The Numerically Stable Reconstruction of {Jacobi} Matrices from Spectral Data", journal = NumerMath, volume = "44", pages = "317--336", } @Article{Gre52, author = "B. Green", year = "1952", title = "The Orthogonal Approximation of an Oblique Structure in Factor Analysis", journal = Psychometrika, volume = "17", pages = "429--440", } @Techreport{Gre81, author = "A. Greenbaum", year = "1981", title = "Behavior of the Conjugate Gradient Algorithm in Finite Precision Arithmetic", number = "UCRL 85752", institution = "Lawrence Livermore Laboratory", address = "Livermore, CA, USA", } @Article{GriL81b, author = "R. G. Grimes and J. G. Lewis", year = "1981", title = "Condition Number Estimation for Sparse Matrices", journal = SIAMSciStat, volume = "2", pages = "384--388", } @Article{GunWM76, author = "R. F. Gunst and J. T. Webster and R. L. Mason", year = "1976", title = "A Comparison of Least Squares and Latent Root Regression Estimators", journal = Techno, volume = "18", pages = "75--83", } @Article{Gup72, author = "K. K. Gupta", year = "1972", title = "Solution of Eigenvalue Problems by {Sturm} Sequence Method", journal = IntNumerEng, volume = "4", pages = "379--404", } @Book{HagY81, author = "L. A. Hageman and D. M. Young", year = "1981", title = "Applied Iterative Methods", publisher = Academic, address = "New York, NY, USA", } @Article{Hag84, author = "W. Hager", year = "1984", title = "Condition Estimates", journal = SIAMSciStat, volume = "5", pages = "311--316", } @Book{Hag88, author = "W. Hager", year = "1988", title = "Applied Numerical Linear Algebra", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Book{Hal58, author = "P. Halmos", year = "1958", title = "Finite Dimensional Vector Spaces", publisher = VanNostrand, address = "New York, NY, USA", } @Article{Ham74, author = "S. Hammarling", year = "1974", title = "A Note on Modifications to the {Givens} Plane Rotation", journal = InstMathApp, volume = "13", pages = "215--218", } @Article{Ham85, author = "S. J. Hammarling", year = "1985", title = "The Singular Value Decomposition in Multivariate Statistics", journal = SIGNUM, volume = "20", pages = "2--25", } @Article{Han62, author = "E. R. Hansen", year = "1962", title = "On Quasicyclic {Jacobi} Methods", journal = JACM, volume = "9", pages = "118--135", } @Article{Han63, author = "E. R. Hanson", year = "1963", title = "On Cyclic {Jacobi} Methods", journal = SIAMAppMath, volume = "11", pages = "448--459", } @Article{Han87, author = "P. C. Hansen", year = "1987", title = "The Truncated {SVD} as a Method for Regularization", journal = BIT, volume = "27", pages = "534--553", } @Incollection{Han88, author = "P. C. Hansen", year = "1988", title = "Reducing the Number of Sweeps in {Hestenes} Method", booktitle = "Singular Value Decomposition and Signal Processing", editor = "E. F. Deprettere", publisher = NorthHolland, } @Article{HanL69, author = "R. J. Hanson and C. L. Lawson", year = "1969", title = "Extensions and Applications of the {Householder} Algorithm for Solving Linear Least Squares Problems", journal = MathComp, volume = "23", pages = "787--812", } @Article{HanN81, author = "R. J. Hanson and M. J. Norris", year = "1981", title = "Analysis of Measurements Based on the Singular Value Decomposition", journal = SIAMSciStat, volume = "2", pages = "363--374", } @Article{Har82, author = "V. Hari", year = "1982", title = "On the Global Convergence of the {Eberlein} Method for Real Matrices", journal = NumerMath, volume = "39", pages = "361--370", } @Phdthesis{Hea78, author = "M. T. Heath", year = "1978", title = "Numerical Algorithms for Nonlinearly Constrained Optimization", number = "STAN-CS-78-656", school = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Proceedings{Hea86, editor = "M. T. Heath", year = "1986", title = "Proceedings of First {SIAM} Conference on Hypercube Multiprocessors", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Proceedings{Hea87, editor = "M. T. Heath", year = "1987", title = "Hypercube Multiprocessors", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Article{HeaLPW86, author = "M. T. Heath and A. J. Laub and C. C. Paige and R. C. Ward", year = "1986", title = "Computing the {SVD} of a Product of Two Matrices", journal = SIAMSciStat, volume = "7", pages = "1147--1159", } @Article{HeaR88, author = "M. T. Heath and C. H. Romine", year = "1988", title = "Parallel Solution of Triangular Systems on Distributed Memory Multiprocessors", journal = SIAMSciStat, volume = "9", pages = "558--588", } @Article{HeaS86, author = "M. T. Heath and D. C. Sorensen", year = "1986", title = "A Pipelined Method for Computing the {QR} Factorization of a Sparse Matrix", journal = LinAlgApp, volume = "77", pages = "189--203", } @Article{Hel76, author = "D. Heller", year = "1976", title = "Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems", journal = SIAMNumAnal, volume = "13", pages = "484--496", } @Article{Hel78, author = "D. Heller", year = "1978", title = "A Survey of Parallel Algorithms in Numerical Linear Algebra", journal = SIAMReview, volume = "20", pages = "740--777", } @Article{HelI83, author = "D. E. Heller and I. C. F. Ipsen", year = "1983", title = "Systolic Networks for Orthogonal Decompositions", journal = SIAMSciStat, volume = "4", pages = "261--269", } @Article{Hel68, author = "B. W. Helton", year = "1968", title = "Logarithms of Matrices", journal = ProcAMS, volume = "19", pages = "733--736", } @Inproceedings{HenHP88, author = "C. S. Henkel and M. T. Heath and R. J. Plemmons", year = "1988", title = "{Cholesky} Downdating on a Hypercube", booktitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", editor = "G. Fox", publisher = ACMPress, address = "New York, NY, USA", pages = "1592--1598", } @Article{Hen58, author = "P. Henrici", year = "1958", title = "On the Speed of Convergence of Cyclic and Quasicyclic {Jacobi} Methods for Computing the Eigenvalues of {Hermitian} Matrices", journal = SIAMAppMath, volume = "6", pages = "144--162", bibdate = "Tue Mar 14 19:21:50 1995", } @Article{Hen62, author = "P. Henrici", year = "1962", title = "Bounds for Iterates, Inverses, Spectral Variation, and Fields of Values of Non-Normal Matrices", journal = NumerMath, volume = "4", pages = "24--40", } @Article{HenZ68, author = "P. Henrici and K. Zimmermann", year = "1968", title = "An Estimate for the Norms of Certain cyclic {Jacobi} Operators", journal = LinAlgApp, volume = "1", pages = "489--501", } @Book{Hes80, author = "M. R. Hestenes", year = "1980", title = "Conjugate Direction Methods in Optimization", publisher = Springer, address = "Berlin, Germany", } @Article{HesS52, author = "M. R. Hestenes and E. Stiefel", year = "1952", title = "Methods of Conjugate Gradients for Solving Linear Systems", journal = JResNatBurStand, volume = "49", pages = "409--436", } @Phdthesis{Hig85, author = "N. J. Higham", year = "1985", title = "Nearness Problems in Numerical Linear Algebra", school = "University of Manchester", address = "UK", } @Article{Hig86c, author = "N. J. Higham", year = "1986", title = "{Newton}'s Method for the Matrix Square Root", journal = MathComp, volume = "46", pages = "537--550", } @Article{Hig86a, author = "N. J. Higham", year = "1986", title = "Computing the Polar Decomposition with Applications", journal = SIAMSciStat, volume = "7", pages = "1160--1174", } @Article{Hig86b, author = "N. J. Higham", year = "1986", title = "Efficient Algorithms for computing the condition number of a tridiagonal matrix", journal = SIAMSciStat, volume = "7", pages = "150--165", } @Article{Hig87c, author = "N. J. Higham", year = "1987", title = "A Survey of Condition Number Estimation for Triangular Matrices", journal = SIAMReview, volume = "29", pages = "575--596", } @Article{Hig87b, author = "N. J. Higham", year = "1987", title = "Error Analysis of the {Bj}{\"o}rck-{Pereyra} Algorithms for Solving {Vandermonde} Systems", journal = NumerMath, volume = "50", pages = "613--632", } @Article{Hig87a, author = "N. J. Higham", year = "1987", title = "Computing Real Square Roots of a Real Matrix", journal = LinAlgApp, volume = "88/89", pages = "405--430", } @Techreport{Hig88f, author = "N. J. Higham", year = "1988", title = "Matrix Nearness Problems and Applications", number = "161", institution = "Mathematics, University of Manchester", address = "UK", note = "To appear in Proceedings of the IMA Conference on Applications of Matrix Theory, eds. S. Barnett and M. J. C. Gover", } @Article{Hig88e, author = "N. J. Higham", year = "1988", title = "{Fortran} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation", journal = ACMMathSoft, volume = "14", pages = "381--396", } @Article{Hig88d, author = "N. J. Higham", year = "1988", title = "The Symmetric {Procrustes} Problem", journal = BIT, volume = "28", pages = "133--143", } @Article{Hig88c, author = "N. J. Higham", year = "1988", title = "Fast Solution of {Vandermonde}-like Systems Involving Orthogonal Polynomials", journal = IMANumerAna, volume = "8", pages = "473--486", } @Article{Hig88b, author = "N. J. Higham", year = "1988", title = "Computing a Nearest Symmetric Positive Semidefinite Matrix", journal = LinAlgApp, volume = "103", pages = "103--118", } @Techreport{Hig88a, author = "N. J. Higham", year = "1988", title = "The Accuracy of Solutions to Triangular Systems", number = "158", institution = "Mathematics, University of Manchester", address = "UK", } @Incollection{Hig89, author = "N. J. Higham", year = "1989", title = "Analysis of the {Cholesky} Decomposition of a Semi-definite Matrix", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. J. Hammarling", publisher = OxfordPress, } @Article{HigH89, author = "N. J. Higham and D. J. Higham", year = "1989", title = "Large Growth Factors in {Gaussian} Elimination with Pivoting", journal = SIAMMatrix, volume = "10", pages = "155--164", } @Techreport{HigS88, author = "N. J. Higham and R. S. Schreiber", year = "1988", title = "Fast Polar Decomposition of an Arbitrary Matrix", number = "88-942", institution = "Computer Science, Cornell University", address = "Ithaca, NY 14853", } @Incollection{Hoa77, author = "D. Hoaglin", year = "1977", title = "Mathematical Software and Exploratory Data Analysis", booktitle = "Mathematical Software {III}", editor = "John Rice", publisher = Academic, address = "New York, NY, USA", pages = "139--159", } @Article{Hoc65, author = "R. W. Hockney", year = "1965", title = "A Fast Direct Solution of {Poisson}'s Equation Using {Fourier} Analysis", journal = JACM, volume = "12", pages = "95--113", } @Article{Hoc83, author = "R. Hockney", year = "1983", title = "Characterizing Computers and Optimizing the {FACR($\ell$)} {Poisson} Solver on Parallel Unicomputers", journal = IEEETransComp, volume = "C-32", pages = "933--941", } @Book{HocJ88, author = "R. W. Hockney and C. R. Jesshope", year = "1988", title = "Parallel Computers 2", publisher = AdamHilger, address = "Bristol and Philadelphia", } @Article{HofP78, author = "W. Hoffmann and B. N. Parlett", year = "1978", title = "A New Proof of Global Convergence for the Tridiagonal {QL} Algorithm", journal = SIAMNumAnal, volume = "15", pages = "929--937", } @Article{Hot57, author = "H. Hotelling", year = "1957", title = "The Relations of the Newer Multivariate Statistical Methods to Factor Analysis", journal = BritStatPsych, volume = "10", pages = "69--79", } @Article{Hou58, author = "A. S. Householder", year = "1958", title = "Unitary Triangularization of a Nonsymmetric Matrix", journal = JACM, volume = "5", pages = "339--342", } @Article{Hou68, author = "A. S. Householder", year = "1968", title = "Moments and Characteristic Roots {II}", journal = NumerMath, volume = "11", pages = "126--128", } @Book{Hou74, author = "A. S. Householder", year = "1974", title = "The Theory of Matrices in Numerical Analysis", publisher = DoverPub, address = "New York, NY, USA", } @Article{Hua75, author = "C. P. Huang", year = "1975", title = "A {Jacobi}-Type Method for Triangularizing an Arbitrary Matrix", journal = SIAMNumAnal, volume = "12", pages = "566--570", } @Article{Hua81, author = "C. P. Huang", year = "1981", title = "On the Convergence of the {QR} Algorithm with Origin Shifts for Normal Matrices", journal = IMANumerAna, volume = "1", pages = "127--133", } @Article{HulS66, author = "T. E. Hull and J. R. Swenson", year = "1966", title = "Tests of Probabilistic Models for Propagation of Roundoff Errors", journal = CACM, volume = "9", pages = "108--113", } @Article{Ike79, author = "Y. Ikebe", year = "1979", title = "On Inverses of {Hessenberg} Matrices", journal = LinAlgApp, volume = "24", pages = "93--97", } @Article{IpsSS86, author = "I. C. F. Ipsen and Y. Saad and M. Schultz", year = "1986", title = "Dense Linear Systems on a Ring of Processors", journal = LinAlgApp, volume = "77", pages = "205--239", } @Book{IseP87, editor = "A. Iserles and M. J. D. Powell", year = "1987", title = "The State of the Art in Numerical Analysis", publisher = OxfordPress, } @Article{Jac46, author = "C. G. J. Jacobi", year = "1846", title = "{\"U}ber ein leichtes Verfahren die in der Theorie der S{\"a}cul{\"a}rst{\"o}rungen vorkommenden Gleichungen numerisch aufzul{\"o}sen", journal = Crelle, volume = "30", pages = "51--94", } @Article{JanW77, author = "M. Jankowski and M. Wozniakowski", year = "1977", title = "Iterative Refinement Implies Numerical Stability", journal = BIT, volume = "17", pages = "303--311", } @Article{JeaY83, author = "K. C. Jea and D. M. Young", year = "1983", title = "On the Simplification of Generalized Conjugate Gradient Methods for Nonsymmetrizable Linear Systems", journal = LinAlgApp, volume = "52/53", pages = "399--417", } @Article{Jen77a, author = "A. Jennings", year = "1977", title = "Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method", journal = InstMathApp, volume = "20", pages = "61--72", } @Book{Jen77b, author = "A. Jennings", year = "1977", title = "Matrix Computation for Engineers and Scientists", publisher = JohnWileySons, address = "New York, NY, USA", } @Article{JenO71, author = "A. Jennings and D. R. L. Orr", year = "1971", title = "Application of the Simultaneous Iteration Method to Undamped Vibration Problems", journal = IntNumerEng, volume = "3", pages = "13--24", } @Article{JenO77, author = "A. Jennings and M. R. Osborne", year = "1977", title = "Generalized Eigenvalue Problems for Certain Unsymmetric Band Matrices", journal = LinAlgApp, volume = "29", pages = "139--150", } @Article{JenS75, author = "A. Jennings and W. J. Stewart", year = "1975", title = "Simultaneous Iteration for the Partial Eigensolution of Real Matrices", journal = InstMathApp, volume = "15", pages = "351--362", } @Article{JenO74, author = "L. S. Jennings and M. R. Osborne", year = "1974", title = "A Direct Error Analysis for Least Squares", journal = NumerMath, volume = "22", pages = "322--332", } @Article{Jen72, author = "P. S. Jenson", year = "1972", title = "The Solution of Large Symmetric Eigenproblems by Sectioning", journal = SIAMNumAnal, volume = "9", pages = "534--545", } @Article{JohP71, author = "J. Johnson and C. L. Phillips", year = "1971", title = "An Algorithm for the Computation of the Integral of the State Transition Matrix", journal = IEEETransAC, volume = "AC-16", pages = "204--205", } @Article{JohMP83, author = "O. G. Johnson and C. A. Micchelli and G. Paul", year = "1983", title = "Polynomial Preconditioners for Conjugate Gradient Calculations", journal = SIAMNumAnal, volume = "20", pages = "362--376", } @Techreport{Joh84, author = "S. L. Johnsson", year = "1984", title = "Odd-Even Cyclic Reduction on Ensemble Architectures and the Solution of Tridiagonal Systems of Equations", number = "YALEU DCS RR-339", institution = "Computer Science, Yale University", address = "New Haven, CT, USA", } @Article{Joh85, author = "S. L. Johnsson", year = "1985", title = "Solving Narrow Banded Systems on Ensemble Architectures", journal = ACMMathSoft, volume = "11", pages = "271--288", } @Incollection{Joh86, author = "S. L. Johnsson", year = "1986", title = "Band Matrix System Solvers on Ensemble Architectures", booktitle = "Supercomputers: Algorithms, Architectures, and Scientific Computation", editor = "F. A. Matsen and T. Tajima", publisher = TexasPress, address = "Austin, TX, USA", pages = "196--216", } @Article{Joh87b, author = "S. L. Johnsson", year = "1987", title = "Solving Tridiagonal Systems on Ensemble Architectures", journal = SIAMSciStat, volume = "8", pages = "354--392", } @Article{Joh87a, author = "S. L. Johnsson", year = "1987", title = "Communication Efficient Basic Linear Algebra Computations on Hypercube Multiprocessors", journal = ParDistComp, volume = "4", pages = "133--172", } @Techreport{JohH87c, author = "S. L. Johnsson and C. T. Ho", year = "1987", title = "Multiple Tridiagonal Systems, the Alternating Direction Methods, and {Boolean} Cube Configured Multiprocessors", number = "YALEU DCS RR-532", institution = "Computer Science, Yale University", address = "New Haven, CT, USA", } @Techreport{JohH87, author = "S. L. Johnsson and C. T. Ho", year = "1987", title = "Algorithms for Multiplying Matrices of Arbitrary Shapes Using Shared Memory Primatives on a {Boolean} Cube", number = "YALEU DCS RR-569", institution = "Computer Science, Yale University", address = "New Haven, CT, USA", } @Article{JohH88, author = "S. L. Johnsson and C. T. Ho", year = "1988", title = "Algorithms for Matrix Transposition on {Boolean} {$N$}-Cube Configured Ensemble Architectures", journal = SIAMMatrix, volume = "9", pages = "419--454", } @Article{Joh71, author = "R. L. Johnston", year = "1971", title = "{Gershgorin} Theorems for Partitioned Matrices", journal = LinAlgApp, volume = "4", pages = "205--220", } @Article{Jor87, author = "H. Jordan", year = "1987", title = "Interpreting Parallel Processor Performance Measurements", journal = SIAMSciStat, volume = "8", pages = "s220--s226", } @Inproceedings{Jor84, author = "T. Jordan", year = "1984", title = "Conjugate Gradient Preconditioners for Vector and Parallel Processors", booktitle = "Proceedings of the Conference on Elliptic Problem Solvers", editor = "G. Birkoff and A. Schoenstadt", publisher = Academic, address = "New York, NY, USA", } @Article{Kag77a, author = "B. K{\aa}gstr{\"o}m", year = "1977", title = "Bounds and Perturbation Bounds for the Matrix Exponential", journal = BIT, volume = "17", pages = "39--57", } @Techreport{Kag77b, author = "B. K{\aa}gstr{\"o}m", year = "1977", title = "Numerical Computation of Matrix Functions", number = "UMINF-58.77", institution = "Information Processing, University of Ume{\aa}", address = "Ume{\aa}, Sweden", } @Article{KagR80b, author = "B. K{\aa}gstr{\"o}m and A. Ruhe", year = "1980", title = "An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix", journal = ACMMathSoft, volume = "6", pages = "398--419", } @Article{KagR80a, author = "B. K{\aa}gstr{\"o}m and A. Ruhe", year = "1980", title = "Algorithm~560~{JNF}: An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix", journal = ACMMathSoft, volume = "6", pages = "437--443", } @Article{Kag85, author = "B. K{\aa}gstr{\"o}m", year = "1985", title = "The Generalized Singular Value Decomposition and the General {$A - \lambda B$} Problem", journal = BIT, volume = "24", pages = "568--583", } @Article{Kag86, author = "B. K{\aa}gstr{\"o}m", year = "1986", title = "{RGSVD}: An Algorithm for Computing the {Kronecker} Structure and Reducing Subspaces of Singular {$A - \lambda B$} Pencils", journal = SIAMSciStat, volume = "7", pages = "185--211", } @Techreport{KagL88, author = "B. K{\aa}gstr{\"o}m and P. Ling", year = "1988", title = "Level 2 and 3 {BLAS} Routines for the {IBM 3090 VF/400}: Implementation and Experiences", number = "UMINF-154.88", institution = "Information Processing, University of Ume{\aa}", address = "S-901 87 Ume{\aa}, Sweden", } @Techreport{KagNP87, author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa", year = "1987", title = "Parallel Algorithms for Solving the Triangular {Sylvester} Equation on a Hypercube Multiprocessor", number = "UMINF-136.87", institution = "Information Processing, University of Ume{\aa}", address = "S-901 87 Ume{\aa}, Sweden", } @Techreport{KagNP88, author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa", year = "1988", title = "Parallel Shared Memory Algorithms for Solving the Triangular {Sylvester} Equation", number = "UMINF-155.88", institution = "Information Processing, University of Ume{\aa}", address = "S-901 87 Ume{\aa}, Sweden", } @Proceedings{KagR83, editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", year = "1983", title = "Proceedings of the Conference on Matrix Pencils, {Pite} {Havsbad} 1982", series = "Lecture Notes in Mathematics", volume = "973", publisher = Springer, address = "New York and Berlin", } @Techreport{KagW87, author = "B. K{\aa}gstr{\"o}m and L. Westin", year = "1987", title = "{GSYLV}- {Fortran} Routines for the Generalized {Schur} Method with dif$^{-1}$ estimators for Solving the Generalized {Sylvester} Equation", number = "UMINF-132.86", institution = "Information Processing, University of Ume{\aa}", address = "S-901 87 Ume{\aa}, Sweden", } @Article{Kah66, author = "W. Kahan", year = "1966", title = "Numerical Linear Algebra", journal = CanMathBull, volume = "9", pages = "757--801", } @Techreport{Kah67, author = "W. Kahan", year = "1967", title = "Inclusion Theorems for Clusters of Eigenvalues of {Hermitian} Matrices", type = "report", institution = "Computer Science, University of Toronto", address = "Toronto, Canada", } @Article{Kah75, author = "W. Kahan", year = "1975", title = "Spectra of Nearly {Hermitian} Matrices", journal = ProcAMS, volume = "48", pages = "11--17", } @Techreport{KahP74, author = "W. Kahan and B. N. Parlett", year = "1974", title = "An Analysis of {Lanczos} Algorithms for Symmetric Matrices", number = "ERL-M467", institution = "University of California, Berkeley", address = "Berkeley, CA, USA", } @Incollection{KahP76, author = "W. Kahan and B. N. Parlett", year = "1976", title = "How Far Should You Go with the {Lanczos} Process?", booktitle = "Sparse Matrix Computations", editor = "J. Bunch and D. Rose", publisher = Academic, address = "New York, NY, USA", pages = "131--144", } @Article{KahPJ82, author = "W. Kahan and B. N. Parlett and E. Jiang", year = "1982", title = "Residual Bounds on Approximate Eigensystems of Nonnormal Matrices", journal = SIAMNumAnal, volume = "19", pages = "470--484", } @Book{KahMN88, author = "D. Kahaner and C. B. Moler and S. Nash", year = "1988", title = "Numerical Methods and Software", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{Kan66, author = "S. Kaniel", year = "1966", title = "Estimates for Some Computational Techniques in Linear Algebra", journal = MathComp, volume = "20", pages = "369--378", } @Article{KapB84, author = "R. N. Kapur and J. C. Browne", year = "1984", title = "Techniques for Solving Block Tridiagonal Systems on Reconfigurable Array Computers", journal = SIAMSciStat, volume = "5", pages = "701--719", } @Article{Kar74, author = "I. Karasalo", year = "1974", title = "A Criterion for Truncation of the {QR} Decomposition Algorithm for the Singular Linear Least Squares Problem", journal = BIT, volume = "14", pages = "156--166", } @Book{Kat66, author = "T. Kato", year = "1966", title = "Perturbation Theory for Linear Operators", publisher = Springer, address = "New York, NY, USA", } @Article{Kau74, author = "L. Kaufman", year = "1974", title = "The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem", journal = SIAMNumAnal, volume = "11", pages = "997--1024", } @Article{Kau77, author = "L. Kaufman", year = "1977", title = "Some Thoughts on the {QZ} Algorithm for Solving the Generalized Eigenvalue Problem", journal = ACMMathSoft, volume = "3", pages = "65--75", } @Article{Kau79, author = "L. Kaufman", year = "1979", title = "Application of Dense {Householder} Transformations to a Sparse Matrix", journal = ACMMathSoft, volume = "5", pages = "442--450", } @Article{Kau83, author = "L. Kaufman", year = "1983", title = "Matrix Methods for Queueing Problems", journal = SIAMSciStat, volume = "4", pages = "525--552", } @Article{Kau87, author = "L. Kaufman", year = "1987", title = "The Generalized {Householder} Transformation and Sparse Matrices", journal = LinAlgApp, volume = "90", pages = "221--234", } @Article{KauG83, author = "J. Kautsky and G. H. Golub", year = "1983", title = "On the Calculation of {Jacobi} Matrices", journal = LinAlgApp, volume = "52/53", pages = "439--456", } @Incollection{Ker82, author = "D. Kershaw", year = "1982", title = "Solution of Single Tridiagonal Linear Systems and Vectorization of the {ICCG} Algorithm on the {Cray}-1", booktitle = "Parallel Computation", editor = "G. Roderigue", publisher = Academic, address = "New York, NY, USA", } @Article{Kie87, author = "A. Kielbasinski", year = "1987", title = "A Note on Rounding Error Analysis of {Cholesky} Factorization", journal = LinAlgApp, volume = "88/89", pages = "487--494", } @Book{Knu81, author = "D. Knuth", year = "1981", title = "Seminumerical-Algorithms", edition = "second", publisher = AddisonWesley, address = "Reading, MA, USA", volume = "2", series = "The Art of Computer Programming", } @Article{Kog55, author = "E. G. Kogbetliantz", year = "1955", title = "Solution of Linear Equations by Diagonalization of Coefficient Matrix", journal = QuartApplMath, volume = "13", pages = "123--132", } @Article{KouP81, author = "S. Kourouklis and C. C. Paige", year = "1981", title = "A Constrained Least Squares Approach to the General {Gauss}-{Markov} Linear Model", journal = AmerStatAssoc, volume = "76", pages = "620--625", } @Article{KriM86a, author = "A. S. Krishnakuma and M. Morf", year = "1986", title = "Eigenvalues of a Symmetric Tridiagonal Matrix: A Divide and Conquer Approach", journal = NumerMath, volume = "48", pages = "349--368", } @Article{Kub61, author = "V. N. Kublanovskaya", year = "1961", title = "On Some Algorithms for the Solution of the Complete Eigenvalue Problem", journal = USSRCompMathPhys, volume = "3", pages = "637--657", } @Article{KubF64, author = "V. N. Kublanovskaya and V. N. Fadeeva", year = "1964", title = "Computational Methods for the Solution of a Generalized Eigenvalue Problem", journal = AMSTrans, volume = "2", pages = "271--290", } @Article{KulM86b, author = "U. W. Kulisch and W. L. Miranker", year = "1986", title = "The Arithmetic of the Digital Computer", journal = SIAMReview, volume = "28", pages = "1--40", } @Article{Kun82, author = "H. T. Kung", year = "1982", title = "Why Systolic Architectures?", journal = Computer, volume = "15", pages = "37--46", } @Article{Bud64, author = "C. D. La Budde", year = "1964", title = "Two Classes of Algorithms for Finding the Eigenvalues and Eigenvectors of Real Symmetric Matrices", journal = JACM, volume = "11", pages = "53--58", } @Article{LamV75, author = "J. Lambiotte and R. G. Voigt", year = "1975", title = "The Solution of Tridiagonal Linear Systems on the {CDC-STAR 100} Computer", journal = ACMMathSoft, volume = "1", pages = "308--329", } @Article{Lan70, author = "P. Lancaster", year = "1970", title = "Explicit Solution of Linear Matrix Equations", journal = SIAMReview, volume = "12", pages = "544--566", } @Book{LanT85, author = "P. Lancaster and M. Tismenetsky", year = "1985", title = "The Theory of Matrices", edition = "second", publisher = Academic, address = "New York, NY, USA", } @Article{Lan50, author = "C. Lanczos", year = "1950", title = "An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators", journal = JResNatBurStand, volume = "45", pages = "255--282", } @Article{LarS78, author = "J. Larson and A. Sameh", year = "1978", title = "Efficient Calculation of the Effects of Roundoff Errors", journal = ACMMathSoft, volume = "4", pages = "228--236", } @Article{Lau81, author = "A. Laub", year = "1981", title = "Efficient Multivariable Frequency Response Computations", journal = IEEETransAC, volume = "AC-26", pages = "407--408", } @Article{Lau85, author = "A. Laub", year = "1985", title = "Numerical Linear Algebra Aspects of Control Design Computations", journal = IEEETransAC, volume = "AC-30", pages = "97--108", } @Article{LawH69, author = "C. L. Lawson and R. J. Hanson", year = "1969", title = "Extensions and Applications of the {Householder} Algorithm for Solving Linear Least Squares Problems", journal = MathComp, volume = "23", pages = "787--812", } @Book{LawH74, author = "C. L. Lawson and R. J. Hanson", year = "1974", title = "Solving Least Squares Problems", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{LawHKK79b, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", year = "1979", title = "Basic Linear Algebra Subprograms for {Fortran} Usage", journal = ACMMathSoft, volume = "5", pages = "308--323", } @Article{LawHKK79a, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", year = "1979", title = "Algorithm~539: Basic Linear Algebra Subprograms for {Fortran} Usage", journal = ACMMathSoft, volume = "5", pages = "324--325", } @Article{Leh63, author = "N. J. Lehmann", year = "1963", title = "Optimale {Eigenwerteinschliessungen}", journal = NumerMath, volume = "5", pages = "246--272", } @Article{Lem73, author = "F. Lemeire", year = "1973", title = "Bounds for Condition Numbers of Triangular and Trapezoid Matrices", journal = BIT, volume = "15", pages = "58--64", } @Book{Leo80, author = "S. J. Leon", year = "1980", title = "Linear Algebra with Applications.", publisher = Macmillan, address = "New York, NY, USA", } @Article{Lev47, author = "N. Levinson", year = "1947", title = "The {Weiner} {RMS} Error Criterion in Filter Design and Prediction", journal = MathPhys, volume = "25", pages = "261--278", } @Techreport{Lew77, author = "J. Lewis", year = "1977", title = "Algorithms for Sparse Matrix Eigenvalue Problems", number = "STAN-CS-77-595", institution = "Department of Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{LiC88, author = "G. Li and T. Coleman", year = "1988", title = "A Parallel Triangular Solver for a Distributed-Memory Multiprocessor", journal = SIAMSciStat, volume = "9", pages = "485--502", } @Book{Lin61, author = "I. Linnik", year = "1961", title = "Method of Least Squares and Principles of the Theory of Observation", publisher = PergamonPress, address = "New York, NY, USA", } @Article{LoPS87, author = "S. Lo and B. Philippe and A. Sameh", year = "1987", title = "A Multiprocessor Algorithm for the Symmetric Tridiagonal Eigenvalue Problem", journal = SIAMSciStat, volume = "8", pages = "s155--s165", } @Article{Loi69, author = "G. Loizou", year = "1969", title = "Nonnormality and {Jordan} Condition Numbers of Matrices", journal = JACM, volume = "16", pages = "580--584", } @Article{Loi72, author = "G. Loizou", year = "1972", title = "On the Quadratic Convergence of the {Jacobi} Method for Normal Matrices", journal = CompJour, volume = "15", pages = "274--276", } @Article{Lot56, author = "M. Lotkin", year = "1956", title = "Characteristic Values of Arbitrary Matrices", journal = QuartApplMath, volume = "14", pages = "267--275", } @Book{Lue73, author = "D. G. Luenberger", year = "1973", title = "Introduction to Linear and Nonlinear Programming", publisher = AddisonWesley, address = "New York, NY, USA", } @Phdthesis{Luk78, author = "F. T. Luk", year = "1978", title = "Sparse and Parallel Matrix Computations", number = "STAN-CS-78-685", school = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{Luk80, author = "F. T. Luk", year = "1980", title = "Computing the Singular Value Decomposition on the {ILLIAC IV}", journal = ACMMathSoft, volume = "6", pages = "524--539", } @Article{Luk86a, author = "F. T. Luk", year = "1986", title = "A Rotation Method for Computing the {QR} Factorization", journal = SIAMSciStat, volume = "7", pages = "452--459", } @Article{Luk86b, author = "F. T. Luk", year = "1986", title = "A Triangular Processor Array for Computing Singular Values", journal = LinAlgApp, volume = "77", pages = "259--274", } @Techreport{LusO83, author = "E. Lusk and R. Overbeek", year = "1983", title = "Implementation of Monitors with Macros: A Programming Aid for the {HEP} and other Parallel Processors", number = "83-97", institution = "Argonne National Laboratory", address = "Argonne, ILL", } @Article{McCS73a, author = "C. McCarthy and G. Strang", year = "1973", title = "Optimal Conditioning of Matrices", journal = SIAMNumAnal, volume = "10", pages = "370--388", } @Article{McC72, author = "S. F. McCormick", year = "1972", title = "A General Approach to One-Step Iterative Methods with Application to Eigenvalue Problems", journal = CompSysSci, volume = "6", pages = "354--372", } @Article{McK62, author = "W. M. McKeeman", year = "1962", title = "Crout with Equilibration and Iteration", journal = CACM, volume = "5", pages = "553--555", } @Article{Mad59, author = "A. Madansky", year = "1959", title = "The Fitting of Straight Lines When Both Variables Are Subject to Error", journal = AmerStatAssoc, volume = "54", pages = "173--205", } @Article{MadRK76, author = "N. Madsen and G. Roderigue and J. Karush", year = "1976", title = "Matrix Multiplication by Diagonals of a Vector Parallel Processor", journal = InfProcLet, pages = "41--45", } @Article{Mah79, author = "K. N. Mahindar", year = "1979", title = "Linear Combinations of {Hermitian} and Real Symmetric Matrices", journal = LinAlgApp, volume = "25", pages = "95--105", } @Article{Mak75, author = "J. Makhoul", year = "1975", title = "Linear Prediction: A Tutorial Review", journal = ProcIEEE, volume = "63(4)", pages = "561--580", } @Article{MalP74, author = "M. A. Malcolm and J. Palmer", year = "1974", title = "A Fast Method For Solving a Class of Tridiagonal Systems of Linear Equations", journal = CACM, volume = "17", pages = "14--17", } @Article{Man77, author = "T. A. Manteuffel", year = "1977", title = "The {Tchebychev} Iteration for Nonsymmetric Linear Systems", journal = NumerMath, volume = "28", pages = "307--327", } @Inproceedings{Man79, author = "T. A. Manteuffel", year = "1979", title = "Shifted Incomplete {Cholesky} Factorization", booktitle = "Sparse Matrix Proceedings 1978", editor = "I. S. Duff and G. W. Stewart", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Book{MarM64, author = "M. Marcus and H. Minc", year = "1964", title = "A Survey of Matrix Theory and Matrix Inequalities", publisher = AllynBacon, address = "Boston, MA, USA", } @Book{MarG76, author = "J. Markel and A. Gray", year = "1976", title = "Linear Prediction of Speech", publisher = Springer, address = "Berlin and New York", } @Article{MarPW65, author = "R. S. Martin and G. Peters and J. H. Wilkinson", year = "1965", title = "Symmetric Decomposition of a Positive Definite Matrix", journal = NumerMath, volume = "7", pages = "362--383", note = "Also in \cite[pages 9--30]{WilR71}", } @Article{MarPW66, author = "R. S. Martin and G. Peters and J. H. Wilkinson", year = "1966", title = "Iterative Refinement of the Solution of a Positive Definite System of Equations", journal = NumerMath, volume = "8", pages = "203--216", note = "Also in \cite[pages 31--44]{WilR71}", } @Article{MarPW70, author = "R. S. Martin and G. Peters and J. H. Wilkinson", year = "1970", title = "The {QR} Algorithm for Real {Hessenberg} Matrices", journal = NumerMath, volume = "14", pages = "219--231", note = "Also in \cite[pages 359--371]{WilR71}", } @Article{MarRW70, author = "R. S. Martin and C. Reinsch and J. H. Wilkinson", year = "1970", title = "The {QR} Algorithm for Band Symmetric Matrices", journal = NumerMath, volume = "16", pages = "85--92", note = "Also in \cite[pages 266--272]{WilR71}", } @Article{MarW65, author = "R. S. Martin and J. H. Wilkinson", year = "1965", title = "Symmetric Decomposition of Positive Definite Band Matrices", journal = NumerMath, volume = "7", pages = "355--361", note = "Also in \cite[pages 50--56]{WilR71}", } @Article{MarW67, author = "R. S. Martin and J. H. Wilkinson", year = "1967", title = "Solution of Symmetric and Unsymmetric Band Equations and the Calculation of Eigenvalues of Band Matrices", journal = NumerMath, volume = "9", pages = "279--301", note = "Also in \cite[pages 70--92]{WilR71}", } @Article{MarW68a, author = "R. S. Martin and J. H. Wilkinson", year = "1968", title = "{Householder}'s Tridiagonalization of a Symmetric Matrix", journal = NumerMath, volume = "11", pages = "181--195", note = "Also in \cite[pages 212--226]{WilR71}", } @Article{MarW68b, author = "R. S. Martin and J. H. Wilkinson", year = "1968", title = "The Modified {LR} Algorithm for Complex {Hessenberg} Matrices", journal = NumerMath, volume = "12", pages = "369--376", note = "Also in \cite[pages 396--403]{WilR71}", } @Article{MarW68c, author = "R. S. Martin and J. H. Wilkinson", year = "1968", title = "Reduction of the Symmetric Eigenproblem {$Ax = \lambda Bx$} and Related Problems to Standard Form", journal = NumerMath, volume = "11", pages = "99--110", } @Article{MarW68d, author = "R. S. Martin and J. H. Wilkinson", year = "1968", title = "Similarity Reduction of a General Matrix to {Hessenberg} Form", journal = NumerMath, volume = "12", pages = "349--368", note = "Also in \cite[pages 339--358]{WilR71}", } @Article{MvdV87, author = "O. McBryan and E. F. van de Velde", year = "1987", title = "Hypercube Algorithms and Implementations", journal = SIAMSciStat, volume = "8", pages = "s227--s287", } @Article{MdV77, author = "J. A. Meijerink and H. A. Van der Vorst", year = "1977", title = "An Iterative Solution Method for Linear Equations Systems of Which the Coefficient Matrix is a Symmetric {$M$}-Matrix", journal = MathComp, volume = "31", pages = "148--162", } @Article{Mei83, author = "J. Meinguet", year = "1983", title = "Refined Error Analyses of {Cholesky} Factorization", journal = SIAMNumAnal, volume = "20", pages = "1243--1250", } @Article{Mel87, author = "R. Melhem", year = "1987", title = "Toward efficient Implementation of Preconditioned Conjugate Gradient Methods on Vector Supercomputers", journal = IntSuper, volume = "1", pages = "70--98", } @Article{Mer85, author = "M. L. Merriam", year = "1985", title = "On the Factorization of Block Tridiagonals With Storage Constraints", journal = SIAMSciStat, volume = "6", pages = "182--192", } @Article{Meu84, author = "G. Meurant", year = "1984", title = "The Block Preconditioned Conjugate Gradient Method on Vector Computers", journal = BIT, volume = "24", pages = "623--633", } @Article{Meu89, author = "G. Meurant", year = "1989", title = "Domain Decomposition Methods for Partial Differential Equations on Parallel Computers", journal = IntSuper, note = "To appear", } @Article{Mil75, author = "W. Miller", year = "1975", title = "Computational Complexity and Numerical Stability", journal = SIAMComp, volume = "4", pages = "97--107", } @Article{MilS78, author = "W. Miller and D. Spooner", year = "1978", title = "Software for Roundoff Analysis, {II}", journal = ACMMathSoft, volume = "4", pages = "369--390", } @Article{MimP82, author = "G. Miminis and C. C. Paige", year = "1982", title = "An Algorithm for Pole Assignment of Time Invariant Linear Systems", journal = IntControl, volume = "35", pages = "341--354", } @Book{Mir55, author = "L. Mirsky", year = "1955", title = "An Introduction to Linear Algebra", publisher = OxfordPress, address = "London, UK", } @Article{Mir60, author = "L. Mirsky", year = "1960", title = "Symmetric Gauge Functions and Unitarily Invariant Norms", journal = QuartMath, volume = "11", pages = "50--59", } @Book{Mod88, author = "J. J. Modi", year = "1988", title = "Parallel Algorithms and Matrix Computation", publisher = OxfordPress, address = "Oxford, UK", } @Article{ModC86, author = "J. J. Modi and M. R. B. Clarke", year = "1986", title = "An Alternative {Givens} Ordering", journal = NumerMath, volume = "43", pages = "83--90", } @Article{ModP85, author = "J. J. Modi and J. D. Pryce", year = "1985", title = "Efficient Implementation of {Jacobi}'s Diagonalization Method on the {DAP}", journal = NumerMath, volume = "46", pages = "443--454", } @Article{Mol67, author = "C. B. Moler", year = "1967", title = "Iterative Refinement in Floating Point", journal = JACM, volume = "14", pages = "316--371", } @Techreport{Mol80, author = "C. B. Moler", year = "1980", title = "{MATLAB} User's Guide", number = "CS81-1", institution = "Computer Science, University of New Mexico", address = "Albuquerque, NM, USA", bibdate = "Tue Mar 14 19:21:58 1995", } @Incollection{Mol86, author = "C. B. Moler", year = "1986", title = "Matrix Computations on Distributed Memory Multiprocessors", booktitle = "Hypercube Multiprocessors", editor = "M. T. Heath", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Manual{MolLB87, author = "C. B. Moler and J. N. Little and S. Bangert", year = "1987", title = "{PC}-{Matlab} Users Guide", publisher = MathWorks, address = "20 N. Main St., Sherborn, MA, USA", } @Article{MolM83, author = "C. B. Moler and D. Morrison", year = "1983", title = "Singular Value Analysis of Cryptograms", journal = AmerMathMonthly, volume = "90", pages = "78--87", } @Article{MolS73b, author = "C. B. Moler and G. W. Stewart", year = "1973", title = "An Algorithm for Generalized Matrix Eigenvalue Problems", journal = SIAMNumAnal, volume = "10", pages = "241--256", } @Article{MolL78, author = "C. B. Moler and C. F. Van Loan", year = "1978", title = "Nineteen Dubious Ways to Compute the Exponential of a Matrix", journal = SIAMReview, volume = "20", pages = "801--836", } @Article{MonL82, author = "R. Montoye and D. Laurie", year = "1982", title = "A Practical Algorithm for the Solution of Triangular Systems on a Parallel Processing System", journal = IEEETransComp, volume = "C-31", pages = "1076--1082", } @Article{Mue66, author = "D. Mueller", year = "1966", title = "{Householder}'s Method for Complex Matrices and {Hermitian} Matrices", journal = NumerMath, volume = "8", pages = "72--92", } @Article{MurW31, author = "F. D. Murnaghan and A. Wintner", year = "1931", title = "A Canonical Form for Real Matrices Under Orthogonal Transformations", journal = ProcNAS, volume = "17", pages = "417--420", } @Article{Nan85, author = "T. Nanda", year = "1985", title = "Differential Equations and the {QR} Algorithm", journal = SIAMNumAnal, volume = "22", pages = "310--321", } @Article{Nas75, author = "J. C. Nash", year = "1975", title = "A One-Sided Transformation Method for the Singular Value Decomposition and Algebraic Eigenproblem", journal = CompJour, volume = "18", pages = "74--76", } @Book{Nas76, author = "M. Z. Nashed", year = "1976", title = "Generalized Inverses and Applications", publisher = Academic, address = "New York, NY, USA", } @Article{Nic74, author = "R. A. Nicolaides", year = "1974", title = "On a Geometrical Aspect of {SOR} and the Theory of Consistent Ordering for Positive Definite Matrices", journal = NumerMath, volume = "23", pages = "99--104", } @Article{NieV83, author = "W. Niethammer and R. S. Varga", year = "1983", title = "The Analysis of {$k$}-step Iterative Methods for Linear Systems from Summability Theory", journal = NumerMath, volume = "41", pages = "177--206", } @Book{NobD77, author = "B. Noble and J. W. Daniel", year = "1977", title = "Applied Linear Algebra", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{NooV75, author = "A. Noor and R. Voigt", year = "1975", title = "Hypermatrix Scheme for the {STAR-100} Computer", journal = CompStruct, volume = "5", pages = "287--296", } @Article{OetP64, author = "W. Oettli and W. Prager", year = "1964", title = "Compatibility of Approximate Solutions of Linear Equations with Given Error Bounds for Coefficients and Right Hand Sides", journal = NumerMath, volume = "6", pages = "405--409", } @Phdthesis{OLe76, author = "D. P. O'Leary", year = "1976", title = "Hybrid Conjugate Gradient Algorithms", number = "STAN-CS-76-548", school = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{OLe80a, author = "D. P. O'Leary", year = "1980", title = "The Block Conjugate Gradient Algorithm and Related Methods", journal = LinAlgApp, volume = "29", pages = "293--322", } @Article{OLe80b, author = "D. P. O'Leary", year = "1980", title = "Estimating Matrix Condition Numbers", journal = SIAMSciStat, volume = "1", pages = "205--209", } @Article{OLeS81, author = "D. P. O'Leary and J. A. Simmons", year = "1981", title = "A Bidiagonalization - Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems", journal = SIAMSciStat, volume = "2", pages = "474--489", } @Article{OLeS85, author = "D. P. O'Leary and G. W. Stewart", year = "1985", title = "Data Flow Algorithms for Parallel Matrix Computations", journal = CACM, volume = "28", pages = "841--853", } @Article{OLeS86, author = "D. P. O'Leary and G. W. Stewart", year = "1986", title = "Assignment and Scheduling in Parallel Matrix Factorization", journal = LinAlgApp, volume = "77", pages = "275--300", } @Book{Opp78, author = "A. V. Oppenheim", year = "1978", title = "Applications of Digital Signal Processing", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Book{Ort72, author = "J. M. Ortega", year = "1972", title = "Numerical Analysis: A Second Course", publisher = Academic, address = "New York, NY, USA", } @Book{Ort88, author = "J. M. Ortega", year = "1988", title = "Matrix Theory: A Second Course", publisher = PlenumPress, address = "New York, NY, USA", } @Article{OrtR88, author = "J. M. Ortega and C. H. Romine", year = "1988", title = "The {$ijk$} Forms of Factorization Methods {II}: Parallel Systems", journal = ParComputing, volume = "7", pages = "149--162", } @Article{OrtV85, author = "J. M. Ortega and R. G. Voigt", year = "1985", title = "Solution of Partial Differential Equations on Vector and Parallel Computers", journal = SIAMReview, volume = "27", pages = "149--240", } @Article{Osb60, author = "E. E. Osborne", year = "1960", title = "On Preconditioning of Matrices", journal = JACM, volume = "7", pages = "338--345", } @Article{Paa71, author = "M. H. C. Paardekooper", year = "1971", title = "An Eigenvalue Algorithm for Skew Symmetric Matrices", journal = NumerMath, volume = "17", pages = "189--202", } @Article{Pai70, author = "C. C. Paige", year = "1970", title = "Practical Use of the Symmetric {Lanczos} Process with Reorthogonalization", journal = BIT, volume = "10", pages = "183--195", } @Phdthesis{Pai71, author = "C. C. Paige", year = "1971", title = "The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices", school = "London University", address = "London, UK", } @Article{Pai73, author = "C. C. Paige", year = "1973", title = "An Error Analysis of a Method for Solving Matrix Equations", journal = MathComp, volume = "27", pages = "355--359", } @Article{Pai74a, author = "C. C. Paige", year = "1974", title = "Bidiagonalization of Matrices and Solution of Linear Equations", journal = SIAMNumAnal, volume = "11", pages = "197--209", } @Article{Pai74b, author = "C. C. Paige", year = "1974", title = "Eigenvalues of Perturbed {Hermitian} Matrices", journal = LinAlgApp, volume = "8", pages = "1--10", } @Article{Pai76, author = "C. C. Paige", year = "1976", title = "Error Analysis of the {Lanczos} Algorithm for Tridiagonalizing a Symmetric Matrix", journal = InstMathApp, volume = "18", pages = "341--349", } @Article{Pai79a, author = "C. C. Paige", year = "1979", title = "Computer Solution and Perturbation Analysis of Generalized Least Squares Problems", journal = MathComp, volume = "33", pages = "171--184", } @Article{Pai79b, author = "C. C. Paige", year = "1979", title = "Fast Numerically Stable Computations for Generalized Linear Least Squares Problems", journal = SIAMNumAnal, volume = "16", pages = "165--171", } @Article{Pai80, author = "C. C. Paige", year = "1980", title = "Accuracy and Effectiveness of the {Lanczos} Algorithm for the Symmetric Eigenproblem", journal = LinAlgApp, volume = "34", pages = "235--258", } @Article{Pai81, author = "C. C. Paige", year = "1981", title = "Properties of Numerical Algorithms Related to Computing Controllability", journal = IEEETransAC, volume = "AC-26", pages = "130--138", } @Article{Pai84, author = "C. C. Paige", year = "1984", title = "A Note on a Result of {Sun} {J}.-{Guang}: Sensitivity of the {CS} and {GSV} Decompositions", journal = SIAMNumAnal, volume = "21", pages = "186--191", } @Article{Pai85, author = "C. C. Paige", year = "1985", title = "The General Linear Model and the Generalized Singular Value Decomposition", journal = LinAlgApp, volume = "70", pages = "269--284", } @Article{Pai86, author = "C. C. Paige", year = "1986", title = "Computing the Generalized Singular Value Decomposition", journal = SIAMSciStat, volume = "7", pages = "1126--1146", } @Article{PaiD86, author = "C. C. Paige and P. Van Dooren", year = "1986", title = "On the Quadratic Convergence of {Kogbetliantz}'s Algorithm for Computing the Singular Value Decomposition", journal = LinAlgApp, volume = "77", pages = "301--313", } @Article{PaiS75, author = "C. C. Paige and M. A. Saunders", year = "1975", title = "Solution of Sparse Indefinite Systems of Linear Equations", journal = SIAMNumAnal, volume = "12", pages = "617--629", } @Techreport{PaiS78, author = "C. C. Paige and M. A. Saunders", year = "1978", title = "A Bidiagonalization Algorithm for Sparse Linear Equations and Least Squares Problems", number = "SOL 78-19", institution = "Operations Research, Stanford University", address = "Stanford, CA, USA", } @Article{PaiS81, author = "C. C. Paige and M. Saunders", year = "1981", title = "Towards A Generalized Singular Value Decomposition", journal = SIAMNumAnal, volume = "18", pages = "398--405", } @Article{PaiS82b, author = "C. C. Paige and M. A. Saunders", year = "1982", title = "{LSQR}: An Algorithm for Sparse Linear Equations and Sparse Least Squares", journal = ACMMathSoft, volume = "8", pages = "43--71", } @Article{PaiS82a, author = "C. C. Paige and M. A. Saunders", year = "1982", title = "Algorithm~583~{LSQR}: Sparse Linear Equations and Least Squares Problems", journal = ACMMathSoft, volume = "8", pages = "195--209", } @Article{PaiL81, author = "C. C. Paige and C. Van Loan", year = "1981", title = "A {Schur} Decomposition for {Hamiltonian} Matrices", journal = LinAlgApp, volume = "41", pages = "11--32", } @Article{Pan84, author = "V. Pan", year = "1984", title = "How Can We Speed Up Matrix Multiplication?", journal = SIAMReview, volume = "26", pages = "393--416", } @Article{Par65, author = "B. N. Parlett", year = "1965", title = "Convergence of the {QR} Algorithm", journal = NumerMath, volume = "7", pages = "187--193", note = "Correction in Numerische Mathematik 10, pp. 163--164", } @Article{Par66, author = "B. N. Parlett", year = "1966", title = "Singular and Invariant Matrices Under the {QR} Algorithm", journal = MathComp, volume = "20", pages = "611--615", } @Article{Par67, author = "B. N. Parlett", year = "1967", title = "Canonical Decomposition of {Hessenberg} Matrices", journal = MathComp, volume = "21", pages = "223--227", } @Article{Par68, author = "B. N. Parlett", year = "1968", title = "Global Convergence of the Basic {QR} Algorithm on {Hessenberg} Matrices", journal = MathComp, volume = "22", pages = "803--817", } @Article{Par71, author = "B. N. Parlett", year = "1971", title = "Analysis of Algorithms for Reflections in Bisectors", journal = SIAMReview, volume = "13", pages = "197--208", } @Techreport{Par74a, author = "B. N. Parlett", year = "1974", title = "Computation of Functions of Triangular Matrices", type = "Memorandum", number = "ERL-M481", institution = "Electronics Research Laboratory, College of Engineering, University of California, Berkeley", address = "Berkeley, CA, USA", } @Article{Par74b, author = "B. N. Parlett", year = "1974", title = "The {Rayleigh} Quotient Iteration and Some Generalizations for Nonnormal Matrices", journal = MathComp, volume = "28", pages = "679--693", } @Article{Par76, author = "B. N. Parlett", year = "1976", title = "A Recurrence Among the Elements of Functions of Triangular Matrices", journal = LinAlgApp, volume = "14", pages = "117--121", } @Article{Par80a, author = "B. N. Parlett", year = "1980", title = "A New Look at the {Lanczos} Algorithm for Solving Symmetric Systems and Linear Equations", journal = LinAlgApp, volume = "29", pages = "323--346", } @Book{Par80b, author = "B. N. Parlett", year = "1980", title = "The Symmetric Eigenvalue Problem", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{ParNO85, author = "B. N. Parlett and B. Nour-Omid", year = "1985", title = "The Use of a Refined Error Bound When Updating Eigenvalues of Tridiagonals", journal = LinAlgApp, volume = "68", pages = "179--220", } @Article{ParP73, author = "B. N. Parlett and W. G. Poole", year = "1973", title = "A Geometric Theory for the {QR}, {LU}, and Power Iterations", journal = SIAMNumAnal, volume = "10", pages = "389--412", } @Article{ParR70, author = "B. N. Parlett and J. K. Reid", year = "1970", title = "On the Solution of a System of Linear Equations Whose Matrix is Symmetric But Not Definite", journal = BIT, volume = "10", pages = "386--397", } @Article{ParR81, author = "B. N. Parlett and J. K. Reid", year = "1981", title = "Tracking the Progress of the {Lanczos} Algorithm for Large Symmetric Eigenproblems", journal = IMANumerAna, volume = "1", pages = "135--155", } @Article{ParR69, author = "B. N. Parlett and C. Reinsch", year = "1969", title = "Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors", journal = NumerMath, volume = "13", pages = "292--304", note = "Also in \cite[pages 315--326]{WilR71}", } @Article{ParS79, author = "B. N. Parlett and D. S. Scott", year = "1979", title = "The {Lanczos} Algorithm with Selective Orthogonalization", journal = MathComp, volume = "33", pages = "217--238", } @Article{ParSS82, author = "B. N. Parlett and H. Simon and L. M. Stringer", year = "1982", title = "On Estimating the Largest Eigenvalue with the {Lanczos} Algorithm", journal = MathComp, volume = "38", pages = "153--166", } @Article{PatJ84, author = "N. Patel and H. Jordan", year = "1984", title = "A Parallelized Point Rowwise Successive Over-Relaxation Method on a Multiprocessor", journal = ParComputing, volume = "1", pages = "207--222", } @Article{PatS73, author = "M. S. Paterson and L. J. Stockmeyer", year = "1973", title = "On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials", journal = SIAMComp, volume = "2", pages = "60--66", } @Article{Pea01, author = "K. Pearson", year = "1901", title = "On Lines and Planes of Closest Fit to Points in Space", journal = PhilMag, volume = "2", pages = "559--572", } @Article{PetW69, author = "G. Peters and J. H. Wilkinson", year = "1969", title = "Eigenvalue of {$Ax = \lambda Bx$} with Band Symmetric {$A$} and {$B$}", journal = CompJour, volume = "12", pages = "398--404", } @Article{PetW70a, author = "G. Peters and J. H. Wilkinson", year = "1970", title = "{$Ax = \lambda Bx$} and the Generalized Eigenproblem", journal = SIAMNumAnal, volume = "7", pages = "479--492", } @Article{PetW70b, author = "G. Peters and J. H. Wilkinson", year = "1970", title = "The Least Squares Problem and Pseudo-Inverses", journal = CompJour, volume = "13", pages = "309--316", } @Incollection{PetW71, author = "G. Peters and J. H. Wilkinson", year = "1971", title = "The Calculation of Specified Eigenvectors by Inverse Iteration", booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra", editor = "J. H. Wilkinson and C. Reinsch", publisher = Springer, address = "New York, NY, USA", pages = "418--439", } @Article{PetW79, author = "G. Peters and J. H. Wilkinson", year = "1979", title = "Inverse Iteration, Ill-Conditioned Equations, and {Newton}'s Method", journal = SIAMReview, volume = "21", pages = "339--360", } @Article{Phi71, author = "J. L. Phillips", year = "1971", title = "The Triangular Decomposition of {Hankel} Matrices", journal = MathComp, volume = "25", pages = "599--602", } @Article{Ple74, author = "R. J. Plemmons", year = "1974", title = "Linear Least Squares by Elimination and {MGS}", journal = JACM, volume = "21", pages = "581--585", } @Article{Ple86, author = "R. J. Plemmons", year = "1986", title = "A Parallel Block Iterative Scheme Applied to Computations in Structural Analysis", journal = SIAMAlgMeth, volume = "7", pages = "337--347", } @Article{PooO87, author = "E. L. Poole and J. M. Ortega", year = "1987", title = "Multicolor {ICCG} Methods for Vector Computers", journal = SIAMNumAnal, volume = "24", pages = "1394--1418", } @Article{PopT57, author = "D. A. Pope and C. Tompkins", year = "1957", title = "Maximizing Functions of Rotations: Experiments Concerning Speed of Diagonalization of Symmetric Matrices Using {Jacobi}'s Method", journal = JACM, volume = "4", pages = "459--466", } @Incollection{PotJV87, author = "A. Pothen and S. Jha and U. Vemapulati", year = "1987", title = "Orthogonal Factorization on a Distributed Memory Multiprocessor", booktitle = "Hypercube Multiprocessors", editor = "M. T. Heath", publisher = SIAMPub, address = "Philadelphia, PA, USA", } @Inproceedings{PowR68, author = "M. J. D. Powell and J. K. Reid", year = "1968", title = "On Applying {Householder}'s Method to Linear Least Squares Problems", booktitle = "Proceedings {IFIP} Congress", pages = "122--126", } @Article{Pry84, author = "J. D. Pryce", year = "1984", title = "A New Measure of Relative Error for Vectors", journal = SIAMNumAnal, volume = "21", pages = "202--221", } @Article{Pry85, author = "J. D. Pryce", year = "1985", title = "Multiplicative Error Analysis of Matrix Transformation Algorithms", journal = IMANumerAna, volume = "5", pages = "437--445", } @Article{Rat82, author = "W. Rath", year = "1982", title = "Fast {Givens} Rotations for Orthogonal Similarity", journal = NumerMath, volume = "40", pages = "47--56", } @Article{Rei67, author = "J. K. Reid", year = "1967", title = "A Note on the Least Squares Solution of a Band System of Linear Equations by {Householder} Reductions", journal = CompJour, volume = "10", pages = "188--189", } @Article{Rei71a, author = "J. K. Reid", year = "1971", title = "A Note on the Stability of {Gaussian} Elimination", journal = InstMathApp, volume = "8", pages = "374--375", } @Incollection{Rei71b, author = "J. K. Reid", year = "1971", title = "On the Method of Conjugate Gradients for the Solution of Large Sparse Linear Equations", booktitle = "Large Sparse Sets of Linear Equations", editor = "J. K. Reid", publisher = Academic, address = "New York, NY, USA", pages = "231--254", } @Article{Rei72, author = "J. K. Reid", year = "1972", title = "The Use of Conjugate Gradients for Systems of Linear Equations Possessing Property~{A}", journal = SIAMNumAnal, volume = "9", pages = "325--332", } @Article{ReiB68, author = "C. Reinsch and F. L. Bauer", year = "1968", title = "Rational {QR} Transformations with {Newton}'s Shift for Symmetric Tridiagonal Matrices", journal = NumerMath, volume = "11", pages = "264--272", note = "Also in \cite[pages 257--265]{WilR71}", } @Article{Ric66b, author = "J. R. Rice", year = "1966", title = "Experiments on {Gram}-{Schmidt} Orthogonalization", journal = MathComp, volume = "20", pages = "325--328", } @Article{Ric66a, author = "J. R. Rice", year = "1966", title = "A Theory of Condition", journal = SIAMNumAnal, volume = "3", pages = "287--310", } @Book{Ric81, author = "J. R. Rice", year = "1981", title = "Matrix Computations and Mathematical Software", publisher = Academic, address = "New York, NY, USA", } @Article{Rin55, author = "R. F. Rinehart", year = "1955", title = "The Equivalence of Definitions of a Matrix Function", journal = AmerMathMonthly, volume = "62", pages = "395--414", } @Article{Ris73, author = "J. Rissanen", year = "1973", title = "Algorithms for Triangular Decomposition of Block {Hankel} and {Toeplitz} Matrices with Application to Factoring Positive Matrix Polynomials", journal = MathComp, volume = "27", pages = "147--154", } @Article{Rob77, author = "H. H. Robertson", year = "1977", title = "The Accuracy of Error Estimates for Systems of Linear Algebraic Equations", journal = InstMathApp, volume = "20", pages = "409--414", } @Article{Rod73, author = "G. Rodrigue", year = "1973", title = "A Gradient Method for the Matrix Eigenvalue Problem {$Ax = \lambda Bx$}", journal = NumerMath, volume = "22", pages = "1--16", } @Article{RodW84a, author = "G. Roderigue and D. Wolitzer", year = "1984", title = "Preconditioning by Incomplete Block Cyclic Reduction", journal = MathComp, volume = "42", pages = "549--566", } @Book{Rod82a, editor = "G. Roderigue", year = "1982", title = "Parallel Computations", publisher = Academic, address = "New York, NY, USA", } @Article{Ros69, author = "D. J. Rose", year = "1969", title = "An Algorithm for Solving a Special Class of Tridiagonal Systems of Linear Equations", journal = CACM, volume = "12", pages = "234--236", } @Book{RosW72a, editor = "D. J. Rose and R. A. Willoughby", year = "1972", title = "Sparse Matrices and Their Applications", publisher = PlenumPress, address = "New York, NY, USA", } @Article{RodW84b, author = "G. Roderigue and D. Wolitzer", year = "1984", title = "Preconditioning by Incomplete Block Cyclic Reduction", journal = MathComp, volume = "42", pages = "549--566", } @Book{Rod82b, editor = "G. Roderigue", year = "1982", title = "Parallel Computations", publisher = Academic, address = "New York, NY, USA", } @Article{RomO88, author = "C. H. Romine and J. M. Ortega", year = "1988", title = "Parallel Solution of Triangular Systems of Equations", journal = ParComputing, volume = "6", pages = "109--114", } @Article{Ruh67, author = "A. Ruhe", year = "1967", title = "On the Quadratic Convergence of the {Jacobi} Method for Normal Matrices", journal = BIT, volume = "7", pages = "305--313", } @Article{Ruh68, author = "A. Ruhe", year = "1968", title = "On the Quadratic Convergence of a Generalization of the {Jacobi} Method to Arbitrary Matrices", journal = BIT, volume = "8", pages = "210--231", } @Article{Ruh69b, author = "A. Ruhe", year = "1969", title = "The Norm of a Matrix after a Similarity Transformation", journal = BIT, volume = "9", pages = "53--58", } @Article{Ruh69a, author = "A. Ruhe", year = "1969", title = "An Algorithm for Numerical Determination of the Structure of a General Matrix", journal = BIT, volume = "10", pages = "196--216", } @Article{Ruh70a, author = "A. Ruhe", year = "1970", title = "Perturbation Bounds for Means of Eigenvalues and Invariant Subspaces", journal = BIT, volume = "10", pages = "343--354", } @Article{Ruh70b, author = "A. Ruhe", year = "1970", title = "Properties of a Matrix with a Very Ill-Conditioned Eigenproblem", journal = NumerMath, volume = "15", pages = "57--60", } @Article{Ruh74, author = "A. Ruhe", year = "1974", title = "{SOR} Methods for the Eigenvalue Problem with Large Sparse Matrices", journal = MathComp, volume = "28", pages = "695--710", } @Article{Ruh75, author = "A. Ruhe", year = "1975", title = "On the Closeness of Eigenvalues and Singular Values for Almost Normal Matrices", journal = LinAlgApp, volume = "11", pages = "87--94", } @Article{Ruh78, author = "A. Ruhe", year = "1978", title = "A Note on the Efficient Solution of Matrix Pencil Systems", journal = BIT, volume = "18", pages = "276--281", } @Article{Ruh79, author = "A. Ruhe", year = "1979", title = "Implementation Aspects of Band {Lanczos} Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices", journal = MathComp, volume = "33", pages = "680--687", } @Article{Ruh83, author = "A. Ruhe", year = "1983", title = "Numerical Aspects of {Gram}-{Schmidt} Orthogonalization of Vectors", journal = LinAlgApp, volume = "52/53", pages = "591--602", } @Article{Ruh87, author = "A. Ruhe", year = "1987", title = "Closest Normal Matrix Found!", journal = BIT, volume = "27", pages = "585--598", } @Article{RuhW72b, author = "A. Ruhe and T. Wiberg", year = "1972", title = "The Method of Conjugate Gradients Used in Inverse Iteration", journal = BIT, volume = "12", pages = "543--554", } @Incollection{Rut58, author = "H. Rutishauser", year = "1958", title = "Solution of Eigenvalue Problems with the {WR} Transformation", booktitle = "Applied Mathematics Series", publisher = NatBurStd, volume = "49", pages = "47--81", } @Article{Rut66, author = "H. Rutishauser", year = "1966", title = "The {Jacobi} Method for Real Symmetric Matrices", journal = NumerMath, volume = "9", pages = "1--10", note = "Also in \cite[pages 202--211]{WilR71}", } @Article{Rut69, author = "H. Rutishauser", year = "1969", title = "Computation Aspects of {F}.{L}. {Bauer}'s Simultaneous Iteration Method", journal = NumerMath, volume = "13", pages = "4--13", } @Article{Rut70, author = "H. Rutishauser", year = "1970", title = "Simultaneous Iteration Method for Symmetric Matrices", journal = NumerMath, volume = "16", pages = "205--223", note = "Also in \cite[pages 284--302]{WilR71}", } @Article{Saa80, author = "Y. Saad", year = "1980", title = "On the Rates of Convergence of the {Lanczos} and the Block {Lanczos} Methods", journal = SIAMNumAnal, volume = "17", pages = "687--706", } @Article{Saa84, author = "Y. Saad", year = "1984", title = "Practical Use of Some {Krylov} Subspace Methods for Solving Indefinite and Nonsymmetric Linear Systems", journal = SIAMSciStat, volume = "5", pages = "203--228", } @Article{Saa87, author = "Y. Saad", year = "1987", title = "On the {Lanczos} Method for Solving Symmetric Systems with Several Right Hand Sides", journal = MathComp, volume = "48", pages = "651--662", } @Article{Saa81, author = "Y. Saad", year = "1981", title = "{Krylov} Subspace Methods for Solving Large Unsymmetric Linear Systems", journal = MathComp, volume = "37", pages = "105--126", } @Article{Saa82, author = "Y. Saad", year = "1982", title = "The {Lanczos} Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems", journal = SIAMNumAnal, volume = "19", pages = "485--506", } @Article{Saa86, author = "Y. Saad", year = "1986", title = "On the Condition Number of Some {Gram} Matrices Arising from Least Squares Approximation in the Complex Plane", journal = NumerMath, volume = "48", pages = "337--348", } @Techreport{SaaS85a, author = " Y. Saad and M. H. Schultz", year = "1985", title = "Data Communication in Hypercubes", number = "YALEU DCS RR-428", institution = "Computer Science, Yale University", address = "New Haven, CT, USA", } @Techreport{SaaS85b, author = " Y. Saad and M. H. Schultz", year = "1985", title = "Topological Properties of Hypercubes", number = "YALEU DCS RR-389", institution = "Computer Science, Yale University", address = "New Haven, CT, USA", } @Article{SaaS86, author = "Y. Saad and M. Schultz", year = "1986", title = "{GMRES}: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems", journal = SIAMSciStat, volume = "7", pages = "856--869", } @Article{Sam71, author = "A. Sameh", year = "1971", title = "On {Jacobi} and {Jacobi}-Like Algorithms for a Parallel Computer", journal = MathComp, volume = "25", pages = "579--590", } @Article{SamK78, author = "A. Sameh and D. Kuck", year = "1978", title = "On Stable Parallel Linear System Solvers", journal = JACM, volume = "25", pages = "81--91", } @Article{SamLN75, author = "A. Sameh and J. Lermit and K. Noh", year = "1975", title = "On the Intermediate Eigenvalues of Symmetric Sparse Matrices", journal = BIT, volume = "12", pages = "543--554", } @Article{SchS79, author = "K. Schittkowski and J. Stoer", year = "1979", title = "A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing for Subsequent Data Changes", journal = NumerMath, volume = "31", pages = "431--463", } @Article{Sch66, author = "P. Schoenemann", year = "1966", title = "A Generalized Solution of the Orthogonal {Procrustes} Problem", journal = Psychometrika, volume = "31", pages = "1--10", } @Article{Sch64, author = "A. Schonage", year = "1964", title = "On the Quadratic Convergence of the {Jacobi} Process", journal = NumerMath, volume = "6", pages = "410--412", } @Article{Sch79, author = "A. Schonage", year = "1979", title = "Arbitrary Perturbations of {Hermitian} Matrices", journal = LinAlgApp, volume = "24", pages = "143--149", } @Book{Sch87, author = "W. Sch{\"o}nauer", year = "1987", title = "Scientific Computing on Vector Computers", publisher = NorthHolland, address = "Amsterdam, The Netherlands", } @Article{Sch86, author = "R. Schreiber", year = "1986", title = "Solving Eigenvalue and Singular Value Problems on an Undersized Systolic Array", journal = SIAMSciStat, volume = "7", pages = "441--451", } @Article{SchT86, author = "R. Schreiber and W. P. Tang", year = "1986", title = "On Systolic Arrays for Updating the {Cholesky} Factorization", journal = BIT, volume = "26", pages = "451--466", } @Article{SchP87, author = "R. Schreiber and B. N. Parlett", year = "1987", title = "Block Reflectors: Theory and Computation", journal = SIAMNumAnal, volume = "25", pages = "189--205", } @Article{SchL89, author = "R. Schreiber and C. Van Loan", year = "1989", title = "A Storage Efficient {WY} Representation for Products of {Householder} Transformations", journal = SIAMSciStat, volume = "10", pages = "53--57", } @Article{Sch09, author = "I. Schur", year = "1909", title = "On the Characteristic Roots of a Linear Substitution with an Application to the Theory of Integral Equations", journal = MathAnnalen, volume = "66", pages = "488--510", note = "German", } @Article{Sch68, author = "H. R. Schwartz", year = "1968", title = "Tridiagonalization of a Symmetric Band Matrix", journal = NumerMath, volume = "12", pages = "231--241", note = "Also in \cite[pages 273--283]{WilR71}", } @Article{Sch74, author = "H. R. Schwartz", year = "1974", title = "The Method of Coordinate Relaxation for {$(A - \lambda B)x = 0$}", journal = NumerMath, volume = "23", pages = "135--152", } @Techreport{Sco78, author = "D. S. Scott", year = "1978", title = "Analysis of the Symmetric {Lanczos} Process", number = "M78/40", institution = "UCB-ERL, University of California, Berkeley", address = "Berkeley, CA, USA", } @Techreport{Sco79a, author = "D. S. Scott", year = "1979", title = "Block {Lanczos} Software for Symmetric Eigenvalue Problems", number = "ORNL/CSD-48", institution = "Oak Ridge National Laboratory", address = "Oak Ridge, TN, USA", } @Article{Sco79b, author = "D. S. Scott", year = "1979", title = "How to Make the {Lanczos} Algorithm Converge Slowly", journal = MathComp, volume = "33", pages = "239--247", } @Article{Sco84, author = "D. S. Scott", year = "1984", title = "Computing a Few Eigenvalues and Eigenvectors of a Symmetric Band Matrix", journal = SIAMSciStat, volume = "5", pages = "658--666", } @Article{Sco85, author = "D. S. Scott", year = "1985", title = "On the Accuracy of the {Gershgorin} Circle Theorem for Bounding the Spread of a Real Symmetric Matrix", journal = LinAlgApp, volume = "65", pages = "147--155", } @Article{ScoHW86, author = "D. S. Scott and M. T. Heath and R. C. Ward", year = "1986", title = "Parallel Block {Jacobi} Eigenvalue Algorithms Using Systolic Arrays", journal = LinAlgApp, volume = "77", pages = "345--356", } @Article{Sea86, author = "M. K. Seager", year = "1986", title = "Parallelizing Conjugate Gradient for the {Cray X-MP}", journal = ParComputing, volume = "3", pages = "35--47", } @Article{Sea69, author = "J. J. Seaton", year = "1969", title = "Diagonalization of Complex Symmetric Matrices Using a Modified {Jacobi} Method", journal = CompJour, volume = "12", pages = "156--157", } @Article{Ser80, author = "S. Serbin", year = "1980", title = "On Factoring a Class of Complex Symmetric Matrices Without Pivoting", journal = MathComp, volume = "35", pages = "1231--1234", } @Article{SerB79, author = "S. Serbin and S. Blalock", year = "1979", title = "An Algorithm for Computing the Matrix Cosine", journal = SIAMSciStat, volume = "1", pages = "198--204", } @Article{She55, author = "J. W. Sheldon", year = "1955", title = "On the Numerical Solution of Elliptic Difference Equations", journal = TablesAidsComp, volume = "9", pages = "101--112", } @Techreport{ShrS87, author = "G. Shroff and R. Schreiber", year = "1987", title = "Convergence of Block {Jacobi} Methods", number = "87-25", institution = "Computer Science, Rensselaer Polytechnic Institute", address = "Troy, NY, USA", } @Article{Sim84, author = "H. Simon", year = "1984", title = "Analysis of the Symmetric {Lanczos} Algorithm with Reorthogonalization Methods", journal = LinAlgApp, volume = "61", pages = "101--132", } @Article{SinS76, author = "B. Singer and S. Spilerman", year = "1976", title = "The Representation of Social Processes by {Markov} Models", journal = AmerSocio, volume = "82", pages = "1--54", } @Article{Ske79, author = "R. D. Skeel", year = "1979", title = "Scaling for Numerical Stability in {Gaussian} Elimination", journal = JACM, volume = "26", pages = "494--526", } @Article{Ske80, author = "R. D. Skeel", year = "1980", title = "Iterative Refinement Implies Numerical Stability for {Gaussian} Elimination", journal = MathComp, volume = "35", pages = "817--832", } @Article{Ske81, author = "R. D. Skeel", year = "1981", title = "Effect of Equilibration on Residual Size for Partial Pivoting", journal = SIAMNumAnal, volume = "18", pages = "449--455", } @Book{SmiBI+70, author = "B. T. Smith and J. M. Boyle and Y. Ikebe and V. C. Klema and C. B. Moler", year = "1970", title = "Matrix Eigensystem Routines: {EISPACK} Guide", edition = "second", publisher = Springer, address = "New York, NY, USA", } @Article{Smi67, author = "R. A. Smith", year = "1967", title = "The Condition Numbers of the Matrix Eigenvalue Problem", journal = NumerMath, volume = "10", pages = "232--240", } @Book{Smi70, author = "F. Smithies", year = "1970", title = "Integral Equations", publisher = CambridgePress, address = "Cambridge, UK", } @Article{Sor85, author = "D. Sorensen", year = "1985", title = "Analysis of Pairwise Pivoting in {Gaussian} Elimination", journal = IEEETransComp, volume = "C-34", pages = "274--278", } @Article{Ste81a, author = "D. Stevenson", year = "1981", title = "A Proposed Standard for Binary Floating Point Arithmetic", journal = Computer, volume = "14", month = mar, pages = "51--62", } @Article{Ste69, author = "G. W. Stewart", year = "1969", title = "Accelerating the Orthogonal Iteration for the Eigenvectors of a {Hermitian} Matrix", journal = NumerMath, volume = "13", pages = "362--376", } @Article{Ste70, author = "G. W. Stewart", year = "1970", title = "Incorporating Origin Shifts into the {QR} Algorithm for Symmetric Tridiagonal Matrices", journal = CACM, volume = "13", pages = "365--367", } @Article{Ste71, author = "G. W. Stewart", year = "1971", title = "Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators", journal = SIAMNumAnal, volume = "8", pages = "796--808", } @Article{Ste72, author = "G. W. Stewart", year = "1972", title = "On the Sensitivity of the Eigenvalue Problem {$Ax = \lambda Bx$}", journal = SIAMNumAnal, volume = "9", pages = "669--686", } @Article{Ste73a, author = "G. W. Stewart", year = "1973", title = "Conjugate Direction Methods for Solving Systems of Linear Equations", journal = NumerMath, volume = "21", pages = "284--297", } @Article{Ste73b, author = "G. W. Stewart", year = "1973", title = "Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems", journal = SIAMReview, volume = "15", pages = "727--764", } @Book{Ste73c, author = "G. W. Stewart", year = "1973", title = "Introduction to Matrix Computations", publisher = Academic, address = "New York, NY, USA", } @Inproceedings{Ste74, author = "G. W. Stewart", year = "1974", title = "The Numerical Treatment of Large Eigenvalue Problems", booktitle = "Proceedings {IFIP} Congress 74", publisher = NorthHolland, pages = "666--672", } @Article{Ste75a, author = "G. W. Stewart", year = "1975", title = "The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points in the Spectrum", journal = NumerMath, volume = "24", pages = "85--93", } @Article{Ste75b, author = "G. W. Stewart", year = "1975", title = "{Gershgorin} Theory for the Generalized Eigenvalue Problem {$Ax = \lambda Bx$}", journal = MathComp, volume = "29", pages = "600--606", } @Incollection{Ste75c, author = "G. W. Stewart", year = "1975", title = "Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices", booktitle = "Topics in Numerical Analysis {II}", editor = "J. H. Miller", publisher = Academic, address = "New York, NY, USA", pages = "185--196", } @Article{Ste76a, author = "G. W. Stewart", year = "1976", title = "Algorithm~406 {HQR3 and~EXCHNG}: {Fortran} Subroutines for Calculating and Ordering and Eigenvalues of a Real Upper {Hessenberg} Matrix", journal = ACMMathSoft, volume = "2", pages = "275--280", } @Incollection{Ste76b, author = "G. W. Stewart", year = "1976", title = "A Bibliographical Tour of the Large Sparse Generalized Eigenvalue Problem", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = Academic, address = "New York, NY, USA", } @Article{Ste76c, author = "G. W. Stewart", year = "1976", title = "The Economical Storage of Plane Rotations", journal = NumerMath, volume = "25", pages = "137--138", } @Article{Ste76d, author = "G. W. Stewart", year = "1976", title = "Simultaneous Iteration for Computing Invariant Subspaces of Non-{Hermitian} Matrices", journal = NumerMath, volume = "25", pages = "12--36", } @Article{Ste77a, author = "G. W. Stewart", year = "1977", title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear Least Squares Problems", journal = SIAMReview, volume = "19", pages = "634--662", } @Article{Ste77b, author = "G. W. Stewart", year = "1977", title = "Perturbation Bounds for the {QR} Factorization of a Matrix", journal = SIAMNumAnal, volume = "14", pages = "509--518", } @Techreport{Ste77c, author = "G. W. Stewart", year = "1977", title = "Sensitivity Coefficients for the Effects of Errors in the Independent Variables in a Linear Regression", number = "TR-571", institution = "Computer Science, University of Maryland", address = "College Park, MD, USA", } @Incollection{Ste78, author = "G. W. Stewart", year = "1978", title = "Perturbation Theory for the Generalized Eigenvalue Problem", booktitle = "Recent Advances in Numerical Analysis", editor = "C. de Boor and G. H. Golub", publisher = Academic, address = "New York, NY, USA", } @Article{Ste79b, author = "G. W. Stewart", year = "1979", title = "A Note on the Perturbation of Singular Values", journal = LinAlgApp, volume = "28", pages = "213--216", } @Article{Ste79c, author = "G. W. Stewart", year = "1979", title = "Perturbation Bounds for the Definite Generalized Eigenvalue Problem", journal = LinAlgApp, volume = "23", pages = "69--86", } @Article{Ste79a, author = "G. W. Stewart", year = "1979", title = "The Effects of Rounding Error on an Algorithm for Downdating a {Cholesky} Factorization", journal = InstMathApp, volume = "23", pages = "203--213", } @Article{Ste80, author = "G. W. Stewart", year = "1980", title = "The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators", journal = SIAMNumAnal, volume = "17", pages = "403--409", } @Article{Ste81b, author = "G. W. Stewart", year = "1981", title = "On the Implicit Deflation of Nearly Singular Systems of Linear Equations", journal = SIAMSciStat, volume = "2", pages = "136--140", } @Incollection{Ste83, author = "G. W. Stewart", year = "1983", title = "A Method for Computing the Generalized Singular Value Decomposition", booktitle = "Matrix Pencils", editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", publisher = Springer, address = "New York, NY, USA", pages = "207--220", } @Article{Ste84c, author = "G. W. Stewart", year = "1984", title = "Rank Degeneracy", journal = SIAMSciStat, volume = "5", pages = "403--413", } @Article{Ste84a, author = "G. W. Stewart", year = "1984", title = "On the Asymptotic Behavior of Scaled Singular Value and {QR} Decompositions", journal = MathComp, volume = "43", pages = "483--490", } @Article{Ste84d, author = "G. W. Stewart", year = "1984", title = "A Second Order Perturbation Expansion for Small Singular Values", journal = LinAlgApp, volume = "56", pages = "231--236", } @Article{Ste84b, author = "G. W. Stewart", year = "1984", title = "On the Invariance of Perturbed Null Vectors Under Column Scaling", journal = NumerMath, volume = "33,34", pages = "61--66", } @Article{Ste85, author = "G. W. Stewart", year = "1985", title = "A {Jacobi}-Like Algorithm for Computing the {Schur} Decomposition of a Nonhermitian Matrix", journal = SIAMSciStat, volume = "6", pages = "853--862", } @Article{Ste87, author = "G. W. Stewart", year = "1987", title = "Collinearity and Least Squares Regression", journal = StatScience, volume = "2", pages = "68--100", } @Article{Sto73, author = "H. S. Stone", year = "1973", title = "An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations", journal = JACM, volume = "20", pages = "27--38", } @Article{Sto75b, author = "H. S. Stone", year = "1975", title = "Parallel Tridiagonal Equation Solvers", journal = ACMMathSoft, volume = "1", pages = "289--307", } @Book{Str88, author = "G. Strang", year = "1988", title = "Linear Algebra and Its Applications", edition = "third", publisher = Academic, address = "New York, NY, USA", } @Article{Sto75a, author = "H. Stone", year = "1975", title = "Parallel Tridiagonal Equation Solvers", journal = ACMMathSoft, volume = "1", pages = "289--307", } @Article{Str69, author = "V. Strassen", year = "1969", title = "{Gaussian} Elimination is Not Optimal", journal = NumerMath, volume = "13", pages = "354--356", } @Article{Sun82, author = "J. Guang Sun", year = "1982", title = "A Note on {Stewart}'s Theorem for Definite Matrix Pairs", journal = LinAlgApp, volume = "48", pages = "331--339", } @Article{Sun83, author = "J. Guang Sun", year = "1983", title = "Perturbation Analysis for the Generalized Singular Value Problem", journal = SIAMNumAnal, volume = "20", pages = "611--625", } @Article{Swa79, author = "P. N. Swarztrauber", year = "1979", title = "A Parallel Algorithm for Solving General Tridiagonal Equations", journal = MathComp, volume = "33", pages = "185--199", } @Article{SwaS73, author = "P. N. Swarztrauber and R. A. Sweet", year = "1973", title = "The Direct Solution of the Discrete {Poisson} Equation on a Disk", journal = SIAMNumAnal, volume = "10", pages = "900--907", } @Article{Swe74, author = "R. A. Sweet", year = "1974", title = "A Generalized Cyclic Reduction Algorithm", journal = SIAMNumAnal, volume = "11", pages = "506--520", } @Article{Swe77, author = "R. A. Sweet", year = "1977", title = "A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension", journal = SIAMNumAnal, volume = "14", pages = "706--720", } @Article{SymW80, author = "H. J. Symm and J. H. Wilkinson", year = "1980", title = "Realistic Error Bounds for a Simple Eigenvalue and Its Associated Eigenvector", journal = NumerMath, volume = "35", pages = "113--126", } @Article{TanG81, author = "W. P. Tang and G. H. Golub", year = "1981", title = "The Block Decomposition of a {Vandermonde} Matrix and Its Applications", journal = BIT, volume = "21", pages = "505--517", } @Article{ThoW70, author = "G. L. Thompson and R. L. Weil", year = "1970", title = "Reducing the Rank of {$A - \lambda B$}", journal = ProcAMS, volume = "26", pages = "548--554", } @Article{ThoW72, author = "G. L. Thompson and R. L. Weil", year = "1972", title = "Roots of Matrix Pencils {$Ay = \lambda By$}: Existence, Calculations, and Relations to Game Theory", journal = LinAlgApp, volume = "5", pages = "207--226", } @Techreport{TreS87, author = "L. N. Trefethen and R. S. Schreiber", year = "1987", title = "Average Case Stability of {Gaussian} Elimination", number = "88-3", institution = "Numerical Analysis, Department of Mathematics, MIT", address = "MA", } @Article{Tre64, author = "W. F. Trench", year = "1964", title = "An Algorithm for the Inversion of Finite {Toeplitz} Matrices", journal = "J. SIAM", volume = "12", pages = "515--522", } @Article{Tre74, author = "W. F. Trench", year = "1974", title = "Inversion of {Toeplitz} Band Matrices", journal = MathComp, volume = "28", pages = "1089--1095", } @Article{Tsa75, author = "N. K. Tsao", year = "1975", title = "A Note on Implementing the {Householder} Transformation", journal = SIAMNumAnal, volume = "12", pages = "53--58", } @Book{TurA61, author = "H. W. Turnbull and A. C. Aitken", year = "1961", title = "An Introduction to the Theory of Canonical Matrices", publisher = DoverPub, address = "New York, NY, USA", } @Article{Uhl73, author = "F. Uhlig", year = "1973", title = "Simultaneous Block Diagonalization of Two Real Symmetric Matrices", journal = LinAlgApp, volume = "7", pages = "281--289", } @Article{Uhl76, author = "F. Uhlig", year = "1976", title = "A Canonical Form for a Pair of Real Symmetric Matrices that Generate a Nonsingular Pencil", journal = LinAlgApp, volume = "14", pages = "189--210", } @Techreport{Und75, author = "R. Underwood", year = "1975", title = "An Iterative Block {Lanczos} Method for the Solution of Large Sparse Symmetric Eigenproblems", number = "STAN-CS-75-496", institution = "Computer Science, Stanford University", address = "Stanford, CA, USA", } @Article{Van71, author = "J. Vandergraft", year = "1971", title = "Generalized {Rayleigh} Methods with Applications to Finding Eigenvalues of Large Matrices", journal = LinAlgApp, volume = "4", pages = "353--368", } @Article{vdS69, author = "A. van der Sluis", year = "1969", title = "Condition Numbers and Equilibration Matrices", journal = NumerMath, volume = "14", pages = "14--23", } @Article{vdS70, author = "A. van der Sluis", year = "1970", title = "Condition, Equilibration, and Pivoting in Linear Algebraic Systems", journal = NumerMath, volume = "15", pages = "74--86", } @Article{vdS75a, author = "A. van der Sluis", year = "1975", title = "Perturbations of Eigenvalues of Nonnormal Matrices", journal = CACM, volume = "18", pages = "30--36", } @Article{vdS75b, author = "A. van der Sluis", year = "1975", title = "Stability of the Solutions of Linear Least Squares Problem", journal = NumerMath, volume = "23", pages = "241--254", } @Article{vdSV79, author = "A. van der Sluis and G. W. Veltkamp", year = "1979", title = "Restoring Rank and Consistency by Orthogonal Projection", journal = LinAlgApp, volume = "28", pages = "257--278", } @Article{vdSV86, author = "A. van der Sluis and H. A. Van der Vorst", year = "1986", title = "The Rate of Convergence of Conjugate Gradients", journal = NumerMath, volume = "48", pages = "543--560", } @Article{dV77, author = "H. Van de Vel", year = "1977", title = "Numerical Treatment of a Generalized {Vandermonde} System of Equations", journal = LinAlgApp, volume = "17", pages = "149--174", } @Article{dV82b, author = "H. A. Van der Vorst", year = "1982", title = "A Vectorizable Variant of Some {ICCG} Methods", journal = SIAMSciStat, volume = "3", pages = "350--356", } @Article{dV82a, author = "H. A. Van der Vorst", year = "1982", title = "A Generalized {Lanczos} Scheme", journal = MathComp, volume = "39", pages = "559--562", } @Article{Doo79, author = "P. Van Dooren", year = "1979", title = "The Computation of {Kronecker}'s Canonical Form of a Singular Pencil", journal = LinAlgApp, volume = "27", pages = "103--140", } @Article{Doo81b, author = "P. Van Dooren", year = "1981", title = "A Generalized Eigenvalue Approach for Solving {Riccati} Equations", journal = SIAMSciStat, volume = "2", pages = "121--135", } @Article{Doo81a, author = "P. Van Dooren", year = "1981", title = "The Generalized Eigenstructure Problem in Linear System Theory", journal = IEEETransAC, volume = "AC-26", pages = "111--128", } @Incollection{Doo83, author = "P. Van Dooren", year = "1983", title = "Reducing Subspaces: definitions, properties and Algorithms", booktitle = "Matrix Pencils", editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", publisher = Springer, address = "New York, NY, USA", pages = "58--73", } @Phdthesis{Huf87, author = "S. Van Huffel", year = "1987", title = "Analysis of the Total Least Squares Problem and Its Use in Parameter Estimation", school = "Electrical Engineering, Katholieke Universiteit Leuven", address = "Leuven, Belgium", } @Techreport{Huf88, author = "S. Van Huffel", year = "1988", title = "Comments on the Solution of the Nongeneric Total Least Squares Problem", number = "ESAT-KUL-88/3", institution = "Department of Electrical Engineering, Katholieke Universiteit Leuven", address = "Leuven, Belgium", } @Article{HufV88a, author = "S. Van Huffel and J. Vandewalle", year = "1988", title = "The Partial Total Least Squares Algorithm", journal = CompApplMath, volume = "21", pages = "333--342", } @Article{HufV87, author = "S. Van Huffel and J. Vandewalle", year = "1987", title = "Subset Selection Using the Total Least Squares Approach in Collinearity Problems with Errors in the Variables", journal = LinAlgApp, volume = "88/89", pages = "695--714", } @Article{HufVH87, author = "S. Van Huffel and J. Vandewalle and A. Haegemans", year = "1987", title = "An Efficient and Reliable Algorithm for Computing the Singular Subspace of a Matrix Associated with its Smallest Singular Values", journal = CompApplMath, volume = "19", pages = "313--330", } @Article{HufV88b, author = "S. Van Huffel and J. Vandewalle", year = "1988", title = "The Partial Total Least Squares Algorithm", journal = CompApplMath, volume = "21", pages = "333--342", } @Techreport{KatdV77, author = "J. M. Van Kats and H. A. Van der Vorst", year = "1977", title = "Automatic Monitoring of {Lanczos} Schemes for Symmetric or Skew-Symmetric Generalized Eigenvalue Problems", number = "TR 7", institution = "Academische Computer Centre", address = "Utrecht, The Netherlands", } @Article{vK66, author = "H. P. M. van Kempen", year = "1966", title = "On Quadratic Convergence of the Special Cyclic {Jacobi} Method", journal = NumerMath, volume = "9", pages = "19--22", } @Phdthesis{Loa73, author = "C. F. Van Loan", year = "1973", title = "Generalized Singular Values with Algorithms and Applications", school = "University of Michigan", address = "Ann Arbor, MI, USA", } @Article{Loa75a, author = "C. F. Van Loan", year = "1975", title = "A General Matrix Eigenvalue Algorithm", journal = SIAMNumAnal, volume = "12", pages = "819--834", } @Techreport{Loa75b, author = "C. F. Van Loan", year = "1975", title = "A Study of the Matrix Exponential", number = "10", institution = "Numerical Analysis, University of Manchester", address = "UK", } @Article{Loa76, author = "C. F. Van Loan", year = "1976", title = "Generalizing the Singular Value Decomposition", journal = SIAMNumAnal, volume = "13", pages = "76--83", } @Incollection{Loa77a, author = "C. F. Van Loan", year = "1977", title = "On the Limitation and Application of the {Pad}{\'e} Approximation to the Matrix Exponential", booktitle = "{Pad}{\'e} and Rational Approximation", editor = "E. B. Saff and R. S. Varga", publisher = Academic, address = "New York, NY, USA", } @Article{Loa77b, author = "C. F. Van Loan", year = "1977", title = "The Sensitivity of the Matrix Exponential", journal = SIAMNumAnal, volume = "14", pages = "971--981", } @Article{Loa78a, author = "C. F. Van Loan", year = "1978", title = "Computing Integrals Involving the Matrix Exponential", journal = IEEETransAC, volume = "AC-23", pages = "395--404", } @Article{Loa78b, author = "C. F. Van Loan", year = "1978", title = "A Note on the Evaluation of Matrix Polynomials", journal = IEEETransAC, volume = "AC-24", pages = "320--321", } @Incollection{Loa82, author = "C. F. Van Loan", year = "1982", title = "Using the {Hessenberg} Decomposition in Control Theory", booktitle = "Algorithms and Theory in Filtering and Control", editor = "D. C. Sorensen and R. J. Wets", series = "Mathematical Programming Study", number = "18", publisher = NorthHolland, address = "Amsterdam, The Netherlands", pages = "102--111", } @Inproceedings{Loa83, author = "C. F. Van Loan", year = "1983", title = "A Generalized {SVD} Analysis of Some Weighting Methods for Equality-Constrained Least Squares", booktitle = "Proceedings of the Conference on Matrix Pencils", editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", publisher = Springer, address = "New York, NY, USA", } @Article{Loa84, author = "C. F. Van Loan", year = "1984", title = "A Symplectic Method for Approximating All the Eigenvalues of a {Hamiltonian} Matrix", journal = LinAlgApp, volume = "61", pages = "233--252", } @Article{Loa85a, author = "C. F. Van Loan", year = "1985", title = "Computing the {CS} and Generalized Singular Value Decomposition", journal = NumerMath, volume = "46", pages = "479--492", } @Article{Loa85c, author = "C. F. Van Loan", year = "1985", title = "On the Method of Weighting for Equality Constrained Least Squares Problems", journal = SIAMNumAnal, volume = "22", pages = "851--864", } @Article{Loa85b, author = "C. F. Van Loan", year = "1985", title = "How Near is a Stable Matrix to an Unstable Matrix?", journal = ContempMath, volume = "47", pages = "465--477", } @Article{Loa87, author = "C. F. Van Loan", year = "1987", title = "On Estimating the Condition of Eigenvalues and Eigenvectors", journal = LinAlgApp, volume = "88/89", pages = "715--732", } @Article{Var68a, author = "J. M. Varah", year = "1968", title = "The Calculation of the Eigenvectors of a General Complex Matrix by Inverse Iteration", journal = MathComp, volume = "22", pages = "785--791", } @Article{Var68b, author = "J. M. Varah", year = "1968", title = "Rigorous Machine Bounds for the Eigensystem of a General Complex Matrix", journal = MathComp, volume = "22", pages = "793--801", } @Article{Var70a, author = "J. M. Varah", year = "1970", title = "Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Determined", journal = MathComp, volume = "24", pages = "137--149", } @Article{Var79, author = "J. M. Varah", year = "1979", title = "On the Separation of Two Matrices", journal = SIAMNumAnal, volume = "16", pages = "216--222", } @Article{Var72, author = "J. M. Varah", year = "1972", title = "On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations", journal = MathComp, volume = "26", pages = "859--868", } @Article{Var73, author = "J. M. Varah", year = "1973", title = "On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems", journal = SIAMNumAnal, volume = "10", pages = "257--267", } @Article{Var75, author = "J. M. Varah", year = "1975", title = "A Lower Bound for the Smallest Singular Value of a Matrix", journal = LinAlgApp, volume = "11", pages = "1--2", } @Article{Var61, author = "R. S. Varga", year = "1961", title = "On Higher-Order Stable Implicit Methods for Solving Parabolic Partial Differential Equations", journal = MathPhys, volume = "40", pages = "220--231", } @Book{Var62, author = "R. S. Varga", year = "1962", title = "Matrix Iterative Analysis", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Article{Var70b, author = "R. S. Varga", year = "1970", title = "Minimal {Gershgorin} Sets for Partitioned Matrices", journal = SIAMNumAnal, volume = "7", pages = "493--507", } @Article{Var76, author = "R. S. Varga", year = "1976", title = "On Diagonal Dominance Arguments for Bounding {$\|A^{-1}\|$}", journal = LinAlgApp, volume = "14", pages = "211--217", } @Article{Vet75, author = "W. J. Vetter", year = "1975", title = "Vector Structures and Solutions of Linear Matrix Equations", journal = LinAlgApp, volume = "10", pages = "181--188", } @Book{Wac66, author = "E. L. Wachpress", year = "1966", title = "Iterative Solution of Elliptic Systems", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Inproceedings{WalAC+88, author = "D. W. Walker and T. Aldcroft and A. Cisneros and G. Fox and W. Furmanski", year = "1988", title = "{LU} Decomposition of Banded Matrices and the Solution of Linear Systems on Hypercubes", booktitle = "The Third Conference on Hypercube Concurrent Computers and Applications, Vol. {II}, Applications", editor = "G. Fox", publisher = ACMPress, address = "New York, NY, USA", pages = "1635--1655", } @Article{Wal88, author = "H. F. Walker", year = "1988", title = "Implementation of the {GMRES} Method Using {Householder} Transformations", journal = SIAMSciStat, volume = "9", pages = "152--163", } @Article{War75, author = "R. C. Ward", year = "1975", title = "The Combination Shift {QZ} Algorithm", journal = SIAMNumAnal, volume = "12", pages = "835--853", } @Article{War77, author = "R. C. Ward", year = "1977", title = "Numerical Computation of the Matrix Exponential with Accuracy Estimate", journal = SIAMNumAnal, volume = "14", pages = "600--614", } @Article{War81, author = "R. C. Ward", year = "1981", title = "Balancing the Generalized Eigenvalue Problem", journal = SIAMSciStat, volume = "2", pages = "141--152", } @Article{WarG78, author = "R. C. Ward and L. J. Gray", year = "1978", title = "Eigensystem Computation for Skew-Symmetric and a Class of Symmetric Matrices", journal = ACMMathSoft, volume = "4", pages = "278--285", } @Article{Wat82, author = "D. S. Watkins", year = "1982", title = "Understanding the {QR} Algorithm", journal = SIAMReview, volume = "24", pages = "427--440", } @Article{Wat73, author = "G. A. Watson", year = "1973", title = "An Algorithm for the Inversion of Block Matrices of {Toeplitz} Form", journal = JACM, volume = "20", pages = "409--415", } @Article{Wat88, author = "G. A. Watson", year = "1988", title = "The Smallest Perturbation of a Submatrix which Lowers the Rank of the Matrix", journal = IMANumerAna, volume = "8", pages = "295--304", } @Article{Wed72, author = "P.{\AA}. Wedin", year = "1972", title = "Perturbation Bounds in Connection with the Singular Value Decomposition", journal = BIT, volume = "12", pages = "99--111", } @Article{Wed73a, author = "P.{\AA}. Wedin", year = "1973", title = "On the Almost Rank-Deficient Case of the Least Squares Problem", journal = BIT, volume = "13", pages = "344--354", } @Article{Wed73b, author = "P.{\AA}. Wedin", year = "1973", title = "Perturbation Theory for Pseudo-Inverses", journal = BIT, volume = "13", pages = "217--232", } @Article{Wid78, author = "O. Widlund", year = "1978", title = "A {Lanczos} Method for a Class of Nonsymmetric Systems of Linear Equations", journal = SIAMNumAnal, volume = "15", pages = "801--812", } @Article{Wil61, author = "J. H. Wilkinson", year = "1961", title = "Error Analysis of Direct Methods of Matrix Inversion", journal = JACM, volume = "10", pages = "281--330", } @Book{Wil63, author = "J. H. Wilkinson", year = "1963", title = "Rounding Errors in Algebraic Processes", publisher = PrenticeHall, address = "Englewood Cliffs, NJ, USA", } @Book{Wil65a, author = "J. H. Wilkinson", year = "1965", title = "The Algebraic Eigenvalue Problem", publisher = ClaredonPress, address = "Oxford, UK", } @Article{Wil65b, author = "J. H. Wilkinson", year = "1965", title = "Convergence of the {LR}, {QR}, and Related Algorithms", journal = CompJour, volume = "8", pages = "77--84", } @Article{Wil68a, author = "J. H. Wilkinson", year = "1968", title = "Almost Diagonal Matrices with Multiple or Close Eigenvalues", journal = LinAlgApp, volume = "1", pages = "1--12", } @Article{Wil68c, author = "J. H. Wilkinson", year = "1968", title = "Global Convergence of Tridiagonal {QR} Algorithm with Origin Shifts", journal = LinAlgApp, volume = "1", pages = "409--420", } @Inproceedings{Wil68b, author = "J. H. Wilkinson", year = "1968", title = "A Priori Error Analysis of Algebraic Processes", booktitle = "Proceedings International Congress Math. ({Moscow}: {Izdat}. {Mir})", pages = "629--639", } @Article{Wil71, author = "J. H. Wilkinson", year = "1971", title = "Modern Error Analysis", journal = SIAMReview, volume = "14", pages = "548--568", } @Article{Wil72, author = "J. H. Wilkinson", year = "1972", title = "Note on Matrices with a Very Ill-Conditioned Eigenproblem", journal = NumerMath, volume = "19", pages = "176--178", } @Incollection{Wil77, author = "J. H. Wilkinson", year = "1977", title = "Some Recent Advances in Numerical Linear Algebra", booktitle = "The State of the Art in Numerical Analysis", editor = "D. A. H. Jacobs", publisher = Academic, address = "New York, NY, USA", pages = "1--53", } @Incollection{Wil78, author = "J. H. Wilkinson", year = "1978", title = "Linear Differential Equations and {Kronecker}'s Canonical Form", booktitle = "Recent Advances in Numerical Analysis", editor = "C. de Boor and G. H. Golub", publisher = Academic, address = "New York, NY, USA", pages = "231--265", } @Article{Wil79, author = "J. H. Wilkinson", year = "1979", title = "{Kronecker}'s Canonical Form and the {QZ} Algorithm", journal = LinAlgApp, volume = "28", pages = "285--303", } @Book{WilR71, editor = "J. H. Wilkinson and C. Reinsch", year = "1971", title = "Linear Algebra", volume = "2", series = "Handbook for Automatic Computation", publisher = Springer, address = "New York, NY, USA", } @Article{Wil84, author = "J. H. Wilkinson", year = "1984", title = "On Neighboring Matrices with Quadratic Elementary Divisors", journal = NumerMath, volume = "44", pages = "1--21", } @Article{WimZ72, author = "H. Wimmer and A. D. Ziebur", year = "1972", title = "Solving the Matrix Equation {$\sum f_{p}(A)Xg_{p}(A)$}", journal = SIAMReview, volume = "14", pages = "318--323", } @Article{Win68, author = "S. Winograd", year = "1968", title = "A New Algorithm for Inner Product", journal = IEEETransComp, volume = "C-17", pages = "693--694", } @Article{Woz80, author = "H. Wozniakowski", year = "1980", title = "Roundoff Error Analysis of a New Class of Conjugate Gradient Algorithms", journal = LinAlgApp, volume = "29", pages = "507--529", } @Article{Wra73, author = "A. Wragg", year = "1973", title = "Computation of the Exponential of a Matrix {I}: Theoretical Considerations", journal = InstMathApp, volume = "11", pages = "369--375", } @Article{Wra75, author = "A. Wragg", year = "1975", title = "Computation of the Exponential of a Matrix {II}: Practical Considerations", journal = InstMathApp, volume = "15", pages = "273--278", } @Article{Yoh79, author = "J. M. Yohe", year = "1979", title = "Software for Interval Arithmetic: A Reasonable Portable Package", journal = ACMMathSoft, volume = "5", pages = "50--63", } @Article{You70, author = "D. M. Young", year = "1970", title = "Convergence Properties of the Symmetric and Unsymmetric Over-Relaxation Methods", journal = MathComp, volume = "24", pages = "793--807", } @Book{You71, author = "D. M. Young", year = "1971", title = "Iterative Solution of Large Linear Systems", publisher = Academic, address = "New York, NY, USA", } @Article{You72, author = "D. M. Young", year = "1972", title = "Generalization of Property~{$A$} and Consistent Ordering", journal = SIAMNumAnal, volume = "9", pages = "454--463", } @Article{YouJ80, author = "D. M. Young and K. C. Jea", year = "1980", title = "Generalized Conjugate Gradient Acceleration of Nonsymmetrizable Iterative Methods", journal = LinAlgApp, volume = "34", pages = "159--194", } @Article{Zoh69, author = "S. Zohar", year = "1969", title = "{Toeplitz} Matrix Inversion: The Algorithm of {W}.{F}. {Trench}", journal = "JACM", volume = "16", pages = "592--601", }