%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.22", %%% date = "02 November 2023", %%% time = "07:59:44 MDT", %%% filename = "stewart-gilbert-w.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "33987 10213 45536 476499", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Gilbert Wright `Pete' %%% Stewart III; numerical analysis", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is an almost-complete bibliography of %%% works by, and about, the influential %%% numerical analyst, Gilbert Wright (``Pete'') %%% Stewart III, Professor Emeritus of the %%% Department of Computer Science, University of %%% Maryland. The generational suffix III was no %%% longer used in publications after the early %%% 1970s. %%% %%% Professor Stewart's personal Web site %%% is at %%% %%% http://www.cs.umd.edu/~stewart/ %%% %%% with a related site at %%% %%% http://legacydirs.umiacs.umd.edu/~stewart/ %%% %%% At version 1.22, the year coverage looked %%% like this: %%% %%% 1967 ( 2) 1984 ( 10) 2001 ( 5) %%% 1968 ( 2) 1985 ( 4) 2002 ( 4) %%% 1969 ( 9) 1986 ( 10) 2003 ( 4) %%% 1970 ( 5) 1987 ( 9) 2004 ( 3) %%% 1971 ( 6) 1988 ( 7) 2005 ( 3) %%% 1972 ( 4) 1989 ( 6) 2006 ( 2) %%% 1973 ( 5) 1990 ( 14) 2007 ( 0) %%% 1974 ( 6) 1991 ( 15) 2008 ( 2) %%% 1975 ( 5) 1992 ( 6) 2009 ( 3) %%% 1976 ( 12) 1993 ( 15) 2010 ( 4) %%% 1977 ( 5) 1994 ( 15) 2011 ( 3) %%% 1978 ( 5) 1995 ( 10) 2012 ( 1) %%% 1979 ( 10) 1996 ( 3) 2013 ( 1) %%% 1980 ( 3) 1997 ( 12) 2014 ( 0) %%% 1981 ( 6) 1998 ( 13) 2015 ( 1) %%% 1982 ( 2) 1999 ( 5) 2016 ( 2) %%% 1983 ( 4) 2000 ( 4) %%% %%% Article: 170 %%% Book: 11 %%% InCollection: 8 %%% InProceedings: 26 %%% PhdThesis: 1 %%% Proceedings: 32 %%% TechReport: 37 %%% Unpublished: 2 %%% %%% Total entries: 287 %%% %%% Entries in this bibliography have been %%% derived mainly from bibliographies in the %%% BibNet Project and TeX User Group %%% bibliography archives, from the ACM Portal, %%% AMS MathSciNet, EMS zbMATH, and IEEE eXplore %%% databases, and from the University of %%% Maryland Institute for Advanced Computer %%% Studies (UMIACS) publication list at %%% %%% http://www.umiacs.umd.edu/publications/export/bibtex %%% %%% Additional data, including the tables of %%% contents of most of the edited books and %%% proceedings recorded here, have been obtained %%% from numerous library catalog searches. %%% %%% Digital Object Identifier (DOI) or Uniform %%% Resource Locator (URL) values have been found %%% and recorded for about half of the journal %%% articles. %%% %%% All of the books, reports, and papers in the %%% Stewart publication list in the Selected %%% Works volume (entry Kilmer:2010:GWS) are %%% included here, and cross-referenced to that %%% list by a GWS-number key/value pair. That %%% list records 1 technical report, 121 journal %%% articles, 8 books, and 37 conference papers: %%% 167 in all. At version 1.00 of this %%% bibliography, Part 1 (Stewart's publications) %%% contained 229 entries, of which 166 have %%% GWS-number values, and Part 3 %%% (cross-referenced publications) has 1 %%% GWS-number value. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. Cross-referenced proceedings %%% entries appear at the end, because of a %%% restriction in the current BibTeX. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{"\input bibnames.sty " # "\input path.sty " # "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \undefined \ocirc \def \ocirc #1{{\accent'27#1}}\fi" # "\ifx \undefined \r \let \r = \ocirc \fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-do= "Dianne O'Leary, Department of Computer Science, University of Maryland, College Park, MD, USA, email: \path|oleary@cs.umd.edu|"} @String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Institution abbreviations:

@String{inst-CS-U-MARYLAND= "Department of Computer Science, University of Maryland"} @String{inst-CS-U-MARYLAND:adr= "College Park, MD, USA"} @String{inst-IMA= "Institute for Mathematics and Its Applications, University of Minnesota"} @String{inst-IMA= "Institute for Mathematics and its Applications, University of Minnesota"} @String{inst-IMA:adr= "Minneapolis, MN, USA"} @String{inst-LASL= "Los Alamos Scientific Laboratory"} @String{inst-LASL:adr= "Los Alamos, NM, USA"} @String{inst-MATHWORKS= "The MathWorks, Inc."} @String{inst-MATHWORKS:adr= "3 Apple Hill Drive, Natick, MA 01760-2098, USA"} @String{inst-ORNL= "Oak Ridge National Laboratory"} @String{inst-ORNL:adr= "Knoxville, TN, USA"} @String{inst-STANFORD-CS= "Department of Computer Science, Stanford University"} @String{inst-STANFORD-CS:adr= "Stanford, CA"} @String{inst-U-MARYLAND= "University of Maryland"} @String{inst-U-MARYLAND:adr= "College Park, MD, USA"} @String{inst-U-TEXAS-AUSTIN= "University of Texas at Austin"} @String{inst-U-TEXAS-AUSTIN:adr= "Austin, TX, USA"} @String{inst-UMIACS= "Institute for Advanced Computer Studies, University of Maryland"} @String{inst-UMIACS:adr= "College Park, MD, USA"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ACM= "J. Assoc. Comput. Mach."} @String{j-AM-SCI= "American Scientist"} @String{j-ANN-HIST-COMPUT= "Annals of the History of Computing"} @String{j-APPL-NUM-MATH= "Applied Numerical Mathematics: Transactions of IMACS"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-BULL-AMS= "Bulletin of the American Mathematical Society"} @String{j-CACM= "Communications of the Association for Computing Machinery"} @String{j-COMPUT-GRAPH-STAT= "Journal of Computational and Graphical Statistics"} @String{j-COMPUT-MATH-APPL= "Computers and Mathematics with Applications"} @String{j-COMPUT-SCI-ENG= "Computing in Science and Engineering"} @String{j-CPE= "Concurrency: Prac\-tice and Experience"} @String{j-ELECTRON-TRANS-NUMER-ANAL= "Electronic Transactions on Numerical Analysis (ETNA)"} @String{j-FORTRAN-FORUM= "ACM Fortran Forum"} @String{j-IEEE-TRANS-COMPUT= "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-INSTRUM-MEAS= "IEEE Transactions on Instrumentation and Measurement"} @String{j-IEEE-TRANS-SIG-PROC= "IEEE Transactions on Signal Processing"} @String{j-IMA-J-NUMER-ANAL= "IMA Journal of Numerical Analysis"} @String{j-ISIS= "Isis"} @String{j-J-ACM= "Journal of the Association for Computing Machinery"} @String{j-J-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-GRAPH-STAT= "Journal of Computational and Graphical Statistics"} @String{j-J-COMPUT-PHYS= "Journal of Computational Physics"} @String{j-J-INST-MATH-APPL= "Journal of the Institute of Mathematics and its Applications"} @String{j-J-SUPERCOMPUTING= "The Journal of Supercomputing"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and Its Applications"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-MATH-PROG= "Mathematical Programming"} @String{j-NA-DIGEST= "NA Digest"} @String{j-NUM-LIN-ALG-APPL= "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-PARALLEL-COMPUTING= "Parallel Computing"} @String{j-SIAM-J-APPL-MATH= "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-MAT-ANA-APPL= "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-SCI-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-NEWS= "SIAM News"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGNUM= "ACM SIGNUM Newsletter"} @String{j-STAT-SCI= "Statistical Science"} @String{j-STOCH-MODELS= "Stochastic Models"} @String{j-TEX-TUG-NEWS= "{\TeX} and TUG News"} @String{j-TOMS= "ACM Transactions on Mathematical Software"}

%%% ==================================================================== %%% Publishers and their addresses:

@String{pub-ACADEMIC= "Academic Press Inc."} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-BIRKHAUSER= "Birkh{\"{a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-DEKKER= "Marcel Dekker, Inc."} @String{pub-DEKKER:adr= "New York, NY, USA"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-ESP= "Elsevier Science Publishers B.V."} @String{pub-ESP:adr= "Amsterdam, The Netherlands"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-LONGMAN= "Longman Scientific and Technical"} @String{pub-LONGMAN:adr= "Harlow, Essex"} @String{pub-NORTH-HOLLAND= "North-Holland Publishing Co."} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Oxford, UK"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Englewood Cliffs, NJ 07632, USA"} @String{pub-PHYSICA-VERLAG= "Physica-Verlag"} @String{pub-PHYSICA-VERLAG:adr= "Vienna, Austria; Heidelberg, Germany"} @String{pub-SIAM= "SIAM (Society for Industrial and Applied Mathematics)"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-SPRINGER= "Spring{\-}er-Ver{\-}lag"} @String{pub-SPRINGER:adr-NY= "New York"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WILEY-INTERSCIENCE= "Wiley-In{\-}ter{\-}sci{\-}ence"} @String{pub-WILEY-INTERSCIENCE:adr= "New York, NY, USA"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"}

%%% ==================================================================== %%% Part 1 (of 2) --- G. W. Stewart and his works %%% %%% Bibliography entries, sorted by year, and then by citation label, %%% with ``bibsort -byyear'':

%%% TO DO: %%% %%% Find this cited, but possibly unpublished, paper: %%% %%% Stewart, G. W., III, "On Some Methods for Solving Equations Related %%% to Schroder's Iterations," submitted to Soc. Ind. Appl. Math. Rev.

@Article{Stewart:1967:GTF, author = "G. W. {Stewart III}", title = "A generalization of a theorem of {Fan} on {Gershgorin} disks", journal = j-NUM-MATH, volume = "10", pages = "162--162", year = "1967", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02174149", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Thu May 29 14:46:06 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", note = "See original paper by Fan at \path=https://doi.org/10.1215/S0012-7094-58-02538-9=, \path=https://zbmath.org/?q=an:0081.25202=.", URL = "http://zbmath.org/?q=an:0158.03504", ZMnumber = "0158.03504", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J2", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1967:MDM, author = "G. W. {Stewart III}", title = "A Modification of {Davidon}'s Minimization Method to Accept Difference Approximations to Derivatives", journal = j-J-ACM, volume = "14", number = "1", pages = "72--83", month = jan, year = "1967", CODEN = "JACOAH", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Tue Nov 1 09:42:13 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", GWS-number = "J1", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", keywords = "nlop; quasi-Newton", } @Article{Stewart:1968:NAN, author = "G. W. {Stewart III} and Dale W. Lick", title = "Numerical Analysis: Numerical solution of a thin plate heat transfer problem", journal = j-CACM, volume = "11", number = "9", pages = "639--641", month = sep, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.68", MRnumber = "39\#2356", bibdate = "Fri Nov 25 18:20:21 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", abstract = "The numerical solution of a system of linear equations resulting from a discrete approximation to a thin plate heat transfer problem is considered. The slow convergence of point iterative methods is analyzed and shown to be caused by one of the boundary conditions. The difficulty may be removed by a standard line iterative technique.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", GWS-number = "J3", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "block SOR; boundary value problem; heat transfer problem; Poisson equation; successive overrelaxation (SOR); thin domain", xxpages = "639--640", } @TechReport{Stewart:1968:STNa, author = "Gilbert Wright {Stewart III}", title = "Some Topics in Numerical Analysis", type = "Report", number = "ORNL-4303", institution = inst-ORNL, address = inst-ORNL:adr, pages = "vi + 71", month = sep, year = "1968", bibdate = "Wed May 28 18:25:01 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://www.ornl.gov/info/reports/1968/3445605155079.pdf", acknowledgement = ack-nhfb, GWS-number = "T1", remark = "Copy of \cite{Stewart:1969:STNb}.", tableofcontents = "I: Lehmer's method for finding the zeros of a polynomial 1 \\ Introduction / 1 \\ Lehmer's Method / 2 \\ Rounding Error / 11 \\ Error Analysis of the Shifting Algorithm / 21 \\ Error Analysis of the Cohn Algorithm / 27 \\ Asymptotic Behavior / 35 \\ II: Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix / 40 \\ Introduction / 40 \\ A Refinement Procedure for Approximate Eigenvectors / 43 \\ Convergence of the Orthogonal Iteration / 45 \\ Some Miscellaneous Theorems / 49 \\ Accuracy of the Refined Eigenvalues / 58 \\ Accuracy of the Refined Eigenvectors / 65 \\ Bibliography / 71", } @InCollection{Householder:1969:BHD, author = "A. S. Householder and G. W. {Stewart III}", title = "Bigradients, {Hankel} determinants, and the {Pad{\'e}} table", crossref = "Dejon:1969:CAF", pages = "131--150", year = "1969", MRclass = "65.35", MRnumber = "0266406 (42 \#1312)", MRreviewer = "J. F. Traub", bibdate = "Thu May 29 16:03:11 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", ZMnumber = "0181.17404", acknowledgement = ack-nhfb, GWS-number = "N1", } @Article{Householder:1969:CSI, author = "A. S. Householder and G. W. Stewart", title = "Comments on {``Some iterations for factoring a polynomial''}", journal = j-NUM-MATH, volume = "13", number = "5", pages = "470--471", month = oct, year = "1969", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Thu Jan 13 08:40:53 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1969:AOI, author = "G. W. Stewart", title = "Accelerating the orthogonal iteration for the eigenvectors of a {Hermitian} matrix", journal = j-NUM-MATH, volume = "13", number = "4", pages = "362--376", month = aug, year = "1969", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02165413", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sun Oct 17 19:01:15 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://zbmath.org/?q=an:0185.40203", ZMnumber = "0185.40203", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J5", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1969:CGI, author = "G. W. Stewart", title = "On the Continuity of the Generalized Inverse", journal = j-SIAM-J-APPL-MATH, volume = "17", number = "1", pages = "33--45", month = jan, year = "1969", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", GWS-number = "J4", journal-URL = "http://epubs.siam.org/siap", } @Article{Stewart:1969:LMF, author = "G. W. {Stewart III}", title = "On {Lehmer}'s Method for Finding the Zeros of a Polynomial", journal = j-MATH-COMPUT, volume = "23", number = "108", pages = "829--835, s24--s30", month = oct, year = "1969", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Theory/Matrix.bib", note = "See corrigendum \cite{Stewart:1971:CLM}.", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", GWS-number = "J7", journal-URL = "http://www.ams.org/mcom/", kwds = "nlop, polynomial, Lehmer's method", xxpages = "829--836, s24--s30", } @Article{Stewart:1969:SIF, author = "G. W. Stewart", title = "Some iterations for factoring a polynomial", journal = j-NUM-MATH, volume = "13", number = "5", pages = "458--470", month = oct, year = "1969", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02163273", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Thu Jan 13 08:40:53 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://zbmath.org/?q=an:0181.17401", ZMnumber = "0181.17401", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J6", journal-URL = "http://link.springer.com/journal/211", xxpages = "458--471", } @TechReport{Stewart:1969:STF, author = "G. W. {Stewart III}", title = "A Set Theoretic Formulation of Backward Rounding Error Analysis", type = "Computation Center Report", number = "TNN-92", institution = inst-U-TEXAS-AUSTIN, address = inst-U-TEXAS-AUSTIN:adr, pages = "????", month = "????", year = "1969", bibdate = "Thu May 29 16:09:20 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N2", } @PhdThesis{Stewart:1969:STNb, author = "Gilbert Wright {Stewart III}", title = "Some Topics in Numerical Analysis", type = "{Ph.D.} dissertation", school = "University of Tennessee, Knoxville", address = "Knoxville, TN, USA", month = may, year = "1969", bibdate = "Wed May 28 10:56:30 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://genealogy.math.ndsu.nodak.edu/id.php?id=58767; http://search.proquest.com/docview/302349990; http://www.ornl.gov/info/reports/1968/3445605155079.pdf", acknowledgement = ack-nhfb, advisor = "Alston Scott Householder", tableofcontents = "I: Lehmer's method for finding the zeros of a polynomial 1 \\ Introduction / 1 \\ Lehmer's Method / 2 \\ Rounding Error / 11 \\ Error Analysis of the Shifting Algorithm / 21 \\ Error Analysis of the Cohn Algorithm / 27 \\ Asymptotic Behavior / 35 \\ II: Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix / 40 \\ Introduction / 40 \\ A Refinement Procedure for Approximate Eigenvectors / 43 \\ Convergence of the Orthogonal Iteration / 45 \\ Some Miscellaneous Theorems / 49 \\ Accuracy of the Refined Eigenvalues / 58 \\ Accuracy of the Refined Eigenvectors / 65 \\ Bibliography / 71", } @Article{Stewart:1970:AAE, author = "G. W. Stewart", title = "{ACM Algorithm 384}: Eigenvalues and Eigenvectors of a Real Symmetric Matrix [{F2}]", journal = j-CACM, volume = "13", number = "6", pages = "369--371", month = jun, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib", note = "See errata \cite{Stewart:1970:RAE}.", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra); C7300 (Natural sciences computing)", corpsource = "Univ. Texas, Austin, TX, USA", fjournal = "Communications of the ACM", GWS-number = "J10", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "eigenvalues; eigenvalues and eigenfunctions; eigenvectors; matrix algebra; QR algorithm; real symmetric matrix; subroutines", kwds = "nla, eig, QR algorithm, symmetric matrix", } @Article{Stewart:1970:CSS, author = "G. W. Stewart", title = "On the Convergence of {Sebasti{\~a}o e Silva}'s Method for Finding a Zero of a Polynomial", journal = j-SIAM-REVIEW, volume = "12", number = "3", pages = "458--460", month = "????", year = "1970", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1012085", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:20 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/12/3; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://zbmath.org/?q=an:0198.20905", ZMnumber = "0198.20905", acknowledgement = ack-nhfb, fjournal = "SIAM Review", GWS-number = "J11", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "July 1970", } @Article{Stewart:1970:IOS, author = "G. W. Stewart", title = "Incorporating Origin Shifts into the {QR} Algorithm for Symmetric Tridiagonal Matrices", journal = j-CACM, volume = "13", number = "6", pages = "365--367", month = jun, year = "1970", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/362384.362501", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib", URL = "http://zbmath.org/?q=an:0195.45001", ZMnumber = "0195.45001", abstract = "The $ Q R $ iteration for the eigenvalues of a symmetric tridiagonal matrix can be accelerated by incorporating a sequence of origin shifts. The origin shift may be either subtracted directly from the diagonal elements of the matrix or incorporated by means of an implicit algorithm. Both methods have drawbacks-the direct method can unnecessarily degrade small eigenvalues, while the implicit method can effectively loose the shift and thereby retard the convergence. A new method which has neither drawback is presented. Both the algorithm proposed here and the implicit algorithm are safer than the explicit algorithm. The implicit algorithm requires somewhat less computation, but the new algorithm will give faster convergence in some cases, an important consideration when eigenvectors are being calculated.", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra)", corpsource = "Univ. Tex., Austin, TX, USA", fjournal = "Communications of the ACM", GWS-number = "J9", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "computers, data processing; convergence of numerical methods; eigenfunctions; eigenvalues; eigenvalues and; eigenvectors; iterative methods; mathematics; matrix algebra; origin shifts; QR method; symmetric tridiagonal matrix; tridiagonal matrices", kwds = "nla, eig, QR algorithm, symmetric matrix, tridiagonal matrix", } @Article{Stewart:1970:RAE, author = "G. W. Stewart", title = "Remark on ``{Algorithm 384}: Eigenvalues and Eigenvectors of a Real Symmetric Matrix [{F2}]''", journal = j-CACM, volume = "13", number = "12", pages = "750--750", month = dec, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Apr 08 20:40:01 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib", note = "See \cite{Stewart:1970:AAE}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "eigenvalues; eigenvectors; QR algorithm; real symmetric matrix", kwds = "nla, eig, QR algorithm, symmetric matrix", } @Article{Stewart:1970:SIF, author = "G. W. Stewart", title = "On {Samelson}'s iteration for factoring polynomials", journal = j-NUM-MATH, volume = "15", number = "4", pages = "306--314", month = aug, year = "1970", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02165121", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRnumber = "65H05 65D05", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://zbmath.org/?q=an:0231.65050", ZMnumber = "0231.65050", acknowledgement = ack-nhfb, classification = "C4190 (Other numerical methods)", corpsource = "Univ. Texas, Austin, TX, USA", fjournal = "Numerische Mathematik", GWS-number = "J8", journal-URL = "http://link.springer.com/journal/211", keywords = "iterative methods; polynomials", } @Article{Householder:1971:NFP, author = "A. S. Householder and G. W. Stewart", title = "The Numerical Factorization of a Polynomial", journal = j-SIAM-REVIEW, volume = "13", number = "1", pages = "38--46", month = "????", year = "1971", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1013002", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:25 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/13/1; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", GWS-number = "J12", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1971", } @TechReport{Moler:1971:AGM, author = "Cleve B. Moler and Gilbert W. Stewart", title = "An algorithm for the generalized matrix eigenvalue problem {$ A x = \lambda B x $}", type = "Technical Report", number = "STAN-CS-71-232", institution = inst-STANFORD-CS, address = inst-STANFORD-CS:adr, pages = "50", year = "1971", bibdate = "Sat Apr 07 09:36:51 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "Issued jointly as report CNA 32 by the Center for Numerical Analysis, the University of Texas at Austin.", acknowledgement = ack-nhfb, } @Article{Stewart:1971:CLM, author = "G. W. {Stewart III}", title = "Corrigendum: {``On Lehmer's Method for Finding the Zeros of a Polynomial''}", journal = j-MATH-COMPUT, volume = "25", number = "113", pages = "203--203", month = jan, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database", note = "See \cite{Stewart:1969:LMF}.", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", GWS-number = "J7", journal-URL = "http://www.ams.org/mcom/", } @Article{Stewart:1971:COA, author = "G. W. Stewart", title = "On a companion operator for analytic functions", journal = j-NUM-MATH, volume = "18", number = "1", pages = "26--43", month = feb, year = "1971", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01398457", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRnumber = "65H99 15A06 15A57", bibdate = "Mon Oct 18 20:12:42 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://zbmath.org/?q=an:0211.18805", ZMnumber = "0211.18805; 0217.52705", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J14", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1971:EAA, author = "G. W. Stewart", title = "Error Analysis of the Algorithm for Shifting the Zeros of a Polynomial by Synthetic Division", journal = j-MATH-COMPUT, volume = "25", number = "113", pages = "135--139", year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", GWS-number = "J13", journal-URL = "http://www.ams.org/mcom/", } @Article{Stewart:1971:EBA, author = "G. W. Stewart", title = "Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators", journal = j-SIAM-J-NUMER-ANAL, volume = "8", number = "4", pages = "796--808", month = dec, year = "1971", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0708073", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRnumber = "47A15 47A55 47A75", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", URL = "http://zbmath.org/?q=an:0232.47010", ZMnumber = "0232.47010", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J15", journal-URL = "http://epubs.siam.org/sinum", } @Article{Bartels:1972:AAS, author = "Richard H. Bartels and G. W. Stewart", title = "{ACM Algorithm 432}: Solution of the Matrix Equation {{\boldmath $ A X + X B = C $}} [{F4}]", journal = j-CACM, volume = "15", number = "9", pages = "820--826", month = sep, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:23:37 MST 2001", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#BartelsS72; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", GWS-number = "J17", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "linear algebra; linear equations; matrices", kwds = "nla, Schur form, Sylvester equation, Lyapunov equation, matrix equation", oldlabel = "BartelsS72", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BartelsS72", } @Article{Hoberock:1972:IRP, author = "L. L. Hoberock and G. W. {Stewart III}", title = "Input Requirements and Parametric Errors for Systems Identification under Periodic Excitement", journal = "AMSE {Transactions}", volume = "94", number = "??", pages = "296--302", month = "????", year = "1972", ISSN = "0761-2532", ISSN-L = "0761-2532", bibdate = "Thu May 29 16:10:45 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N3", keywords = "Association for the Advancement of Modelling and Simulation Techniques in Enterprises", } @TechReport{Moler:1972:AGM, author = "C. B. Moler and G. W. Stewart", title = "An algorithm for generalized matrix eigenvalue problems", type = "Report", number = "TR-3", institution = "University of Michigan", address = "Ann Arbor, MI, USA", pages = "50", month = feb, year = "1972", MRnumber = "65F15", bibdate = "Fri Mar 21 15:55:27 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://zbmath.org/?q=an:0225.65046", ZMnumber = "0225.65046", abstract = "A method, called the $ Q Z $ algorithm, is presented for the solution of the matrix eigenvalue problem $ A x = \lambda B x $ with the general square matrices $A$ and $B$. Particular attention is paid to the degeneracies which result when $B$ is singular. No inversions of $B$ or its submatrices are used. The algorithm is a generalization of the $ Q R$ algorithm, and reduces to it when $ B = I$. Problems involving powers of $ \lambda $ are also mentioned", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra)", corpsource = "Univ. Michigan, Ann Arbor, MI, USA", keywords = "algorithm; degeneracies; eigenvalues and eigenfunctions; generalized matrix eigenvalue problems; matrix algebra; methods; numerical; QZ", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1972:SEP, author = "G. W. Stewart", title = "On the Sensitivity of the Eigenvalue Problem {$ A x = \lambda B x $}", journal = j-SIAM-J-NUMER-ANAL, volume = "9", number = "4", pages = "669--686", month = dec, year = "1972", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0709056", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRnumber = "65F15 15A18 15A42", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", URL = "http://zbmath.org/?q=an:0252.65026", ZMnumber = "0252.65026", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J16", journal-URL = "http://epubs.siam.org/sinum", } @Article{Moler:1973:AGM, author = "C. B. Moler and G. W. Stewart", title = "An Algorithm for Generalized Matrix Eigenvalue Problems", journal = j-SIAM-J-NUMER-ANAL, volume = "10", number = "2", pages = "241--256", month = apr, year = "1973", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRnumber = "65F15", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", URL = "http://zbmath.org/?q=an:0225.65046", ZMnumber = "0225.65046", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Univ. New Mexico, Albuquerque, NM, USA", fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J18", journal-URL = "http://epubs.siam.org/sinum", keywords = "algorithm; degeneracies; eigenvalues and eigenfunctions; general square; generalization of the QR; generalized matrix eigenvalue problems; matrices; matrix algebra; nla, geig, QZ algorithm; singular", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1973:CDM, author = "G. W. Stewart", title = "Conjugate direction methods for solving systems of linear equations", journal = j-NUM-MATH, volume = "21", number = "4", pages = "285--297", month = aug, year = "1973", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290F (Interpolation and function approximation); B0290H (Linear algebra); C4130 (Interpolation and function approximation); C4140 (Linear algebra)", corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA", fjournal = "Numerische Mathematik", GWS-number = "J20", journal-URL = "http://link.springer.com/journal/211", keywords = "conjugate; conjugate direction methods; iterations; iterative methods; matrix; matrix algebra; systems of linear equations", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1973:EPB, author = "G. W. Stewart", title = "Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems", journal = j-SIAM-REVIEW, volume = "15", number = "4", pages = "727--764", month = "????", year = "1973", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1015095", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:54 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/15/4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", GWS-number = "J19", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1973", } @Book{Stewart:1973:IMC, author = "G. W. (Gilbert W.) Stewart", title = "Introduction to Matrix Computations", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xiii + 441", year = "1973", ISBN = "0-12-670350-7", ISBN-13 = "978-0-12-670350-4", LCCN = "QA188 .S71 1973", MRclass = "65FXX", MRnumber = "0458818 (56 \#17018)", MRreviewer = "James H. Wilkinson", bibdate = "Sun Nov 23 10:56:10 MST 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", series = "Computer Science and Applied Mathematics, Editor: Werner Rheinboldt", URL = "http://catalog.hathitrust.org/api/volumes/oclc/658076.html; http://catdir.loc.gov/catdir/description/els031/72082636.html; http://catdir.loc.gov/catdir/toc/els031/72082636.html; http://www.gbv.de/dms/hbz/toc/ht000832348.pdf; http://www.loc.gov/catdir/description/els031/72082636.html; http://www.loc.gov/catdir/toc/els031/72082636.htmlQ", acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah, GWS-number = "B1", subject = "Matrices; Data processing", tableofcontents = "Preface / ix \\ Acknowledgments / xiii \\ 1. Preliminaries \\ \\ 1. The Space $R^n$ / 2 \\ 2. Linear Independence, Subspaces, and Bases / 9 \\ 3. Matrices / 20 \\ 4. Operations with Matrices / 29 \\ 5. Linear Transformations and Matrices / 46 \\ 6. Linear Equations and Inverses / 54 \\ 7. A Matrix Reduction and Some Consequences / 63 \\ \\ 2. Practicalities \\ \\ 1. Errors, Arithmetic, and Stability / 69 \\ 2. An Informal Language / 83 \\ 3. Coding Matrix Operations / 93 \\ 3. The Direct Solution of Linear Systems \\ \\ 1. Triangular Matrices and Systems / 106 \\ 2. Gaussian Elimination / 113 \\ 3. Triangular Decomposition / 131 \\ 4. The Solution of Linear Systems / 144 \\ 5. The Effects of Rounding Error / 148 \\ \\ 4. Norms, Limits, and Condition Numbers \\ \\ 1. Norms and Limits / 161 \\ 2. Matrix Norms / 173 \\ 3. Inverses of Perturbed Matrices / 184 \\ 4. The Accuracy of Solutions of Linear Systems / 192 \\ 5. Iterative Refinement of Approximate Solutions of Linear Systems / 200 \\ \\ 5. The Linear Least Squares Problem \\ 1. Orthogonality / 209 \\ 2. The Linear Least Squares Problem / 217 \\ 3. Orthogonal Triangularization / 230 \\ 4. The Iterative Refinement of Least Squares Solutions / 245 \\ \\ 6. Eigenvalues and Eigenvectors \\ \\ 1. The Space $\mathbb{C}^n$ / 251 \\ 2. Eigenvalues and Eigenvectors / 262 \\ 3. Reduction of Matrices by Similarity Transformations / 275 \\ 4. The Sensitivity of Eigenvalues and Eigenvectors / 289 \\ 5. Hermitian Matrices / 307 \\ 6. The Singular Value Decomposition / 317 \\ \\ 7. The $QR$ Algorithm \\ \\ 1. Reduction to Hessenberg and Tridiagonal Forms / 328 \\ 2. The Power and Inverse Power Methods / 340 \\ 3. The Explicitly Shifted $QR$ Algorithm / 351 \\ 4. The Implicitly Shifted $QR$ Algorithm / 368 \\ 5. Computing Singular Values and Vectors / 381 \\ 6. The Generalized Eigenvalue Problem $A - \lambda B$ / 387 \\ \\ Appendix 1. The Greek Alphabet and Latin Notational Correspondents / 395 \\ \\ Appendix 2. Determinants / 396 \\ Appendix 3. Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination / 405 \\ \\ Appendix 4. Of Things Not Treated / 413 \\ Bibliography / 417 \\ Index of Notation / 425 \\ Index of Algorithms / 427 \\ Index / 429", } @Article{Stewart:1973:SIF, author = "G. W. Stewart", title = "Some iterations for factoring a polynomial. {II}: {A} generalization of the secant method", journal = j-NUM-MATH, volume = "22", number = "1", pages = "33--36", month = feb, year = "1973", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sun Oct 17 16:12:48 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J21", journal-URL = "http://link.springer.com/journal/211", } @Article{Blevins:1974:CED, author = "M. M. Blevins and G. W. Stewart", title = "Calculating the Eigenvectors of Diagonally Dominant Matrices", journal = j-J-ACM, volume = "21", number = "2", pages = "261--271", month = apr, year = "1974", CODEN = "JACOAH", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", abstract = "An algorithm is proposed for calculating the eigenvectors of a diagonally dominant matrix all of whose elements are known to high relative accuracy. Eigenvectors corresponding to pathologically close eigenvalues are treated by computing the invariant subspace that they span. If the off-diagonal elements of the matrix are sufficiently small, the method is superior to standard techniques, and indeed it may produce a complete set of eigenvectors with an amount of work proportional to the square of the order of the matrix. An analysis is given of the effects of perturbations in the matrix on the eigenvectors.", acknowledgement = ack-nhfb, classification = "921", fjournal = "Journal of the Association for Computing Machinery", GWS-number = "J24", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", journalabr = "J Assoc Comput Mach", keywords = "diagonal dominance; eig; mathematical techniques; nla", } @Article{Soderstrom:1974:NPI, author = "Torsten S{\"o}derstr{\"o}m and G. W. Stewart", title = "On the Numerical Properties of an Iterative Method for Computing the {Moore--Penrose} Generalized Inverse", journal = j-SIAM-J-NUMER-ANAL, volume = "11", number = "1", pages = "61--74", month = mar, year = "1974", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J23", journal-URL = "http://epubs.siam.org/sinum", kwds = "nla, ginv, iter", } @Article{Stewart:1974:CMI, author = "G. W. Stewart", title = "The Convergence of Multipoint Iterations to Multiple Zeros", journal = j-SIAM-J-NUMER-ANAL, volume = "11", number = "6", pages = "1105--1120", month = dec, year = "1974", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J22", journal-URL = "http://epubs.siam.org/sinum", } @Article{Stewart:1974:MPE, author = "G. W. Stewart", title = "Modifying Pivot Elements in {Gaussian} Elimination", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "537--542", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA", fjournal = "Mathematics of Computation", GWS-number = "J25", journal-URL = "http://www.ams.org/mcom/", keywords = "analysis; Gaussian elimination; inverse; matrix algebra; pivot elements; pivoting; rank one modification; rounding error; sparseness; stable", kwds = "nla, sparse, linear system, lud, pivoting", treatment = "T Theoretical or Mathematical", } @InProceedings{Stewart:1974:NTL, author = "G. W. Stewart", title = "The Numerical Treatment of Large Eigenvalue Problems", crossref = "Rosenfeld:1974:IPP", pages = "666--672", year = "1974", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N4", } @Article{Stewart:1975:CMC, author = "G. W. Stewart", title = "The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points in the Spectrum", journal = j-NUM-MATH, volume = "24", number = "2", pages = "85--93", month = apr, year = "1975", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Carnegie-Mellon Univ., Computer Sci. Dept., Pittsburgh, PA, USA", fjournal = "Numerische Mathematik", GWS-number = "J26", journal-URL = "http://link.springer.com/journal/211", keywords = "bounds; convergence; convergence of numerical methods; eigenvalue; eigenvalues and eigenfunctions; error vectors; isolated extreme points; linear system; matrix algebra; method of conjugate gradients", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1975:GTG, author = "G. W. Stewart", title = "{Gershgorin} Theory for the Generalized Eigenvalue Problem {$ A x = \lambda B x $}", journal = j-MATH-COMPUT, volume = "29", number = "130", pages = "600--606", month = apr, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Parallel/par.lin.alg.bib; Theory/Matrix.bib", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. Computer Sci., Carnegie-Mellon Univ., Pittsburgh, PA, USA", fjournal = "Mathematics of Computation", GWS-number = "J27", journal-URL = "http://www.ams.org/mcom/", keywords = "chordal metric; eigenvalues and eigenfunctions; generalized eigenvalue problem; Gershgorin's theorem; infinite eigenvalues; linear algebra; multiple eigenvalues; perturbation bounds; Riemann sphere", kwds = "la, pert, geig, Gerschgorin's theorem", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1975:IPT, author = "G. W. Stewart", title = "An inverse perturbation theorem for the linear least squares problem", journal = j-SIGNUM, volume = "10", number = "2--3", pages = "39--40", month = nov, year = "1975", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Tue Apr 12 07:50:01 MDT 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, Baltimore, MD, USA", fjournal = "ACM SIGNUM Newsletter", GWS-number = "J28", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", keywords = "inverse perturbation theorem; least squares approximations; linear least squares; matrix; minimisation; perturbation techniques; vectors", mynote = "Nov", treatment = "T Theoretical or Mathematical", } @InCollection{Stewart:1975:MSI, author = "G. W. Stewart", title = "Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices", crossref = "Miller:1975:TNA", pages = "185--196", year = "1975", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, GWS-number = "N5", } @Article{Daniel:1976:RSA, author = "J. W. Daniel and W. B. Gragg and L. Kaufman and G. W. Stewart", title = "Reorthogonalization and Stable Algorithms for Updating the {Gram--Schmidt} {$ Q R $} Factorization", journal = j-MATH-COMPUT, volume = "30", number = "136", pages = "772--795", month = oct, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-nhfb, classcodes = "C4110 (Error analysis in numerical methods); C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci. and Math., Univ. of Texas, Austin, TX, USA", fjournal = "Mathematics of Computation", GWS-number = "J31", journal-URL = "http://www.ams.org/mcom/", keywords = "error analysis; Gram Schmidt $QR$ factorisation; matrix algebra; process; reorthogonalization; stable algorithms", kwds = "nla, qrd, updating, Gram--Schmidt algorithm", treatment = "T Theoretical or Mathematical", } @TechReport{Golub:1976:RDLa, author = "Gene H. Golub and Virginia Klema and G. W. Stewart", title = "Rank Degeneracy and Least Squares Problems", type = "Technical Report", number = "TR-456", institution = inst-U-MARYLAND, address = inst-U-MARYLAND:adr, pages = "????", month = jun, year = "1976", bibdate = "Wed May 28 17:40:15 2014", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-maryland.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "Also published as Stanford University Computer Science Department Technical Report STAN-CS-76-559.", abstract = "This paper is concerned with least squares problems when the least squares matrix \$A\$ is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when \$A\$ has numerical rank \$r\$ there is a distinguished \$r\$ dimensional subspace of the column space of \$A\$ that is insensitive to how it is approximated by \$r\$ independent columns of \$A\$. The consequences of this fact for the least squares problem are examined. Algorithms are described for approximating the stable part of the column space of \$A\$.", acknowledgement = ack-nhfb, keywords = "nla, svd, qrd, condition estimation, rank determination, pert, variable selection", xxnote = "Check: is this the same as Golub:1976:RDLb? If so, which report number is correct??", } @TechReport{Golub:1976:RDLb, author = "G. H. Golub and Virginia Klema and G. W. {Stewart III}", title = "Rank Degeneracy and Least Squares Problems", type = "Report", number = "TR-751", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", month = "????", year = "1976", bibdate = "Thu May 29 16:12:45 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N6", xxnote = "Check: is this the same as Golub:1976:RDLa? If so, which report number is correct??", } @Article{Gragg:1976:SVS, author = "W. B. Gragg and G. W. Stewart", title = "A Stable Variant of the Secant Method for Solving Nonlinear Equations", journal = j-SIAM-J-NUMER-ANAL, volume = "13", number = "6", pages = "889--903", month = dec, year = "1976", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J29", journal-URL = "http://epubs.siam.org/sinum", } @Article{Stewart:1976:AHE, author = "G. W. Stewart", title = "{Algorithm 506}: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]", journal = j-TOMS, volume = "2", number = "3", pages = "275--280", month = sep, year = "1976", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355694.355700", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 18:03:53 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib; Theory/gvl.bib", note = "See also \cite{Flamm:1982:RHE}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J33", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "nla, eig, $QR$ algorithm, Hessenberg matrix, software", xxnote = "See also (in fortran2.bib) \cite{Flamm:1982:RHE}.", } @InCollection{Stewart:1976:BTL, author = "G. W. Stewart", title = "A Bibliographical Tour of the Large Sparse Generalized Eigenvalue Problem", crossref = "Bunch:1976:SMC", pages = "113--130", year = "1976", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N7", } @InProceedings{Stewart:1976:CVM, author = "G. W. {Stewart III}", title = "Compilers, Virtual Memory, and Matrix Computations", crossref = "Hoaglin:1976:CSS", pages = "85--88", year = "1976", bibdate = "Thu May 29 16:23:20 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N8", } @Article{Stewart:1976:DCR, author = "G. W. Stewart", title = "Detecting and Correcting Rank Degeneracy", journal = j-SIAM-REVIEW, volume = "18", number = "4", pages = "829--829", month = "????", year = "1976", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Stewart:1976:ESP, author = "G. W. Stewart", title = "The Economical Storage of Plane Rotations", journal = j-NUM-MATH, volume = "25", number = "2", pages = "137--138", month = jun, year = "1976", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J32", journal-URL = "http://link.springer.com/journal/211", keywords = "compacted; economical storage; matrix algebra; matrix computations; plane rotations; single number", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1976:SIC, author = "G. W. Stewart", title = "Simultaneous iteration for computing invariant subspaces of {non-Hermitian} matrices", journal = j-NUM-MATH, volume = "25", number = "2", pages = "123--136", month = jun, year = "1976", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290F (Interpolation and function approximation); B0290H (Linear algebra); C4130 (Interpolation and function approximation); C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J30", journal-URL = "http://link.springer.com/journal/211", keywords = "convergence of numerical methods; convergence theory; dominant invariant subspaces; iterative methods; matrix algebra; nested sequence; non Hermitian matrices; orthonormal bases; simultaneous iteration technique", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1977:PBF, author = "G. W. Stewart", title = "Perturbation Bounds for the {$ Q R $} Factorization of a Matrix", journal = j-SIAM-J-NUMER-ANAL, volume = "14", number = "3", pages = "509--518", month = jun, year = "1977", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J34", journal-URL = "http://epubs.siam.org/sinum", } @Article{Stewart:1977:PPI, author = "G. W. Stewart", title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear Least Squares Problems", journal = j-SIAM-REVIEW, volume = "19", number = "4", pages = "634--662", month = "????", year = "1977", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1019104", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:52:46 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/19/4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", GWS-number = "J35", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1977", } @InProceedings{Stewart:1977:RDL, author = "G. W. Stewart", title = "Research, Development, and {LINPACK}", crossref = "Rice:1977:MSS", pages = "1--14", year = "1977", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, GWS-number = "N9", } @TechReport{Stewart:1977:SCE, author = "G. W. Stewart", title = "Sensitivity Coefficients for the Effects of Errors in the Independent Variables in a Linear Regression", number = "TR-571", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "1977", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, } @Article{Moler:1978:HFA, author = "Cleve B. Moler and G. W. Stewart", title = "On the {Householder--Fox} Algorithm for Decomposing a Projection", journal = j-J-COMPUT-PHYS, volume = "28", number = "1", pages = "82--91", month = jul, year = "1978", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(78)90048-7", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sun Jan 1 09:15:29 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0021999178900487", acknowledgement = ack-nhfb, classcodes = "A0210 (Algebra, set theory, and graph theory); A0270 (Computational techniques); C4140 (Linear algebra)", corpsource = "Univ. of New Mexico, Albuquerque, NM, USA", fjournal = "Journal of Computational Physics", GWS-number = "J36", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", keywords = "approximate projection; Cholesky decomposition; Householder--Fox algorithm; matrix algebra; orthonormal basis for; projection range; rounding error", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1978:BRV, author = "G. W. Stewart", title = "Book Review: {{\booktitle{Vorlesungen {\"u}ber numerische Mathematik}}, by Heinz Rutishauser}", journal = j-BULL-AMS, volume = "84", number = "4", pages = "660--664", month = jul, year = "1978", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/s0002-9904-1978-14517-0", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Aug 26 10:27:58 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", remark = "The final paragraph says: ``However, the virtues of the work far outweigh its defects. It is unfortunate that it is available only in German; for it deserves to be more widely read. Rutishauser's audience is not only the student, but the instructor teaching a numerical analysis course for the first time, and especially the mathematician who wants to find out what this important branch of applied mathematics is all about.''", } @InCollection{Stewart:1978:PTG, author = "G. W. Stewart", title = "Perturbation Theory for the Generalized Eigenvalue Problem", crossref = "deBoor:1978:SRA", pages = "193--206", year = "1978", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N10", } @TechReport{Stewart:1978:SFS, author = "G. W. Stewart", title = "{SRRIT} --- {A FORTRAN} Subroutine to Calculate the Dominant Invariant Subspaces of a Real Matrix", type = "Technical Report", number = "TRR-514", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "1978", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/other/g-w-stewart.bib; Theory/Matrix.bib", acknowledgement = ack-nhfb, kwds = "nla, eig, subspace iteration, invariant subspace, software, nonsymmetric matrix", } @Article{Bavely:1979:ACR, author = "Connice A. Bavely and G. W. Stewart", title = "An Algorithm for Computing Reducing Subspaces by Block Diagonalization", journal = j-SIAM-J-NUMER-ANAL, volume = "16", number = "2", pages = "359--367", month = apr, year = "1979", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F30", MRnumber = "80c:65094", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database; Parallel/par.lin.alg.bib; Theory/Matrix.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J37", journal-URL = "http://epubs.siam.org/sinum", kwds = "nla, eig, invariant subspace, nonsymmetric matrix", } @Article{Cline:1979:ECN, author = "A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson", title = "An Estimate for the Condition Number of a Matrix", journal = j-SIAM-J-NUMER-ANAL, volume = "16", number = "2", pages = "368--375", month = apr, year = "1979", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0716029", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F35 (65F05)", MRnumber = "80g:65048", MRreviewer = "R. P. Tewarson", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", URL = "http://zbmath.org/?q=an:0403.65012", ZMnumber = "0403.65012", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra)", corpsource = "Computer Sci. Dept., Univ. of Texas, Austin, TX, USA", fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J42", journal-URL = "http://epubs.siam.org/sinum", keywords = "cond; condition estimation; err; linear systems; math; matrix algebra; matrix of coefficients; nla", treatment = "T Theoretical or Mathematical", } @Book{Dongarra:1979:LUG, author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", title = "{LINPACK} Users' Guide", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "320", year = "1979", ISBN = "0-89871-172-X (paperback)", ISBN-13 = "978-0-89871-172-1 (paperback)", LCCN = "QA76.73 .L22 L5 1979; QA184 .L56 1982; QA214 .L56 1979", bibdate = "Mon Dec 13 15:18:20 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", abstract = "The authors of this carefully structured guide are the principal developers of LINPACK, a unique package of Fortran subroutines for analyzing and solving various systems of simultaneous linear algebraic equations and linear least squares problems. This guide supports both the casual user of LINPACK who simply requires a library subroutine, and the specialist who wishes to modify or extend the code to handle special problems. It is also recommended for classroom work.", acknowledgement = ack-nhfb, GWS-number = "B2", keywords = "book, Cholesky decomposition, cond, downd, linpack, lud, lud, math, nla, qrd, qrd, soft, software, survey, svd, svd, upd, updating", subject = "LINPACK (Computer system); Equations, Simultaneous; Data processing; Matrices; Data processing.; LINPACK (Computer system); LINPACK (Syst{\`e}me d'ordinateur); {\'E}quations simultan{\'e}es; Informatique", tableofcontents = "General matrices \\ Band matrices \\ Positive definite matrices \\ Positive definite band matrices \\ Symmetric indefinite matrices \\ Triangular matrices \\ Tridiagonal matrices \\ The Cholesky decomposition \\ The $QR$ decomposition \\ Updating $QR$ and Cholesky decompositions \\ The singular value decomposition \\ References \\ Basic linear algebra subprograms \\ Timing data \\ Program listings \\ BLA listings", xxauthor = "J. J. Dongarra and C. B. Moler and J. R. Bunch and G. W. Stewart", } @TechReport{Moler:1979:EMF, author = "Cleve B. Moler and G. W. (Gilbert W.) Stewart", title = "An efficient matrix factorization for digital image processing", type = "Report", number = "LA-7637-MS", institution = inst-LASL, address = inst-LASL:adr, pages = "15", month = jan, year = "1979", bibdate = "Tue May 25 08:46:03 2010", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "Jan 1979, also Univ. California report UC-32", subject = "matrices; data processing", } @Article{OLeary:1979:ELE, author = "Dianne P. O'Leary and G. W. Stewart and James S. Vandergraft", title = "Estimating the Largest Eigenvalue of a Positive Definite Matrix", journal = j-MATH-COMPUT, volume = "33", number = "148", pages = "1289--1292", month = oct, year = "1979", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "80d:65048", bibdate = "Wed Sep 28 14:04:23 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-njh # " and " # ack-nhfb, classcodes = "C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "Mathematics of Computation", GWS-number = "J41", journal-URL = "http://www.ams.org/mcom/", keywords = "dominant; eigenvalue; eigenvalues and eigenfunctions; eigenvector; positive definite matrix; power method; Rayleigh quotient", kwds = "nla, eig, power method, symmetric matrix", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1979:ERE, author = "G. W. Stewart", title = "The Effects of Rounding Error on an Algorithm for Downdating a {Cholesky} Factorization", journal = j-J-INST-MATH-APPL, volume = "23", number = "2", pages = "203--213", month = mar, year = "1979", CODEN = "JMTAA8", DOI = "https://doi.org/10.1093/imamat/23.2.203", ISSN = "0020-2932", ISSN-L = "0020-2932", MRclass = "65G05 (65F30)", MRnumber = "80i:65046", MRreviewer = "H. Ratschek", bibdate = "Fri Apr 5 05:48:27 MST 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib; https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Journal of the Institute of Mathematics and its Applications", GWS-number = "J40", journal-URL = "http://imamat.oxfordjournals.org/content/by/year", kwds = "math, nla, rounding error, updating, Cholesky decomposition, qrd", } @Article{Stewart:1979:NPS, author = "G. W. Stewart", title = "A Note on the Perturbation of Singular Values", journal = j-LINEAR-ALGEBRA-APPL, volume = "28", pages = "213--216", month = dec, year = "1979", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(79)90134-4", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A42", MRnumber = "81a:15019", MRreviewer = "J. de Pillis", bibdate = "Tue Feb 16 18:50:44 MST 2016", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379579901344", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J39", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, svd, pert", } @Article{Stewart:1979:PBD, author = "G. W. Stewart", title = "Perturbation Bounds for the Definite Generalized Eigenvalue Problem", journal = j-LINEAR-ALGEBRA-APPL, volume = "23", pages = "69--85", month = feb, year = "1979", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(79)90094-6", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (65F15)", MRnumber = "80c:15007", MRreviewer = "F. Szidarovszky", bibdate = "Tue Feb 16 18:50:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379579900946", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J38", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Stewart:1979:PH, author = "G. W. Stewart", title = "Preface: {A. S. Householder}", journal = j-LINEAR-ALGEBRA-APPL, volume = "28", pages = "1--3 + 1", month = dec, year = "1979", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(79)90112-5", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "01A70", MRnumber = "82g:01071", bibdate = "Tue Feb 16 18:50:44 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379579901125", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Stewart:1980:BMI, author = "G. W. Stewart", title = "The behavior of a multiplicity independent root-finding scheme in the presence of error", journal = j-BIT, volume = "20", number = "4", pages = "526--528", month = dec, year = "1980", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01933649", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65H05 (65G05)", MRnumber = "82b:65043", bibdate = "Wed Jan 4 18:52:16 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=4&spage=526", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", GWS-number = "J44", journal-URL = "http://link.springer.com/journal/10543", } @Article{Stewart:1980:EGR, author = "G. W. Stewart", title = "The Efficient Generation of Random Orthogonal Matrices With an Application to Condition Estimators", journal = j-SIAM-J-NUMER-ANAL, volume = "17", number = "3", pages = "403--409 (loose microfiche supplement)", month = jun, year = "1980", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65C99 (65F35)", MRnumber = "83e:65018", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J43", journal-URL = "http://epubs.siam.org/sinum", } @Article{Stewart:1981:CDH, author = "G. W. Stewart", title = "Constrained definite {Hessians} tend to be well conditioned", journal = j-MATH-PROG, volume = "21", pages = "235--238", year = "1981", CODEN = "MHPGA4", ISSN = "0025-5610", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", GWS-number = "J46", journal-URL = "http://link.springer.com/journal/10107", } @Article{Stewart:1981:IDN, author = "G. W. Stewart", title = "On the Implicit Deflation of Nearly Singular Systems of Linear Equations", journal = j-SIAM-J-SCI-STAT-COMP, volume = "2", number = "2", pages = "136--140", month = jun, year = "1981", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0902011", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65F05", MRnumber = "82f:65030", bibdate = "Mon Mar 31 09:58:56 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", GWS-number = "J45", journal-URL = "http://epubs.siam.org/loi/sjoce3", keywords = "iterative methods; linear algebra; linear equations; matrix algebra; nearly singular systems; sparsity", onlinedate = "June 1981", treatment = "A Application; T Theoretical or Mathematical", } @Article{Stewart:1981:MCH, author = "G. W. Stewart", title = "Matrix calculations on hand-held calculators", journal = j-SIGNUM, volume = "16", number = "1", pages = "10--13", month = mar, year = "1981", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Tue Apr 12 07:50:09 MDT 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", } @Article{Stewart:1982:CDP, author = "G. W. Stewart", title = "Computing the {$ C S $} decomposition of a partitioned orthonormal matrix", journal = j-NUM-MATH, volume = "40", number = "3", pages = "297--306", month = dec, year = "1982", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F25 (65F30)", MRnumber = "84h:65042", MRreviewer = "John Todd", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J47", journal-URL = "http://link.springer.com/journal/211", keywords = "CS decomposition; matrix algebra; orthogonal transformations; partitioned orthonormal matrix", treatment = "T Theoretical or Mathematical", } @InCollection{Anandalingam:1983:AIB, author = "G. Anandalingam and R. Mathieu and L. Pittard and N. Sinha", booktitle = "Impacts of Recent Computer Advances on Operations Research", title = "Artificial intelligence based approaches for solving hierarchical optimization problems", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "289--301", year = "1983", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/multilevel-prog.bib", acknowledgement = ack-nhfb, } @Article{Stewart:1983:CEB, author = "G. W. Stewart", title = "Computable Error Bounds for Aggregated {Markov} Chains", journal = j-J-ACM, volume = "30", number = "2", pages = "271--285", month = apr, year = "1983", CODEN = "JACOAH", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", abstract = "A method is described for computing the steady-state probability vector of a nearly completely decomposable Markov chain. The method is closely related to the one proposed by H. A. Simon and A. Ando and developed by P. J. Courtois. However, the method described here does not require the determination of a completely decomposable stochastic approximation to the transition matrix, and hence it is applicable to nonstochastic matrices. An error analysis of the procedure which results in effectively computable error bounds is given.", acknowledgement = ack-nhfb, classification = "922", descriptors = "Markov process; transition matrix; eigenvalue; error bound; transient Markov chain; steady state", fjournal = "Journal of the Association for Computing Machinery", GWS-number = "J48", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", journalabr = "J Assoc Comput Mach", keywords = "aggregation; eig; Markov chain; nla; pert; probability", remark = "For some discrete finite Markov chains, the matrix a of transition probabilities can be partitioned so that the off diagonal blocks are smaller (in norm) than the square submatrices on the diagonal. Thus, a can be approximated by a block-diagonal matrix. The computation of the left eigenvector with eigenvalue 1, which gives the steady-state probabilities of the chain, then reduces to the computation of left eigenvectors of the submatrices on \ldots{}.", } @Article{Stewart:1983:MCG, author = "G. W. Stewart", title = "A method for computing the generalized singular value decomposition", journal = j-LECT-NOTES-MATH, volume = "973", pages = "207--220", year = "1983", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0062104", ISBN = "0-387-11983-3, 3-540-11983-3 (print), 3-540-39447-8 (e-book)", ISBN-13 = "978-0-387-11983-0, 978-3-540-11983-8 (print), 978-3-540-39447-1 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/lnm1980.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0062104/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0062089", book-URL = "http://www.springerlink.com/content/978-3-540-39447-1", fjournal = "Lecture Notes in Mathematics", GWS-number = "N12", journal-URL = "http://link.springer.com/bookseries/304", remark = "See \cite{Kaagstrom:1983:MPP} for proceedings volume.", } @InCollection{Dongarra:1984:LPS, author = "J. J. Dongarra and G. W. Stewart", title = "{LINPACK} --- {A} Package for Solving Linear Systems", crossref = "Cowell:1984:SDM", pages = "20--48", year = "1984", bibdate = "Fri Aug 23 12:59:02 MDT 1996", bibsource = "Compendex database; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib", abstract = "LINPACK is a collection of Fortran subroutines that analyze and solve linear equations and linear least squares problems. The package solves linear systems whose matrices are general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal. In addition, the package computes the $ Q R $ and singular value decompositions of rectangular matrices and applies them to least squares problems.", acknowledgement = ack-nhfb, affiliation = "Argonne Natl Lab, Mathematics \& Computer Science Div, Argonne, IL, USA", affiliationaddress = "Argonne Natl Lab, Mathematics \& Computer Science Div, Argonne, IL, USA", classification = "723; 731; 921", GWS-number = "N13", journalabr = "Sources and Dev of Math Software", keywords = "COMPUTER PROGRAMMING; COMPUTER PROGRAMMING --- Subroutines; COMPUTER PROGRAMMING LANGUAGES --- FORTRAN; COMPUTER SOFTWARE --- Modular Construction; FORTRAN SUBROUTINES; LINEAR SYSTEMS; LINPACK; MATHEMATICAL TECHNIQUES --- Linear Algebra; Subroutines", } @Article{McAllister:1984:RRR, author = "D. F. McAllister and G. W. Stewart and W. J. Stewart", title = "On a {Rayleigh--Ritz} Refinement Technique for Nearly Uncoupled Stochastic Matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "60", number = "??", pages = "1--25", month = aug, year = "1984", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(84)90067-3", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (15A51)", MRnumber = "85h:65082", MRreviewer = "L. Berg", bibdate = "Wed Nov 30 13:49:30 MST 2011", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379584900673", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J51", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, Markov chain, nearly uncoupled system, Rayleigh--Ritz method, aggregation", mynote = "NB: not copied.", } @Article{Stewart:1984:ABS, author = "G. W. Stewart", title = "On the Asymptotic Behavior of Scaled Singular Value and {$ Q R $} Decompositions", journal = j-MATH-COMPUT, volume = "43", number = "168", pages = "483--489", month = oct, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F35 (15A23 65D10)", MRnumber = "86f:65085", MRreviewer = "Alan L. Andrew", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", GWS-number = "J53", journal-URL = "http://www.ams.org/mcom/", kwds = "la, qrd, svd, scaling", xxpages = "483--490", } @Article{Stewart:1984:IPN, author = "G. W. Stewart", title = "On the invariance of perturbed null vectors under column scaling", journal = j-NUM-MATH, volume = "44", number = "1", pages = "61--65", month = jun, year = "1984", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F20 (65F35)", MRnumber = "86d:65053", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Computer Sci., Univ. of Maryland, College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J52", journal-URL = "http://link.springer.com/journal/211", keywords = "column scaling; estimation technique; invariance; latent root regression; least squares approximations; perturbation techniques; perturbed degenerate matrix; perturbed null vectors; total least squares", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1984:RD, author = "G. W. Stewart", title = "Rank Degeneracy", journal = j-SIAM-J-SCI-STAT-COMP, volume = "5", number = "2", pages = "403--413", month = jun, year = "1984", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0905030", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65F25 (65F15)", MRnumber = "85h:65086", MRreviewer = "G. C. Barozzi", bibdate = "Mon Mar 31 09:59:22 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", acknowledgement = ack-nhfb, classification = "B0210 (Algebra); C1110 (Algebra)", corpsource = "Computer Sci. Dept., Univ. of Maryland, College Park, MD, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", GWS-number = "J49", journal-URL = "http://epubs.siam.org/loi/sjoce3", keywords = "errors; matrix algebra; matrix rank; perturbation theory; rank degeneracy", onlinedate = "June 1984", treatment = "T Theoretical or Mathematical", } @InProceedings{Stewart:1984:SNU, author = "G. W. Stewart", title = "On the Structure of Nearly Uncoupled {Markov} Chains", crossref = "Iazeolla:1984:MCP", pages = "287--302", year = "1984", bibdate = "Thu May 29 16:31:34 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N14", } @Article{Stewart:1984:SOP, author = "G. W. Stewart", title = "A Second Order Perturbation Expansion for Small Singular Values", journal = j-LINEAR-ALGEBRA-APPL, volume = "56", number = "??", pages = "231--235", month = jan, year = "1984", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(84)90128-9", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F20 (15A18)", MRnumber = "85c:65047", MRreviewer = "Ekkehard Wagenf{\"u}hrer", bibdate = "Wed Nov 30 13:49:20 MST 2011", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379584901289", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J50", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, svd, pert", xxpages = "231--236", } @Article{Trevathan:1984:DAN, author = "Charles E. Trevathan and Thomas D. Taylor and Raymond G. Hartenstein and Ann. C. Merwarth and William N. Stewart", title = "Development and Application of {NASA}'s First Standard Spacecraft Computer", journal = j-CACM, volume = "27", number = "9", pages = "902--913", year = "1984", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 07:26:34 MST 2001", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm27.html#TrevathanTHMS84; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1980.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", oldlabel = "TrevathanTHMS84", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/TrevathanTHMS84", } @Article{Gill:1985:PRB, author = "P. E. Gill and W. Murray and M. A. Saunders and G. W. Stewart and M. H. Wright", title = "Properties of a Representation of a Basis for the Null Space", journal = j-MATH-PROG, volume = "33", pages = "172--186", year = "1985", CODEN = "MHPGA4", ISSN = "0025-5610", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", GWS-number = "J57", journal-URL = "http://link.springer.com/journal/10107", } @Article{OLeary:1985:DFA, author = "Dianne P. O'Leary and G. W. Stewart", title = "Data-flow algorithms for parallel matrix computation", journal = j-CACM, volume = "28", number = "8", pages = "840--853", month = aug, year = "1985", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/4021.4025", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65W05 (65Fxx)", MRnumber = "86j:65197", bibdate = "Thu May 30 09:41:10 MDT 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cacm1980.bib", URL = "http://www.acm.org/pubs/toc/Abstracts/0001-0782/4025.html", abstract = "In this article we develop some algorithms and tools for solving matrix problems on parallel processing computers. Operations are synchronized through data-flow alone, which makes global synchronization unnecessary and enables the algorithms to be implemented on machines with very simple operating systems and communication protocols. As examples, we present algorithms that form the main modules for solving Liapounov matrix equations. We compare this approach to wave front array processors and systolic arrays, and note its advantages in handling mis-sized problems, in evaluating variations of algorithms or architectures, in moving algorithms from system to system, and in debugging parallel algorithms on sequential machines.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", GWS-number = "J56", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "algorithms, nla, prll, eig, Sylvester equation, Cholesky decomposition, matrix equation", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Parallel processors.", xxpages = "841--853", } @Article{Stewart:1985:JLA, author = "G. W. Stewart", title = "A {Jacobi}-Like Algorithm for Computing the {Schur} Decomposition of a Non-{Hermitian} Matrix", journal = j-SIAM-J-SCI-STAT-COMP, volume = "6", number = "4", pages = "853--864", month = oct, year = "1985", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0906058", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65F15 (65W05)", MRnumber = "86j:65047", MRreviewer = "Cs. J. Heged{\H{u}}s", bibdate = "Mon Mar 31 09:59:35 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", acknowledgement = ack-nhfb, classification = "C4130 (Interpolation and function approximation); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", GWS-number = "J55", journal-URL = "http://epubs.siam.org/loi/sjoce3", keywords = "Hermitian matrix; iterative method; iterative methods; Jacobi-like algorithm; matrix algebra; nonHermitian matrix; off-diagonal elements; parallel implementation; parallel processing; plane rotations; Schur decomposition; unitary similarity transformations; upper triangular form", mynote = "Also Maryland Tech. Rep. TR-1321", onlinedate = "October 1985", treatment = "T Theoretical or Mathematical", xxpages = "853--862", } @Article{Stewart:1985:NCD, author = "G. W. Stewart", title = "A Note on Complex Division", journal = j-TOMS, volume = "11", number = "3", pages = "238--241", month = sep, year = "1985", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/214408.214414", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Aug 26 23:38:15 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See corrigendum \cite{Stewart:1986:CNC} and the faster and more robust algorithm in \cite{Priest:2004:ESC}.", URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/", abstract = "An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J54", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "algorithms; complex arithmetic; computer arithmetic; na", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{George:1986:P, author = "Alan George and G. W. Stewart and Robert Voigt", title = "Preface", journal = j-LINEAR-ALGEBRA-APPL, volume = "77", number = "??", pages = "1--2", month = may, year = "1986", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(86)90158-8", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Nov 30 13:50:06 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379586901588", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{OLeary:1986:ASP, author = "Dianne P. O'Leary and G. W. Stewart", title = "Assignment and Scheduling in Parallel Matrix Factorization", journal = j-LINEAR-ALGEBRA-APPL, volume = "77", number = "??", pages = "275--299", month = may, year = "1986", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(86)90172-2", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65W05 (65F30)", MRnumber = "837 869", bibdate = "Wed Nov 30 13:50:06 MST 2011", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", note = "Special volume on parallel computing.", URL = "http://www.sciencedirect.com/science/article/pii/0024379586901722", abstract = "We consider the problem of factoring a dense $ n \times n $ matrix on a network consisting of $P$ MIMD processors, with no shared memory, when the network is smaller than the number of elements in the matrix ($ P < n^2$). The specific example analyzed is a computational network that arises in computing the $ L U$, $ Q R$, or Cholesky factorizations. We prove that if the nodes of the network are evenly distributed among processors and if computations are scheduled by a round-robin or a least-recently-executed scheduling algorithm, then optimal order of speedup is achieved. However, such speedup is not necessarily achieved for other scheduling algorithms or if the computation for the nodes is inappropriately split across processors, and we give examples of these phenomena. Lower bounds on execution time for the algorithm are established for two important node-assignment strategies.", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J58", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, prll, lud, Cholesky decomposition, communication, message passing", xxpages = "275--300", } @TechReport{OLeary:1986:DMP, author = "Dianne P. O'Leary and G. W. Stewart and Robert van de Geijn", title = "{DOMINO}: a Message Passing Environment for Parallel Computations", number = "TR-1648", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, month = apr, year = "1986", bibdate = "Thu May 29 16:58:30 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N16", keywords = "Netlib; Oak Ridge National Laboratory (ORNL)", } @TechReport{OLeary:1986:MCM, author = "Dianne P. O'Leary and Roger Pierson and G. W. Stewart and Mark Weiser", title = "The {Maryland Crab}: A module for building parallel computers", type = "Technical Report", number = "CS-1660", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "1986", bibdate = "Thu May 29 16:59:46 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "Also issued as University of Maryland Institute for Advanced Computer Studies Report UMIACS-86-9.", acknowledgement = ack-nhfb, GWS-number = "N17", } @Article{Stewart:1986:CNC, author = "G. W. Stewart", title = "Corrigendum: ``{A} Note on Complex Division''", journal = j-TOMS, volume = "12", number = "3", pages = "285--285", month = sep, year = "1986", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/7921.356182", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Sep 30 01:17:25 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Stewart:1985:NCD}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J54", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @InProceedings{Stewart:1986:CPA, author = "G. W. Stewart", title = "Communication in Parallel Algorithms: An Example", crossref = "Boardman:1986:CSS", pages = "11--14", year = "1986", bibdate = "Thu May 29 17:05:41 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N18", } @InProceedings{Stewart:1986:CSR, author = "G. W. Stewart", title = "Collinearity, Scaling, and Rounding Error", crossref = "Allen:1986:CSS", pages = "195--198", year = "1986", bibdate = "Thu May 29 16:56:44 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N15", } @Article{Golub:1987:GEY, author = "G. H. Golub and Alan Hoffman and G. W. Stewart", title = "A Generalization of the {Eckart--Young--Mirsky} Matrix Approximation Theorem", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", number = "??", pages = "317--327", year = "1987", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(87)90114-5", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "41A45 (15A60 62J05 65F99)", MRnumber = "88f:41039", MRreviewer = "R. A. Lorentz", bibdate = "Thu Jan 23 11:18:08 MST 1997", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J59", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, matrix approximation", mynote = "Stanford NA-86-35, March 1986 (by GHG and GSW).", xxpages = "317--328", } @InProceedings{Higham:1987:NLA, author = "Nicholas J. Higham and G. W. Stewart", title = "Numerical Linear Algebra in Statistical Computing", crossref = "Iserles:1987:SAN", pages = "41--57", year = "1987", bibdate = "Thu May 29 17:14:49 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb # "\slash " # ack-njh, GWS-number = "N19", xxpages = "41--58", } @Article{OLeary:1987:DSA, author = "D. P. O'Leary and G. W. Stewart", title = "From Determinacy to Systaltic Arrays", journal = j-IEEE-TRANS-COMPUT, volume = "C-36", number = "11", pages = "1355--1359", month = nov, year = "1987", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/TC.1987.5009475", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009475", abstract = "In this paper we extend a model of Karp and Miller for parallel computation. We show that the extended model is deterministic, in the sense that under different scheduling regimes each process in the computation consumes the same input and generates the same output. Moreover, if the computation halts, the final state is independent of scheduling. The model is applied to the generation of precedence graphs, from which lower time bounds may be deduced, and to the synchronization of systolic arrays by local rather than global control.", acknowledgement = ack-nhfb, author-affiliation = "Department of Computer Science, University of Maryland, College Park, MD 20742.", book-DOI = "https://doi.org/10.1109/TC.1987.5009475", fjournal = "IEEE Transactions on Computers", GWS-number = "J61", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Stewart:1987:CLSa, author = "G. W. Stewart", title = "Collinearity and Least Squares Regression", journal = j-STAT-SCI, volume = "2", number = "1", pages = "68--84", month = feb, year = "1987", CODEN = "STSCEP", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", bibdate = "Fri May 30 12:48:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/statsci.bib", URL = "http://projecteuclid.org/euclid.ss/1177013439", acknowledgement = ack-nhfb, fjournal = "Statistical Science", GWS-number = "J60", journal-URL = "http://projecteuclid.org/all/euclid.ss", mynote = "4 comments by other authors and a rejoinder by GSW, pp. 84-100.", } @Article{Stewart:1987:CLSb, author = "G. W. Stewart", title = "[{Collinearity} and Least Squares Regression]: Rejoinder", journal = j-STAT-SCI, volume = "2", number = "1", pages = "98--100", month = feb, year = "1987", CODEN = "STSCEP", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", bibdate = "Fri May 30 12:48:25 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/statsci.bib", URL = "http://projecteuclid.org/euclid.ss/1177013444", acknowledgement = ack-nhfb, fjournal = "Statistical Science", journal-URL = "http://projecteuclid.org/all/euclid.ss", } @TechReport{Stewart:1987:ISC, author = "G. W. Stewart", title = "Invariant subspaces and capital punishment (a participatory paper)", type = "Technical Report", number = "CS-TR 1923", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1987", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "September", } @Article{Stewart:1987:PIA, author = "G. W. Stewart", title = "A parallel implementation of the {$ Q R $}-algorithm", journal = j-PARALLEL-COMPUTING, volume = "5", number = "1--2", pages = "187--196", month = jul, year = "1987", CODEN = "PACOEJ", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", MRclass = "65W05 (65F15)", MRnumber = "88d:65191", bibdate = "Mon Apr 14 12:07:40 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib", note = "Proceedings of the international conference on vector and parallel computing---issues in applied research and development (Loen, 1986)", acknowledgement = ack-nhfb, classification = "C4240 (Programming and algorithm theory)", conflocation = "Loen, Norway; 2-6 June 1986", conftitle = "International Conference on Vector and Parallel Computing --- Issues in Applied Research and Development", corpsource = "Inst. for Phys. Sci. and Technol., Maryland Univ., College Park, MD, USA", fjournal = "Parallel Computing", GWS-number = "J62", journal-URL = "http://www.sciencedirect.com/science/journal/01678191/", keywords = "eigenvalues; Maryland CRAB; nonHermitian matrix; parallel algorithms; parallel implementation; QR-algorithm", sponsororg = "IBM Norway; R. Norwegian Council Sci. and Ind. Res.; AMDAHL; FPS; CRAY", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1987:RBC, author = "G. W. Stewart", title = "Review of {{\booktitle{Matrix Computations}}, by Gene H. Golub and Charles F. Van Loan}", journal = j-LINEAR-ALGEBRA-APPL, volume = "95", number = "??", pages = "211--215", month = oct, year = "1987", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(87)90036-X", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Nov 30 13:50:37 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/002437958790036X", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Buell:1988:LEP, author = "D. A. Buell and D. A. Carlson and Yuan-chieh Chow and K. Culik and N. Deo and R. Finkel and E. N. Houstis and E. M. Jacobson and Z. M. Kedem and J. S. Kowalik and P. J. Kuekes and J. L. Martin and G. A. Michael and N. S. Ostlund and J. Potter and D. K. Pradhan and M. J. Quinn and G. W. Stewart and Q. F. Stout and L. Watson and J. Webb", title = "Letter to the {Editor}: Parallel algorithms and architectures: report of a workshop", journal = j-J-SUPERCOMPUTING, volume = "1", number = "3", pages = "301--325", month = apr, year = "1988", CODEN = "JOSUED", DOI = "https://doi.org/10.1007/BF00154341", ISSN = "0920-8542 (print), 1573-0484 (electronic)", ISSN-L = "0920-8542", bibdate = "Wed Jul 6 11:12:58 MDT 2005", bibsource = "ftp://ftp.ira.uka.de/pub/Parallel/JOURNAL.SUPER.bib; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=1&issue=3; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/jsuper.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=1&issue=3&spage=301", acknowledgement = ack-nhfb, classification = "C4100 (Numerical analysis); C4240 (Programming and algorithm theory); C5220 (Computer architecture)", fjournal = "The Journal of Supercomputing", GWS-number = "N20", journal-URL = "http://link.springer.com/journal/11227", keywords = "algorithm design; architectural design; computing power; experimental environment; high-level descriptions; language; massive speedup; notations; parallel algorithms; parallel architectures; parallelism; program compilers; prototypes; scientific data; supercomputer architectures; translation", treatment = "P Practical", } @Article{Golub:1988:GEY, author = "G. H. Golub and A. Hoffman and G. W. Stewart", title = "A Generalization of the {Eckart--Young--Mirsky} Approximation Theorem", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", pages = "317--328", year = "1988", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Meyer:1988:DPE, author = "Carl D. Meyer and G. W. Stewart", title = "Derivatives and Perturbations of Eigenvectors", journal = j-SIAM-J-NUMER-ANAL, volume = "25", number = "3", pages = "679--691", month = jun, year = "1988", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F15 (15A22 60J10)", MRnumber = "89g:65043", MRreviewer = "Ludwig Elsner", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", GWS-number = "J64", journal-URL = "http://epubs.siam.org/sinum", } @Article{Stewart:1988:CCR, author = "G. W. Stewart", title = "A Curiosity Concerning the Representation of Integers in Noninteger Bases", journal = j-MATH-COMPUT, volume = "51", number = "184", pages = "755--756", month = oct, year = "1988", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008775", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "11A63", MRnumber = "89c:11017", MRreviewer = "Graham Lord", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database; Theory/Matrix.bib", URL = "http://zbmath.org/?q=an:0699.10020", ZMnumber = "0699.10020", acknowledgement = ack-nhfb, classcodes = "C1160 (Combinatorial mathematics); C5230 (Digital arithmetic methods)", corpsource = "Maryland Univ., College Park, MD, USA", fjournal = "Mathematics of Computation", GWS-number = "J63", journal-URL = "http://www.ams.org/mcom/", keywords = "digital arithmetic; digits; integers representation; noninteger bases; number theory", kwds = "math, number theory", treatment = "T Theoretical or Mathematical", } @InProceedings{Stewart:1988:PLA, author = "G. W. Stewart", title = "Parallel Linear Algebra in Statistical Computing", crossref = "Edwards:1988:CPC", pages = "3--14", year = "1988", bibdate = "Thu May 29 17:39:56 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N21", } @Article{Tomayko:1988:AOT, author = "James E. Tomayko and Henry S. Tropp and W. Buchholz and Grace Murray Hopper and C. Strachey and Eric A. Weiss and Robert M. Stewart and Bernard A. Galler", title = "Anecdotes: Origin of the Term Bit; Origin of the Word Byte; The First Bug; Whence the ``Bug''; An Impossible Program; Reminiscences of {Los Alamos}; {Los Alamos} from Below; {Jonathan Swift}'s Computing Invention; Debugging", journal = j-ANN-HIST-COMPUT, volume = "10", number = "4", pages = "336--348", month = oct # "\slash " # dec, year = "1988", CODEN = "AHCOE5", ISSN = "0164-1239", bibdate = "Fri Nov 1 15:29:13 MST 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib", URL = "http://dlib.computer.org/an/books/an1988/pdf/a4336.pdf; http://www.computer.org/annals/an1988/a4336abs.htm", acknowledgement = ack-nhfb, fjournal = "Annals of the History of Computing", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650", } @InProceedings{OLeary:1989:DTO, author = "Diane P. O'Leary and G. W. Stewart and Robert van de Geijn", title = "{DOMINO}: A Transportable Operating System for Parallel Computation", crossref = "Wouk:1989:PPM", pages = "25--34", year = "1989", bibdate = "Thu May 29 18:08:12 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N22", } @InCollection{Saltzman:1989:IIP, author = "M. J. Saltzman and R. Subramaniam and R. E. Marsten", title = "Implementing an interior point {LP} algorithm on a supercomputer", crossref = "Sharda:1989:IRC", pages = "158--168", year = "1989", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, } @Article{Stenbakken:1989:AGT, author = "G. N. Stenbakken and T. M. Souders and G. W. Stewart", title = "Ambiguity groups and testability", journal = j-IEEE-TRANS-INSTRUM-MEAS, volume = "38", number = "5", pages = "941--947", month = "????", year = "1989", CODEN = "IEIMAO", DOI = "https://doi.org/10.1109/19.39034", ISSN = "0018-9456 (print), 1557-9662 (electronic)", ISSN-L = "0018-9456", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=39034", acknowledgement = ack-nhfb, author-affiliation = "Nat. Inst. of Stand. \& Technol., Gaithersburg, MD, USA", book-DOI = "https://doi.org/10.1109/19.39034", fjournal = "IEEE Transactions on Instrumentation and Measurement", GWS-number = "J66", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19", } @Article{Stewart:1989:SPP, author = "G. W. Stewart", title = "On Scaled Projections and Pseudo-Inverses", journal = j-LINEAR-ALGEBRA-APPL, volume = "112", number = "??", pages = "189--193", month = jan, year = "1989", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(89)90594-6", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A09", MRnumber = "90d:15005", MRreviewer = "J. Segethov{\'a}", bibdate = "Wed Nov 30 13:51:07 MST 2011", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", note = "See answer \cite{OLeary:1990:BSP} to a question raised in this paper.", URL = "http://www.sciencedirect.com/science/article/pii/0024379589905946", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J65", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, projection, ginv", xxpages = "189--194", } @Article{OLeary:1990:CEE, author = "D. P. O'Leary and G. W. Stewart", title = "Computing the Eigenvalues and Eigenvectors of Symmetric Arrowhead Matrices", journal = j-J-COMPUT-PHYS, volume = "90", number = "2", pages = "497--505", month = oct, year = "1990", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(90)90177-3", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Mon Jan 2 07:55:44 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/0021999190901773", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", GWS-number = "J67", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", } @Article{Stewart:1990:CMC, author = "G. W. Stewart", title = "Communication and matrix computations on large message passing systems", journal = j-PARALLEL-COMPUTING, volume = "16", number = "1", pages = "27--40", month = nov, year = "1990", CODEN = "PACOEJ", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", bibdate = "Mon Apr 14 11:08:33 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib", acknowledgement = ack-nhfb, classification = "C4140 (Linear algebra); C5230 (Digital arithmetic methods); C7310 (Mathematics)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "Parallel Computing", GWS-number = "J68", journal-URL = "http://www.sciencedirect.com/science/journal/01678191/", keywords = "communication; digital arithmetic; fine; floating point operations; grain communication; large message passing; mathematics computing; matrix algebra; matrix algorithms; matrix computations; systems", treatment = "P Practical", } @TechReport{Stewart:1990:ICC, author = "G. W. Stewart", title = "Incremental condition calculation and column selection", type = "Technical Report", number = "CS-TR 2495", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1990", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "July", } @InProceedings{Stewart:1990:IMS, author = "G. W. (Pete) Stewart", title = "An iterative method for solving linear inequalities", crossref = "Cox:1990:RNC", pages = "241--247", year = "1990", MRnumber = "65K05 65F10 15A39 90C05", bibdate = "Tue Nov 2 19:30:33 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", URL = "http://zbmath.org/?q=an:0234.68003", ZMnumber = "0721.65033", acknowledgement = ack-nhfb, GWS-number = "N23", mynote = "Maryland TR-1833, April 1987", } @Book{Stewart:1990:MPT, author = "Gilbert Wright (Gilbert W.) Stewart and {Ji-guang} Sun", title = "Matrix Perturbation Theory", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xv + 365", year = "1990", ISBN = "0-12-670230-6 (hardcover)", ISBN-13 = "978-0-12-670230-9 (hardcover)", LCCN = "QA871 .S775 1990", bibdate = "Thu May 29 07:15:52 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager", series = "Computer science and scientific computing", URL = "http://catalog.hathitrust.org/api/volumes/oclc/21227976.html; http://www.loc.gov/catdir/description/els032/90033378.htm; http://www.loc.gov/catdir/description/els032/90033378.html; http://www.loc.gov/catdir/toc/els031/90033378.htm; http://www.loc.gov/catdir/toc/els031/90033378.html", acknowledgement = ack-nhfb, GWS-number = "B3", subject = "Perturbation (Mathematics); Matrices", tableofcontents = "I. Preliminaries \\ 1. Notation \\ 2. The $QR$ decomposition \\ projections \\ 3. Eigenvalues and eigenvectors \\ 4. The singular value decomposition \\ II. Norms and metrics \\ 1. Vector norms \\ 2. Matrix norms \\ 3. Unitarily invariant norms \\ 4. Metrics on subspaces of C'n' \\ III. Linear systems and least squares problems \\ 1. The pseudo-inverse and least squares \\ 2. Inverses and linear systems \\ 3. The pseudo-inverse \\ 4. Projections \\ 5. The Linear least squares problem \\ IV. The perturbation of Eigenvalues \\ 1. General perturbation theorems \\ 2. Gerschgorin theory: differentiability \\ 3. Normal and diagonalizable matrices \\ 4. Hermitian matrices \\ 5. Some further results \\ V. Invariant subspaces \\ 1. The theory of simple invariant subspaces \\ 2. Perturbation of invariant subspaces \\ 3. Hermitian matrices \\ 4. The singular value decomposition \\ VI. Generalized Eigenvalue problems \\ 1. Background \\ 2. Regular matrix pairs \\ 3. Definite matrix pairs \\ References \\ Notation \\ Index", } @InProceedings{Stewart:1990:PTL, author = "G. W. Stewart", title = "Perturbation theory and least squares with errors in the variables", crossref = "Brown:1990:SAM", pages = "171--181", year = "1990", DOI = "https://doi.org/10.1090/conm/112/1087108", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, book-URL = "http://www.ams.org/conm/112/", GWS-number = "N24", } @TechReport{Stewart:1990:PTS, author = "G. W. Stewart", title = "Perturbation theory for the singular value decomposition", type = "Technical Report", number = "CS-TR 2539", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1990", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "Sept", } @InProceedings{Stewart:1990:SNU, author = "G. W. Stewart", title = "On the Sensitivity of Nearly Uncoupled {Markov} Chains", crossref = "Stewart:1990:NSM", pages = "105--119", year = "1990", bibdate = "Thu May 29 18:15:40 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N25", } @Article{Stewart:1990:SPT, author = "G. W. Stewart", title = "Stochastic Perturbation Theory", journal = j-SIAM-REVIEW, volume = "32", number = "4", pages = "579--610", month = dec, year = "1990", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1032121", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "15A06 (15A09 15A12 15A18 15A52 15A60)", MRnumber = "91m:15007", MRreviewer = "James Weldon Demmel", bibdate = "Sat Mar 29 09:54:48 MDT 2014", bibsource = "Compendex database; http://epubs.siam.org/toc/siread/32/4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", abstract = "In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares and the eigenvalue problem.", acknowledgement = ack-nhfb, affiliation = "Univ of Maryland", affiliationaddress = "College Park, MD, USA", classification = "921; 922", fjournal = "SIAM Review", GWS-number = "J69", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "Mathematical Techniques; Perturbation Techniques; Probability --- Random Processes; Stochastic Perturbation Theory", mynote = "Maryland CS-TR-2129, October 88", onlinedate = "December 1990", } @TechReport{Stewart:1990:UAS, author = "G. W. Stewart", title = "An updating algorithm for subspace tracking", type = "Technical Report", number = "CS-TR 2494", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1990", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "revised January 1991", acknowledgement = ack-nhfb, } @TechReport{Adams:1991:DAEa, author = "G. Adams and M. F. Griffin and G. W. Stewart", title = "Direction-of-arrival estimation using the rank-revealing {$ U R V $} decomposition", type = "Technical Report", number = "CS-TR 2640", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1991", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "March", } @InProceedings{Adams:1991:DAEb, author = "G. Adams and M. F. Griffin and G. W. Stewart", title = "Direction-of-arrival estimation using the rank-revealing {$ U R V $} decomposition", crossref = "IEEE:1991:ICA", pages = "1385--1388 (vol. 2)", year = "1991", DOI = "https://doi.org/10.1109/ICASSP.1991.150681", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=150681", acknowledgement = ack-nhfb, author-affiliation = "United Technol. Res. Center, East Hartford, CT, USA", book-DOI = "https://doi.org/10.1109/ICASSP.1991.150681", GWS-number = "N27", } @InProceedings{Griffin:1991:UMR, author = "M. F. Griffin and G. W. Stewart", title = "Updating {MUSIC} and root-{MUSIC} with the rank-revealing {$ U R V $} decomposition", crossref = "Chen:1991:CRT", pages = "277--281 (vol. 1)", year = "1991", DOI = "https://doi.org/10.1109/ACSSC.1991.186456", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=186456", acknowledgement = ack-nhfb, author-affiliation = "Advanced Digital Systems, East Hartford, CT, USA", book-DOI = "https://doi.org/10.1109/ACSSC.1991.186456", } @TechReport{Stewart:1991:ARR, author = "G. W. Stewart", title = "On an algorithm for refining a rank-revealing {$ U R V $} factorization and a perturbation theorem for singular values", type = "Technical Report", number = "CS-TR 2626", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1991", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "March", } @Article{Stewart:1991:DMS, author = "G. W. Stewart and G. Zhang", title = "On a Direct Method for the Solution of Nearly Uncoupled {Markov} Chains", journal = j-NUM-MATH, volume = "59", number = "1", pages = "1--11", month = apr, year = "1991", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F05 (60J10 65G05)", MRnumber = "92i:65062", MRreviewer = "Ching-Tsuan Pan", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib; Theory/Matrix.bib", acknowledgement = ack-nhfb, classification = "B0240Z (Other and miscellaneous); C1140Z (Other and miscellaneous)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J72", journal-URL = "http://link.springer.com/journal/211", keywords = "diagonal pivoting; direct method; LDU; LU decomposition; Markov chain; Markov processes; nearly uncoupled Markov chains; nearly uncoupled system; nla; plain Gaussian elimination; rounding errors", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1991:EGM, author = "G. W. Stewart and G. Zhang", title = "Eigenvalues of Graded Matrices and the Condition Numbers of a Multiple Eigenvalue", journal = j-NUM-MATH, volume = "58", number = "7", pages = "703--712", month = feb, year = "1991", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F15", MRnumber = "92a:65121", MRreviewer = "Assem Deif", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib; Theory/Matrix.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Inst. for Adv. Comput. Studies, Maryland Univ., College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J71", journal-URL = "http://link.springer.com/journal/211", keywords = "canonical angles; condition numbers; eigenvalues; eigenvalues and eigenfunctions; graded matrices; graded structure; la; matrix algebra; multiple eigenvalue; pert; perturbations", treatment = "T Theoretical or Mathematical", } @Article{Stewart:1991:FFT, author = "G. W. Stewart", title = "{FTP} --- File Transfer Program", journal = j-SIGNUM, volume = "26", number = "4", pages = "2--3", month = oct, year = "1991", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Tue Apr 12 07:50:21 MDT 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", mynote = "Same as \cite{Stewart:1991:FTR} I think, but different title!", } @Article{Stewart:1991:FTR, author = "G. W. Stewart", title = "{FTPing} Technical Reports", journal = j-NA-DIGEST, volume = "91", number = "39", pages = "??--??", year = "1991", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "Electronic mail magazine: \path|na.help@na-net.ornl.gov|", acknowledgement = ack-nhfb, fjournal = "NA Digest", mynote = "Sunday, September 29, 1991", } @Article{Stewart:1991:JGP, author = "G. W. Stewart", title = "{Jeep}: A General Purpose Style File", journal = j-TEX-TUG-NEWS, volume = "0", number = "0", pages = "3--4", month = "????", year = "1991", ISSN = "1065-240X", bibdate = "Thu May 29 18:19:23 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://tug.ctan.org/tex-archive/digests/ttn/ttn0n0.tex", acknowledgement = ack-nhfb, fjournal = "{\TeX} and TUG News", GWS-number = "N28", } @TechReport{Stewart:1991:LLS, author = "G. W. Stewart", title = "{Lanczos} and linear systems", type = "Technical Report", number = "CS-TR 2641", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", year = "1991", bibdate = "Fri Jun 10 12:38:34 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "March", } @InProceedings{Stewart:1991:PTS, author = "G. W. Stewart", title = "Perturbation Theory for the Singular Value Decomposition", crossref = "Vaccaro:1991:SSP", pages = "99--109", year = "1991", bibdate = "Thu May 29 18:17:42 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N26", } @Article{Stewart:1991:TSR, author = "G. W. Stewart", title = "Two Simple Residual Bounds for the Eigenvalues of a {Hermitian} Matrix", journal = j-SIAM-J-MAT-ANA-APPL, volume = "12", number = "2", pages = "205--208", month = apr, year = "1991", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A42)", MRnumber = "92j:15007", bibdate = "Tue Jan 21 08:54:30 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J70", journal-URL = "http://epubs.siam.org/simax", mynote = "CS-TR-2364, Dec 89", } @TechReport{Bai:1992:SFS, author = "Zhaojun Bai and G. W. Stewart", title = "{SRRIT} --- A {FORTRAN} subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix", type = "Technical Report", number = "CS-TR-2908", institution = inst-U-MARYLAND, address = inst-U-MARYLAND:adr, pages = "25", month = may, year = "1992", bibdate = "Sat Jan 27 13:40:57 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/other/g-w-stewart.bib; Theory/Matrix.bib", note = "Also issued as University of Maryland Institute for Advanced Computer Studies UMIACS report TR-92-61", abstract = "SRRIT is a FORTRAN program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix A by the method of simultaneous iteration [12]. Specifically, given an integer m, SRRIT attempts to compute a matrix Q with m orthonormal columns and real quasi-triangular matrix T of order m such that the equation AQ=QT is satisfied up to a tolerance specified by the user. The eigenvalues of T are approximations to the m largest eigenvalues of A, and the columns of Q span the invariant subspace corresponding to those eigenvalues. SRRIT references A only through a user provided subroutine to form the product AQ; hence it is suitable for large sparse problems.", acknowledgement = ack-nhfb, keywords = "Matrices.; {Fortran} (Computer program language)", kwds = "nla, eig, subspace iteration, nonsymmetric matrix", } @InProceedings{Griffin:1992:MNU, author = "M. F. Griffin and E. C. Boman and G. W. Stewart", editor = "{IEEE}", title = "Minimum-norm updating with the rank-revealing {$ U R V $} decomposition", crossref = "IEEE:1992:III", pages = "293--296 (vol. 5)", year = "1992", DOI = "https://doi.org/10.1109/ICASSP.1992.226625", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=226625", acknowledgement = ack-nhfb, author-affiliation = "United Technologies Res. Center, East Hartford, CT, USA", book-DOI = "https://doi.org/10.1109/ICASSP.1992.226625", GWS-number = "N29", } @Article{Stewart:1992:EAQ, author = "G. W. Stewart", title = "Error Analysis of {$ Q R $} Updating with Exponential Windowing", journal = j-MATH-COMPUT, volume = "59", number = "199", pages = "135--140", month = jul, year = "1992", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F25 (65G05)", MRnumber = "92k:65074", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; JSTOR database; Theory/Matrix.bib", acknowledgement = ack-nhfb, classcodes = "B0290B (Error analysis in numerical methods); B0290H (Linear algebra); C4110 (Error analysis in numerical methods); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "Mathematics of Computation", GWS-number = "J74", journal-URL = "http://www.ams.org/mcom/", keywords = "algebra; algorithm; convergence of numerical methods; data; error analysis; exponential windowing; forgetting factor; matrix; new data; old; OR updating; QR factorization; rounding errors; unconditionally stable; updating", kwds = "nla, updating, qrd, rounding error", mynote = "Maryland CS-TR 2685, May 1991.", treatment = "T Theoretical or Mathematical", } @TechReport{Stewart:1992:NGS, author = "G. W. Stewart", title = "Note on a Generalized {Sylvester} Equation", type = "IMA Preprint Series", number = "\#985", institution = inst-IMA, address = inst-IMA:adr, pages = "3", month = may, year = "1992", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @Article{Stewart:1992:UAS, author = "G. W. Stewart", title = "An updating algorithm for subspace tracking", journal = j-IEEE-TRANS-SIG-PROC, volume = "40", number = "6", pages = "1535--1541", month = "????", year = "1992", CODEN = "ITPRED", DOI = "https://doi.org/10.1109/78.139256", ISSN = "1053-587X (print), 1941-0476 (electronic)", ISSN-L = "1053-587X", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=139256", acknowledgement = ack-nhfb, author-affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", book-DOI = "https://doi.org/10.1109/78.139256", fjournal = "IEEE Transactions on Signal Processing", GWS-number = "J73", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78", } @Article{Edelman:1993:SO, author = "Alan Edelman and G. W. Stewart", title = "Scaling for Orthogonality", journal = j-IEEE-TRANS-SIG-PROC, volume = "41", number = "4", pages = "1676--1677", month = "????", year = "1993", CODEN = "ITPRED", DOI = "https://doi.org/10.1109/78.212741", ISSN = "1053-587X (print), 1941-0476 (electronic)", ISSN-L = "1053-587X", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=212741", acknowledgement = ack-nhfb, author-affiliation = "Dept. of Math., California Univ., Berkeley, CA, USA", book-DOI = "https://doi.org/10.1109/78.212741", fjournal = "IEEE Transactions on Signal Processing", GWS-number = "J81", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78", } @InProceedings{Liu:1993:AEB, author = "K. J. R. Liu and D. P. O'Leary and G. W. Stewart and Y.-J. J. Wu", title = "An adaptive {ESPRIT} based on {$ U R V $} decomposition", crossref = "IEEE:2002:IIC", pages = "37--40 (vol. 4)", year = "1993", DOI = "https://doi.org/10.1109/ICASSP.1993.319588", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=319588", abstract = "ESPRIT is an algorithm for determining the fixed directions of arrival of a set of narrow-band signals at an array of sensors. Its computational burden makes it unsuitable for real-time processing of signals with time-varying directions of arrival. The authors develop a new implementation of ESPRIT that has potential for real-time processing. It is based on a rank-revealing URV decomposition, rather than the eigendecomposition or singular value decomposition (SVD) used in previous ESPRIT algorithms. Its performance is demonstrated on simulated data representing both constant and time-varying signals. It is shown that the URV-based ESPRIT algorithm is effective for estimating time-varying directions-of-arrival at considerable computational savings over the SVD-based algorithm.", acknowledgement = ack-nhfb, author-affiliation = "Maryland Univ., College Park, MD, USA", book-DOI = "https://doi.org/10.1109/ICASSP.1993.319588", book-isbn = "0-7803-7402-9", keywords = ", systems; adaptive, processing; algorithm; array, complexity; array, of, processing; computational, savings; computational, signal, systems; parameter, decomposition; performance; rank-revealing, sensors; real-time, ESPRIT, estimation; real-time, filters; time-varying, URV, URV-based", } @Article{Mathias:1993:BAS, author = "R. Mathias and G. W. Stewart", title = "A Block {$ Q R $} Algorithm and the Singular Value Decomposition", journal = j-LINEAR-ALGEBRA-APPL, volume = "182", pages = "91--100", day = "15", month = mar, year = "1993", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Jan 22 09:07:50 MST 1997", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J75", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, nla. pert, svd, QR algorithm", } @Article{Mathias:1993:BQA, author = "R. Mathias and G. W. Stewart", title = "A Block {$ Q R $} Algorithm and the Singular Value Decomposition", journal = j-LINEAR-ALGEBRA-APPL, volume = "188", pages = "91--100", year = "1993", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Schweitzer:1993:LEP, author = "Paul J. Schweitzer and G. W. Stewart", title = "The {Laurent} Expansion of Pencils That Are Singular at the Origin", journal = j-LINEAR-ALGEBRA-APPL, volume = "183", pages = "237--254", day = "1", month = apr, year = "1993", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Jan 22 09:07:50 MST 1997", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J76", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, gieg, Laurent expansion, Kronecker form, rank determination", } @Article{Stewart:1993:ASH, author = "G. W. Stewart", title = "{Alston Scott Householder} (1904--1993)", journal = j-SIAM-NEWS, volume = "26", number = "??", pages = "??--??", month = oct, year = "1993", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Thu Dec 20 09:47:38 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://archive.is/20130115033809/http://sites.uclouvain.be/HHXIX/AlstonHouseholder/#selection-215.0-215.36", acknowledgement = ack-nhfb, } @Article{Stewart:1993:BRB, author = "G. W. Stewart", title = "Book Review: {{\booktitle{Topics in Matrix Analysis}} (Roger A. Horn and Charles R. Johnson)}", journal = j-SIAM-REVIEW, volume = "35", number = "1", pages = "168--169", month = mar, year = "1993", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1035037", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:55:09 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/35/1; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "March 1993", } @InProceedings{Stewart:1993:DRP, author = "G. W. Stewart", title = "Determining Rank in the Presence of Error", crossref = "Moonen:1993:LAL", pages = "275--291", year = "1993", bibdate = "Thu May 29 18:44:24 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N32", } @Article{Stewart:1993:EHS, author = "G. W. Stewart", title = "On the Early History of the Singular Value Decomposition", journal = j-SIAM-REVIEW, volume = "35", number = "4", pages = "551--566", month = dec, year = "1993", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1035134", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "15-03 (01A55 01A60 15A18)", MRnumber = "94f:15001", bibdate = "Sat Mar 29 09:55:16 MDT 2014", bibsource = "Compendex database; http://epubs.siam.org/toc/siread/35/4; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", abstract = "This paper surveys the contributions of five mathematicians --- Eugenio Beltrami (1835-1899), Camille Jordan (1838-1921), James Joseph Sylvester (1814-1897), Erhard Schmidt (1876-1959), and Hermann Weyl (1885-1955) --- who were responsible for establishing the existence of the singular value decomposition and developing its theory.", acknowledgement = ack-nhfb, affiliation = "Univ of Maryland", affiliationaddress = "College Park, MD, USA", classification = "921.1; 921.6", fjournal = "SIAM Review", GWS-number = "J79", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "Algorithms; Computational platforms; Determinants; Geometry; History; Integral equations; Linear algebra; Matrix algebra; Matrix decomposition; Quadratic form; Singular value decomposition", mynote = "Maryland CS-TR 2855, March 92", onlinedate = "December 1993", remark = "See page 556 for Lanczos's contributions to the SVD.", } @InProceedings{Stewart:1993:GEP, author = "G. W. Stewart", title = "{Gaussian} Elimination, Perturbation Theory, and {Markov} Chains", crossref = "Meyer:1993:LAM", pages = "59--69", year = "1993", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, GWS-number = "N31", } @Article{Stewart:1993:PCF, author = "G. W. Stewart", title = "On the Perturbation of {$ L U $}, {Cholesky}, and {$ Q R $} Factorizations", journal = j-SIAM-J-MAT-ANA-APPL, volume = "14", number = "4", pages = "1141--1145", month = oct, year = "1993", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (65F35)", MRnumber = "94i:15007", MRreviewer = "Thomas L. Markham", bibdate = "Tue Jan 21 08:54:30 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J78", journal-URL = "http://epubs.siam.org/simax", } @Article{Stewart:1993:PMC, author = "G. W. Stewart", title = "On the perturbation of {Markov} chains with nearly transient states", journal = j-NUM-MATH, volume = "65", number = "1", pages = "135--141", month = may, year = "1993", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "15A51 (60J10 65J10)", MRnumber = "94d:15021", bibdate = "Thu Jan 23 07:49:52 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J80", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1993:URR, author = "G. W. Stewart", title = "Updating a Rank-Revealing {$ U L V $} Decomposition", journal = j-SIAM-J-MAT-ANA-APPL, volume = "14", number = "2", pages = "494--499", month = apr, year = "1993", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F05", MRnumber = "93m:65039", bibdate = "Tue Jan 21 08:54:30 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J77", journal-URL = "http://epubs.siam.org/simax", mynote = "Maryland CS-TR 2627, March 1991", } @Article{Liu:1994:UET, author = "K. J. R. Liu and D. P. O'Leary and G. W. Stewart and Y.-J. J. Wu", title = "{$ U R V $} {ESPRIT} for tracking time-varying signals", journal = j-IEEE-TRANS-SIG-PROC, volume = "42", number = "12", pages = "3441--3448", month = "????", year = "1994", CODEN = "ITPRED", DOI = "https://doi.org/10.1109/78.340778", ISSN = "1053-587X (print), 1941-0476 (electronic)", ISSN-L = "1053-587X", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=340778", abstract = "ESPRIT is an algorithm for determining the fixed directions of arrival of a set of narrow-band signals at an array of sensors. Unfortunately, its computational burden makes it unsuitable for real time processing of signals with time-varying directions of arrival. The authors develop a new implementation of ESPRIT that has potential for real time processing. It is based on a rank-revealing URV decomposition, rather than the eigendecomposition or singular value decomposition used in previous ESPRIT algorithms. The authors demonstrate its performance on simulated data representing both constant and time-varying signals. They find that the URV-based ESPRIT algorithm is effective for estimating time-varying directions-of-arrival at considerable computational savings over the SVD-based algorithm", acknowledgement = ack-nhfb, author-affiliation = "Dept. of Electr. Eng., Maryland Univ., College Park, MD, USA", book-DOI = "https://doi.org/10.1109/78.340778", fjournal = "IEEE Transactions on Signal Processing", GWS-number = "J85", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78", keywords = "arrival; direction-of-arrival, systems; fixed, estimation; narrow-band, decomposition; performance; rank-revealing, signals; real, directions, ESPRIT; real-time, of, processing; TIME, URV; time-varying, signals; time-varying, systems; tracking", } @Article{Stewart:1994:CMI, author = "G. W. Stewart", title = "On the Convergence of Multipoint Iterations", journal = j-NUM-MATH, volume = "68", number = "1", pages = "143--147", month = jun, year = "1994", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65H05", MRnumber = "95a:65088", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://link.springer.de/link/service/journals/00211/bibs/4068001/40680143.htm; http://science.springer.de/nmee/bibs/4068001/40680143.htm", acknowledgement = ack-nhfb, classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "Numerische Mathematik", GWS-number = "J83", journal-URL = "http://link.springer.com/journal/211", keywords = "convergence of numerical methods; convergence proof; fixed point; iterative methods; multipoint iterations", treatment = "T Theoretical or Mathematical", } @InProceedings{Stewart:1994:D, author = "G. W. Stewart", title = "{$ U T V $} Decompositions", crossref = "Griffiths:1994:NAP", pages = "225--236", year = "1994", bibdate = "Thu May 29 19:00:58 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N34", } @TechReport{Stewart:1994:GQD, author = "G. W. Stewart", title = "On Graded {$ Q R $} Decompositions of Products of Matrices", type = "Technical Report", number = "TR-3263", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "14", month = apr, year = "1994", bibdate = "Sun Feb 26 11:51:53 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @TechReport{Stewart:1994:GSG, author = "G. W. Stewart", title = "Gauss, Statistics, and {Gaussian} Elimination", type = "Technical Report", number = "TR-3307", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "14", month = aug, year = "1994", bibdate = "Sun Oct 16 17:23:56 GMT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @InProceedings{Stewart:1994:LLS, author = "G. W. Stewart", title = "{Lanczos} and linear systems", crossref = "Brown:1994:PCL", pages = "135--139", year = "1994", bibdate = "Sat Jun 11 17:22:09 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; MathSciNet database", acknowledgement = ack-nhfb, GWS-number = "N30", xxpages = "134--139", } @TechReport{Stewart:1994:MCS, author = "G. W. Stewart", title = "On {Markov} Chains with Sluggish Transients", type = "Technical Report", number = "TR-3306", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "8", month = jun, year = "1994", bibdate = "Sun Oct 16 17:33:10 GMT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @Article{Stewart:1994:PTR, author = "G. W. Stewart", title = "Perturbation Theory for Rectangular Matrix Pencils", journal = j-LINEAR-ALGEBRA-APPL, volume = "208/209", pages = "297--301", year = "1994", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A22 (15A18 15A42)", MRnumber = "95f:15013", MRreviewer = "Gerd M. Krause", bibdate = "Wed Jan 22 17:57:24 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J84", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @TechReport{Stewart:1994:SSU, author = "G. W. Stewart", title = "On the Stability of Sequential Updates and Downdates", type = "Technical Report", number = "TR-3238", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "17", month = mar, year = "1994", bibdate = "Sun Feb 26 11:51:53 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @InProceedings{Stewart:1994:TSI, author = "G. W. Stewart and W. J. Stewart and D. F. McAllister", title = "A Two-Stage Iteration for Solving Nearly Completely Decomposable {Markov} Chains", crossref = "Golub:1994:RAI", pages = "201--216", year = "1994", bibdate = "Thu May 29 18:57:02 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N33", } @Article{Stewart:1994:UUD, author = "G. W. Stewart", title = "Updating {$ U R V $} decompositions in parallel", journal = j-PARALLEL-COMPUTING, volume = "20", number = "2", pages = "151--172", day = "24", month = feb, year = "1994", CODEN = "PACOEJ", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", bibdate = "Fri Aug 6 10:13:56 MDT 1999", bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/parco/cas_free/browse/browse.cgi?year=1994&volume=20&issue=2; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib", URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/parco/cas_sub/browse/browse.cgi?year=1994&volume=20&issue=2&aid=828", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra); C4240P (Parallel programming and algorithm theory)", corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", fjournal = "Parallel Computing", GWS-number = "J82", journal-URL = "http://www.sciencedirect.com/science/journal/01678191/", keywords = "$URV$ decomposition; linear array of processors; matrix algebra; parallel algorithms; unitary matrix; upper triangular matrix", treatment = "T Theoretical or Mathematical", } @TechReport{vonMatt:1994:RES, author = "Urs von Matt and G. W. Stewart", title = "Rounding Errors in Solving Block {Hessenberg} Systems", type = "Technical Report", number = "TR-3345", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, pages = "????", month = sep, year = "1994", bibdate = "Sun Oct 16 17:35:06 GMT 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @Book{Gauss:1995:TCO, author = "Carl Friedrich Gauss and G. W. (Gilbert W.) Stewart", title = "Theory of the combination of observations least subject to error: part one, part two, supplement = {Theoria} combinationis observationum erroribus minimus obnoxiae: pars prior, pars posterior, supplementum", volume = "11", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xi + 241", year = "1995", ISBN = "0-89871-347-1 (paperback)", ISBN-13 = "978-0-89871-347-3 (paperback)", LCCN = "QA275 .G37313 1995", bibdate = "Thu May 29 07:41:49 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", note = "Translation by G. W. Stewart of Gauss' classic works.", series = "Classics in applied mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy0739/95006589-d.html; http://www.loc.gov/catdir/enhancements/fy0739/95006589-t.html", abstract = "In the 1820s Gauss published two memoirs on least squares, which contain his final, definitive treatment of the area along with a wealth of material on probability, statistics, numerical analysis, and geodesy. These memoirs, originally published in Latin with German Notices, have been inaccessible to the English-speaking community. Here for the first time they are collected in an English translation. For scholars interested in comparisons the book includes the original text and the English translation on facing pages. More generally the book will be of interest to statisticians, numerical analysts, and other scientists who are interested in what Gauss did and how he set about doing it. An Afterword by the translator, G. W. Stewart, places Gauss's contributions in historical perspective.", acknowledgement = ack-nhfb, author-dates = "1777--1855", GWS-number = "B4", subject = "Error analysis (Mathematics); Th{\'e}orie des erreurs; Least squares; Error analysis (Mathematics); Least squares.", tableofcontents = "Pars prior / Part one \\ \\ Random and regular errors in observations \\ Regular errors excluded \\ Their treatment \\ General properties of random errors \\ The distribution of the error \\ The constant part or mean value of the error \\ The mean square error as a measure of uncertainty \\ Mean error, weight and precision \\ Effect of removing the constant part \\ Interpercentile ranges and probable error \\ properties of the uniform, triangular, and normal distribution \\ Inequalities relating the mean error and interpercentile ranges \\ The fourth moments of the uniform, triangular, and normal distributions \\ The distribution of a function of several errors \\ The mean value of a function of several errors \\ Some special cases \\ Convergence of the estimate of the mean error \\ The mean error of the estimate itself \\ The mean error of the estimate for the mean value \\ Combining errors with different weights \\ Overdetermined systems of equations \\ The problem of obtaining the unknowns as combinations of observations \\ The principle of least squares \\ The mean error of a function of quantities with errors \\ The regression model \\ The best combination for estimating the first unknown \\ The weight of the estimate \\ Estimates of the remaining unknowns and their weights \\ Justification of the principle of least squares \\ The case of a single unknown \\ The arithmetic mean \\ \\ Pars posterior / Part two \\ \\ Existence of the least squares estimates \\ Relation between combinations for different unknowns \\ A formula for the residual sum of squares \\ Another formula for the residual sum of squares \\ Four formulas for the residual sum of squares as a function of the unknowns \\ Errors in the least squares estimates as functions of the errors in the observations \\ Mean errors and correlations \\ Linear functions of the unknowns \\ Least squares with a linear constraint \\ Review of Gaussian elimination \\ Abbreviated computation of the weights of the unknowns \\ Computational details \\ Abbreviated computation of the weight of a linear function of the unknowns \\ Updating the unknowns and their weights when a new observation is added to the system \\ Updating the unknowns and their weights when the weight of an observation changes \\ A bad formula for estimating the errors in the observations from the residual sum of squares \\ The correct formula \\ The mean error of the residual sum of squares \\ Inequalities for the mean error of the residual sum of squares \\ The case of the normal distribution \\ \\ Supplementum / Supplement \\ \\ Problems having constraints on the observations: reduction to an ordinary least squares problem \\ Functions of the observations, their mean errors \\ Estimating a function of observations that are subject to constraints \\ Characterization of permissible estimates \\ The function that gives the most reliable estimate \\ The value of the most reliable estimate \\ Four formulas for the weight of the value of the estimate \\ The case of more than one function \\ The most reliable adjustments of the observations and their use in estimation \\ Least squares characterization of the most reliable adjustment \\ Difficulties in determining weights \\ A better method \\ Computational details \\ Existence of the estimates \\ Estimating the mean error in the observations \\ Estimating the mean error in the observations, continued \\ The mean error in the estimate \\ Incomplete adjustment of observations \\ Relation between complete and incomplete adjustments \\ A block iterative method for adjusting observations \\ The inverse of a symmetric system is a symmetric [matrix??] \\ Fundamentals of geodesy \\ De Krayenhof's triangulation \\ A triangulation from Hannover \\ Determining weights in the Hannover triangulation \\ Anzeigen / Notices: Part one, part two, supplement \\ Afterword \\ Gauss's schooldays \\ Legendre and the priority controversy \\ Beginnings: Mayer, Boscovich and Laplace \\ Gauss and Laplace \\ The theoria motus \\ Laplace and the central limit theorem \\ The Theoria Combinationis Observationum \\ The precision of observations \\ The combination of observations \\ The inversion of linear systems \\ Gaussian elimination and numerical linear algebra \\ The generalized minimum variance theorem \\ References", } @InProceedings{Latouche:1995:NMM, author = "G. Latouche and G. W. Stewart", title = "Numerical Methods for {M/G/1} Type Queues", crossref = "Stewart:1995:CMC", pages = "571--581", year = "1995", bibdate = "Thu May 29 19:15:59 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N35", } @Article{Stewart:1995:GQD, author = "G. W. Stewart", title = "On graded {$ Q R $} decompositions of products of matrices", journal = j-ELECTRON-TRANS-NUMER-ANAL, volume = "3", pages = "39--49", year = "1995", CODEN = "????", ISSN = "1068-9613 (print), 1097-4067 (electronic)", ISSN-L = "1068-9613", bibdate = "Mon Sep 6 12:28:29 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/etna.bib", URL = "http://etna.mcs.kent.edu/vol.3.1995/pp39-49.dir/pp39-49.pdf", abstract = "This paper is concerned with the singular values and vectors of a product $ M_m = A_1 A_2 \cdots A_m $ of matrices of order $n$. The chief difficulty with computing them directly from $ M_m$ is that with increasing $m$ the ratio of the small to the large singular values of $ M_m$ may fall below the rounding unit, so that the former are computed inaccurately. The solution proposed here is to compute recursively the factorization $ M_m = Q R P T$, where $Q$ is orthogonal, $R$ is a graded upper triangular, and $ P T$ is a permutation.", acknowledgement = ack-nhfb, fjournal = "Electronic Transactions on Numerical Analysis", GWS-number = "J89", journal-URL = "http://etna.mcs.kent.edu/", } @Article{Stewart:1995:GSG, author = "G. W. Stewart", title = "{Gauss}, Statistics, and {Gaussian} Elimination", journal = j-J-COMPUT-GRAPH-STAT, volume = "4", number = "1", pages = "1--11", month = mar, year = "1995", CODEN = "????", DOI = "https://doi.org/10.2307/1390624", ISSN = "1061-8600 (print), 1537-2715 (electronic)", ISSN-L = "1061-8600", MRclass = "01A55 (62J05 65-03 65F05)", MRnumber = "95k:01020", bibdate = "Mon May 5 08:43:28 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/jcomputgraphstat.bib", URL = "http://www.jstor.org/stable/1390624", abstract = "Gaussian elimination is the algorithm of choice for the solution of dense linear systems of equations. However, Gauss himself originally introduced his elimination procedure as a way of determining the precision of least squares estimates and only later described the computational algorithm. This article tells the story of Gauss, his algorithm, and its relation to his probabilistic development of least squares.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Graphical Statistics", GWS-number = "J88", journal-URL = "http://www.tandfonline.com/loi/ucgs20", } @TechReport{Stewart:1995:IMS, author = "G. W. Stewart", title = "An Iterative Method for Solving Linear Inequalities", number = "CS-TR-1833", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, day = "6", month = feb, year = "1995", bibdate = "Fri May 30 08:12:21 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/355", abstract = "This paper describes and analyzes a method for finding nontrivial solutions of the inequality $ A x \geq 0 $, where $A$ is an $ m \times n$ matrix of rank $n$. The method is based on the observation that a certain function $f$ has a unique minimum if and only if the inequality {\em fails to have} a nontrivial solution. Moreover, if there is a solution, an attempt to minimize $f$ will produce a sequence that will diverge in a direction that converges to a solution of the inequality. The technique can also be used to solve inhomogeneous inequalities and hence linear programming problems, although no claims are made about competitiveness with existing methods.", acknowledgement = ack-nhfb, keywords = "Technical Report", } @TechReport{Stewart:1995:PSC, author = "G. W. Stewart", title = "On the perturbation of {Schur} complement in positive semidefinite matrix", number = "TR-95-38", institution = inst-UMIACS, address = inst-UMIACS:adr, year = "1995", bibdate = "Fri May 30 07:58:52 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", abstract = "This note gives perturbation bounds for the Schur complement of a positive definite matrix in a positive semidefinite matrix.", acknowledgement = ack-nhfb, } @Article{Stewart:1995:SBH, author = "G. W. Stewart", title = "On the solution of block {Hessenberg} systems", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "3", pages = "287--296", year = "1995", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.1680020309", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65F30", MRnumber = "96a:65069", bibdate = "Thu Jan 23 18:22:28 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/nla.1680020309/abstract", abstract = "This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the Fast Fourier Transform.", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", GWS-number = "J86", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", keywords = "block Hessenberg matrix, Block Toeplitz matrix, linear system, queue", } @Article{Stewart:1995:SSU, author = "G. W. Stewart", title = "On the stability of sequential updates and downdates", journal = j-IEEE-TRANS-SIG-PROC, volume = "43", number = "11", pages = "2642--2648", month = "????", year = "1995", CODEN = "ITPRED", DOI = "https://doi.org/10.1109/78.482114", ISSN = "1053-587X (print), 1941-0476 (electronic)", ISSN-L = "1053-587X", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=482114", abstract = "The updating and downdating of Cholesky decompositions has important applications in a number of areas. There is essentially one standard updating algorithm, based on plane rotations, which is backward stable. Three downdating algorithms have been treated in the literature: the LINPACK algorithm, the method of hyperbolic transformations, and Chambers' (1971) algorithm. Although none of these algorithms is backward stable, the first and third satisfy a relational stability condition. It is shown that relational stability extends to a sequence of updates and downdates. In consequence, other things being equal, if the final decomposition in the sequence is well conditioned, it will be accurately computed, even though intermediate decompositions may be almost completely inaccurate. These results are also applied to the two-sided orthogonal decompositions, such as the URV decomposition", acknowledgement = ack-nhfb, author-affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", book-DOI = "https://doi.org/10.1109/78.482114", fjournal = "IEEE Transactions on Signal Processing", GWS-number = "J87", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78", keywords = "algorithm; backward, decomposition; Cholesky, algorithm; downdating, algorithm; error, algorithm; hyperbolic, analysis; LINPACK, decompositions; matrix, analysis; matrix, updates; numerical, decomposition; orthogonal, rotations; plane, decompositions; relational, stability, stability; rounding, decomposition; roundoff, stable, transformations; sequences; sequential, Chambers', condition; sequential, error, errors; stability; two-sided; updating, downdates; URV, algorithms", } @Article{Chang:1996:NPA, author = "{Xiao-Wen} Chang and Christopher C. Paige and G. W. Stewart", title = "New Perturbation Analyses for the {Cholesky} Factorization", journal = j-IMA-J-NUMER-ANAL, volume = "16", number = "4", pages = "457--484", month = oct, year = "1996", CODEN = "IJNADH", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30", MRnumber = "97g:65089", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; http://www3.oup.co.uk/imanum/hdb/Volume_16/Issue_04/; MathSciNet database", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_16/Issue_04/160457.sgm.abs.html", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", GWS-number = "J91", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Book{Stewart:1996:ANA, author = "G. W. (Gilbert W.) Stewart", title = "Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the {University of Maryland at College Park} and recorded after the fact", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "x + 200", year = "1996", DOI = "https://doi.org/10.1137/1.9781611971491", ISBN = "0-89871-362-5 (paperback)", ISBN-13 = "978-0-89871-362-6 (paperback)", LCCN = "QA297 .S785 1996", MRclass = "65-01", MRnumber = "1372060", bibdate = "Tue May 27 08:35:41 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html; http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html", acknowledgement = ack-nhfb, GWS-number = "B5", keywords = "numerical analysis", subject = "Numerical analysis", tableofcontents = "Part I. Nonlinear Equations \\ \\ Lecture 1. By the Dawn's Early Light \\ Interval Bisection \\ Relative Error \\ \\ Lecture 2. Newton's Method \\ Reciprocals and Square Roots \\ Local Convergence Analysis \\ Slow Death \\ \\ Lecture 3. A Quasi-Newton Method \\ Rates of Convergence \\ Iterating for a Fixed Point \\ Multiple Zeros \\ Ending with a Proposition \\ \\ Lecture 4. The Secant Method \\ Convergence \\ Rate of Convergence \\ Multipoint Methods \\ Muller's Method \\ The Linear-Fractional Method \\ \\ Lecture 5. A Hybrid Method \\ Errors, Accuracy, and Condition Numbers \\ \\ Part II. Computer Arithmetic: \\ \\ \\ Lecture 6. Floating-Point Numbers \\ Overflow and Underflow \\ Rounding Error \\ Floating-point Arithmetic \\ \\ Lecture 7. Computing Sums \\ Backward Error Analysis \\ Perturbation Analysis \\ Cheap and Chippy Chopping \\ \\ Lecture 8. Cancellation \\ The Quadratic Equation \\ That Fatal Bit of Rounding Error \\ Envoi \\ \\ Part III. Linear Equations \\ \\ \\ Lecture 9. Matrices, Vectors, and Scalars \\ Operations with Matrices \\ Rank-One Matrices \\ Partitioned Matrices \\ \\ Lecture 10. Theory of Linear Systems \\ Computational Generalities \\ Triangular Systems \\ Operation Counts \\ \\ Lecture 11. Memory Considerations \\ Row Oriented Algorithms \\ A Column Oriented Algorithm \\ General Observations on Row and Column Orientation \\ Basic Linear Algebra Subprograms \\ \\ Lecture 12. Positive Definite Matrices \\ The Cholesky Decomposition \\ Economics \\ \\ Lecture 13. Inner-Product Form of the Cholesky Algorithm \\ Gaussian Elimination \\ \\ Lecture 14. Pivoting \\ BLAS \\ Upper Hessenberg and Tridiagonal Systems \\ \\ Lecture 15. Vector Norms \\ Matrix Norms \\ Relative Error \\ Sensitivity of Linear Systems \\ \\ Lecture 16. The Condition of Linear Systems \\ Artificial Ill Conditioning \\ Rounding Error and Gaussian Elimination \\ Comments on the Analysis \\ \\ Lecture 17. The Wonderful Residual: A Project \\ Introduction \\ More on Norms \\ The Wonderful Residual \\ Matrices with Known Condition \\ Invert and Multiply \\ Cramer's Rule \\ Submission \\ \\ Part IV. Polynomial Interpolation \\ \\ \\ Lecture 18. Quadratic Interpolation \\ Shifting \\ Polynomial Interpolation \\ Lagrange Polynomials and Existence \\ Uniqueness \\ \\ Lecture 19. Synthetic Division \\ The Newton Form of the Interpolant \\ Evaluation \\ Existence \\ Divided Differences \\ \\ Lecture 20. Error in Interpolation \\ Error Bounds \\ Convergence \\ Chebyshev Points \\ \\ Part V. Numerical Integration and Differentiation \\ \\ \\ Lecture 21. Numerical Integration \\ Change of Intervals \\ The Trapezoidal Rule \\ The Composite Trapezoidal Rule \\ Newton-Cotes Formulas \\ Undetermined Coefficients and Simpson's Rule \\ \\ Lecture 22. The Composite Simpson's Rule \\ Errors in Simpson's Rule \\ Weighting Functions \\ Gaussian Quadrature \\ \\ Lecture 23. The Setting \\ Orthogonal Polynomials \\ Existence \\ Zeros of Orthogonal Polynomials \\ Gaussian Quadrature \\ Error and Convergence \\ Examples \\ \\ Lecture 24. Numerical Differentiation and Integration \\ Formulas From Power Series \\ Limitations \\ Bibliography", } @Article{vonMatt:1996:RES, author = "Urs {von Matt} and G. W. Stewart", title = "Rounding errors in solving block {Hessenberg} systems", journal = j-MATH-COMPUT, volume = "65", number = "213", pages = "115--135", month = jan, year = "1996", CODEN = "MCMPAF", DOI = "https://doi.org/10.1090/S0025-5718-96-00667-9", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F05 (65G05)", MRnumber = "96e:65019", MRreviewer = "Alfonso Laratta", bibdate = "Fri Jul 16 10:38:30 MDT 1999", bibsource = "http://www.ams.org/mcom/1996-65-213; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/", abstract = "A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra); C1110 (Algebra); C4240 (Programming and algorithm theory)", fjournal = "Mathematics of Computation", GWS-number = "J90", journal-URL = "http://www.ams.org/mcom/", keywords = "algebra; algorithm; algorithm theory; block diagonally dominant; block Hessenberg; block Hessenberg system; divide and conquer methods; divide-and-conquer; linear; linear system solution; linear systems; M-matrices; matrices; matrix algebra; rounding error analysis; rounding errors; solution; stable solution", treatment = "T Theoretical or Mathematical", } @Article{Bai:1997:ASF, author = "Z. Bai and G. W. Stewart", title = "{Algorithm 776}. {SRRIT} --- a {FORTRAN} Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix", journal = j-TOMS, volume = "23", number = "4", pages = "494--513", month = dec, year = "1997", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/279232.279234", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p494-bai/", abstract = "SRRIT is a Fortran program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix $A$ by the method of simultaneous iteration. Specifically, given an integer $m$, SRRIT computes a matrix $Q$ with $m$ orthonormal columns and real quasi-triangular matrix $T$ of order $m$ such that the equation $ A Q = Q T $ is satisfied up to a tolerance specified by the user. The eigenvalues of $T$ are approximations to the $m$ eigenvalues of largest absolute magnitude of $A$, and the columns of $Q$ span the invariant subspace corresponding to those eigenvalues. SRRIT references $A$ only through a user-provided subroutine to form the product $ A Q $; hence it is suitable for large sparse problems.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr # " and " # ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J96", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "algorithms, invariant subspace, nonsymmetric eigenvalue problem, project method", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing.", } @Article{Chang:1997:PAF, author = "Xiao-Wen Chang and Christopher C. Paige and G. W. Stewart", title = "Perturbation Analyses for the {$ Q R $} Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "18", number = "3", pages = "775--791", month = jul, year = "1997", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479896297720", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F35 (15A23)", MRnumber = "1 453 550", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/18/3; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/29772", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Chang:1997:PAQ, author = "Xiao-Wen Chang and Christopher C. Paige and G. W. Stewart", title = "Perturbation Analyses for the {$ Q R $} Factorization", journal = j-SIAM-J-MAT-ANA-APPL, volume = "18", number = "3", pages = "775--791", year = "1997", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J93", journal-URL = "http://epubs.siam.org/simax", } @Article{Stewart:1997:BRA, author = "G. W. Stewart", title = "Book Review: {Accuracy and Stability of Numerical Algorithms}, by {Nicholas J. Higham}", journal = j-SIAM-REVIEW, volume = "39", number = "1", pages = "164--166", month = mar, year = "1997", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Tue May 13 16:55:17 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib; http://www.siam.org/journals/sirev/sirev391.htm", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @InProceedings{Stewart:1997:EVN, author = "G. W. Stewart", title = "Errors in Variables for Numerical Analysts", crossref = "vanHuffel:1997:RAT", pages = "3--10", year = "1997", bibdate = "Fri May 30 05:53:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, GWS-number = "N36", } @Article{Stewart:1997:MCS, author = "G. W. Stewart", title = "On {Markov} Chains with Sluggish Transients", journal = j-STOCH-MODELS, volume = "13", pages = "85--95", year = "1997", CODEN = "CSSME8", DOI = "https://doi.org/10.1080/15326349708807414", ISSN = "1532-6349 (print), 1532-4214 (electronic)", ISSN-L = "1532-6349", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib", abstract = "In this note it is shown how to construct a Markov chain whose subdominant eigenvalue does not predict the decay of its transient", acknowledgement = ack-nhfb, fjournal = "Stochastic Models", GWS-number = "J95", journal-URL = "http://www.tandfonline.com/loi/lstm19", xxpages = "85--94", } @Article{Stewart:1997:PCF, author = "G. W. Stewart", title = "On the Perturbation of {$ L U $} and {Cholesky} Factors", journal = j-IMA-J-NUMER-ANAL, volume = "17", number = "1", pages = "1--6", month = jan, year = "1997", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/17.1.1", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30", MRnumber = "97m:65090", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_01/; MathSciNet database", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_01/170001.sgm.abs.html", abstract = "In a recent paper, Chang and Paige have shown that the usual perturbation bounds for Cholesky factors can systematically overestimate the errors. In this note we sharpen their results and extend them to the factors of the LU decomposition. The results are based on a new formula for the first-order terms of the error in the factors.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", GWS-number = "J92", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Stewart:1997:TMG, author = "G. W. Stewart", title = "The Triangular Matrices of {Gaussian} Elimination and Related Decompositions", journal = j-IMA-J-NUMER-ANAL, volume = "17", number = "1", pages = "7--16", month = jan, year = "1997", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/17.1.7", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F30", MRnumber = "97i:65076", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_01/; MathSciNet database", URL = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_01/170007.sgm.abs.html", abstract = "It has become commonplace that triangular systems are solved to higher accuracy than their condition would warrant. This observation is not true in general, and counterexamples are easy to construct. However, it is often true of the triangular matrices from pivoted $ L U $ or $ Q R $ decompositions. It is shown that this fact is closely connected with the rank-revealing character of these decompositions.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", GWS-number = "J94", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Stewart:1997:WML, author = "G. W. Stewart", title = "On the weighting method for least squares problems with linear equality constraints", journal = j-BIT-NUM-MATH, volume = "37", number = "4", pages = "961--967", month = dec, year = "1997", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF02510363", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65F20", MRnumber = "98g:65035", bibdate = "Fri Nov 13 07:00:34 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://www.mai.liu.se/BIT/contents/bit37.html", abstract = "The weighting method for solving a least squares problem with linear equality constraints multiplies the constraints by a large number and appends them to the top of the least squares problem, which is then solved by standard techniques. In this paper we give a new analysis of the method, based on the QR decomposition, that exhibits many features of the algorithm. In particular it suggests a natural criterion for choosing the weighting factor.", acknowledgement = ack-nhfb, fjournal = "BIT Numerical Mathematics", GWS-number = "J97", journal-URL = "http://link.springer.com/journal/10543", } @InProceedings{Boisvert:1998:DNLa, author = "Ronald F. Boisvert and Jack J. Dongarra and Roldan Pozo and Karin A. Remington and G. W. Stewart", title = "Developing numerical libraries in {Java}", crossref = "ACM:1998:AWJ", pages = "??--??", year = "1998", bibdate = "Thu Apr 27 10:43:08 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/java.bib; https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib", URL = "http://www.cs.ucsb.edu/conferences/java98/papers/jnt.pdf; http://www.cs.ucsb.edu/conferences/java98/papers/jnt.ps; http://www.netlib.org/utk/people/JackDongarra/PAPERS/jnt.ps; http://www.netlib.org/utk/people/JackDongarra/pdf/jnt.pdf", acknowledgement = ack-nhfb, } @Article{Boisvert:1998:DNLb, author = "Ronald F. Boisvert and Jack J. Dongarra and Roldan Pozo and Karin A. Remington and G. W. Stewart", title = "Developing numerical libraries in {Java}", journal = j-CPE, volume = "10", number = "11--13", pages = "1117--1129", month = sep, year = "1998", CODEN = "CPEXEI", DOI = "https://doi.org/10.1002/(SICI)1096-9128(199809/11)10:11/13<1117::AID-CPE386>3.3.CO;2-9", ISSN = "1040-3108 (print), 1096-9128 (electronic)", ISSN-L = "1040-3108", bibdate = "Tue Sep 7 06:06:44 MDT 1999", bibsource = "http://www.interscience.wiley.com/jpages/1040-3108/; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/cpe.bib; https://www.math.utah.edu/pub/tex/bib/java.bib; http://www3.interscience.wiley.com/journalfinder.html", note = "Special Issue: Java for High-performance Network Computing.", URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=10050395; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=10050395&PLACEBO=IE.pdf", acknowledgement = ack-nhfb, fjournal = "Concurrency, practice and experience", GWS-number = "J101", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291532-0634/issues", } @Article{Oleary:1998:CNR, author = "D. P. Oleary and G. W. Stewart", title = "On the convergence of a new {Rayleigh} quotient method with applications to large eigenproblems", journal = j-ELECTRON-TRANS-NUMER-ANAL, volume = "7", pages = "182--189", year = "1998", CODEN = "????", ISSN = "1068-9613 (print), 1097-4067 (electronic)", ISSN-L = "1068-9613", bibdate = "Mon Sep 6 12:28:29 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/etna.bib", note = "Large scale eigenvalue problems (Argonne, IL, 1997)", URL = "http://etna.mcs.kent.edu/vol.7.1998/pp182-189.dir/pp182-189.pdf", acknowledgement = ack-nhfb, fjournal = "Electronic Transactions on Numerical Analysis", journal-URL = "http://etna.mcs.kent.edu/", } @TechReport{Roginsky:1998:TDE, author = "Jacob Roginsky and G. W. Stewart", title = "Time-Domain Extraction of Broad-Band Sources by {Tikhonov--Phillips} Regularization of Triangular {Toeplitz} Kernels", type = "Technical Report", number = "UMIACS-TR-95-87", institution = inst-UMIACS, address = inst-UMIACS:adr, day = "15", month = oct, year = "1998", bibdate = "Fri May 30 07:42:32 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/755", abstract = "Single receiver source deconvolution in a shallow-water environment is an ill-posed problem whose difficulty is compounded by the multipath nature of the propagation operator. If only sources that are quiescent prior to some initial time to are considered, the result of discretizing the problem in the time domain is an ill-conditioned triangular Toeplitz system. In this paper we show how an algorithm of Elden can be used to implement Tikhonov--Phillips regularization for this system. Unlike the multichannel deconvolution techniques used in underwater acoustics, this method can extract source signatures using the outputs of a single sensor. In addition, when the propagation is multipath and source signature extraction is performed as part of an optimization procedure for environmental inversion, we can work with shorter time windows so that the process becomes computationally more efficient than frequency domain deconvolution. A number of examples of the use of the Tikhonov--Phillips regularization method for source series extraction are provided. (Also cross-referenced as UMIACS-TR-95-87).", acknowledgement = ack-nhfb, } @Book{Stewart:1998:AGG, author = "G. W. (Gilbert W.) Stewart", title = "Afternotes goes to graduate school: lectures on advanced numerical analysis", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xii + 245", year = "1998", DOI = "https://doi.org/10.1137/1.9781611971422", ISBN = "0-89871-404-4 (paperback)", ISBN-13 = "978-0-89871-404-3 (paperback)", LCCN = "QA297 .S784 1998", MRclass = "65-01", MRnumber = "1613128 (98m:65004)", bibdate = "Fri Nov 16 09:49:25 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager", note = "A series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact.", URL = "http://www.loc.gov/catdir/enhancements/fy0726/97044449-d.html; http://www.loc.gov/catdir/enhancements/fy0726/97044449-t.html", acknowledgement = ack-nhfb, GWS-number = "B6", subject = "Numerical analysis", tableofcontents = "Part I. Approximation \\ Lecture 1. General observations \\ Decline and fall \\ The linear sine \\ Approximation in normed linear spaces \\ Significant differences \\ Lecture 2. The space $C[0,1]$ \\ Existence of best approximations \\ Uniqueness of best approximations \\ Convergence in $C[0,1]$ \\ The Weierstrass approximation theorem \\ Bernstein polynomials \\ Comments \\ Lecture 3. Chebyshev approximation \\ Uniqueness \\ Convergence of Chebyshev approximations \\ Rates of convergence \\ Part II. Linear and Cubic Splines \\ Lecture 10. Piecewise linear interpolation \\ The error in $L(f)$ \\ Approximations in the $\infty$-norm \\ Hat functions \\ Integration \\ Least squares approximation \\ Implementations issues \\ Lecture 11. Cubic splines \\ Derivation of the cubic spline \\ End conditions \\ Convergence \\ Locality \\ Part III. Eigensystems \\ Part IV. Krylov Sequence Methods \\ Part V. Iterations, Linear and Nonlinear", } @Article{Stewart:1998:AM, author = "G. W. Stewart", title = "On the Adjugate Matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "283", number = "1--3", pages = "151--164", day = "1", month = nov, year = "1998", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri May 28 09:34:24 MDT 1999", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1998/283/1-3/6217.pdf; http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1998&volume=283&issue=1-3&aid=6217", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J100", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Stewart:1998:HTS, author = "Michael Stewart and G. W. Stewart", title = "On Hyperbolic Triangularization: Stability and Pivoting", journal = j-SIAM-J-MAT-ANA-APPL, volume = "19", number = "4", pages = "847--860", month = oct, year = "1998", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479897319581", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31958", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Book{Stewart:1998:MAV, author = "G. W. (Gilbert W.) Stewart", title = "Matrix algorithms. Volume 1. Basic decompositions", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xix + 458", year = "1998", DOI = "https://doi.org/10.1137/1.9781611971408", ISBN = "0-89871-414-1", ISBN-13 = "978-0-89871-414-2", LCCN = "QA188 .S714 1998", MRclass = "65-01 (65Fxx)", MRnumber = "1653546", bibdate = "Tue May 27 07:40:02 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", note = "Basic decompositions", abstract = "This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions---that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the $ L U $ and $ Q R $ decompositions---their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.", acknowledgement = ack-nhfb, GWS-number = "B7", tableofcontents = "Algorithms \\ Notation \\ Preface \\ 1. Matrices, algebra, and analysis \\ 2. Matrices and machines \\ 3. Gaussian elimination \\ 4. The $QR$ decomposition and least squares \\ 5. Rank-reducing decompositions \\ References \\ Index", } @TechReport{Stewart:1998:SC, author = "G. W. Stewart", title = "On Sublinear Convergence", type = "Technical report", number = "UMIACS-TR-95-92", institution = inst-UMIACS, address = inst-UMIACS:adr, month = "1998/10/15/", year = "1998", bibdate = "Fri May 30 07:40:54 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/760", abstract = "This note develops a theory of sublinearly converging sequences, including a categorization of the rates of convergence and a method for determining the rate from an iteration function. (Also cross-referenced as UMIACS-TR-95-92)", acknowledgement = ack-nhfb, keywords = "Technical Report", } @TechReport{Stewart:1998:TAE, author = "G. W. Stewart", title = "Two Algorithms for the Efficient Computation of Truncated Pivoted {$ Q R $} Approximations to a Sparse Matrix", type = "Technical Report", number = "UMIACS-TR-98-12", institution = inst-UMIACS, address = inst-UMIACS:adr, day = "15", month = oct, year = "1998", bibdate = "Fri May 30 07:46:55 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/941", abstract = "In this note we propose two algorithms to compute truncated pivoted $ Q R $ approximations to a sparse matrix. One is based on the Gram--Schmidt algorithm, and the other on Householder triangularization. Both algorithms leave the original matrix unchanged, and the only additional storage requirements are arrays to contain the factorization itself. Thus, the algorithms are particularly suited to determining low-rank approximations to a sparse matrix. (Also cross-referenced as UMIACS-TR-98-12)", acknowledgement = ack-nhfb, keywords = "Technical Report", } @TechReport{Stewart:1998:TMG, author = "G. W. Stewart", title = "The Triangular Matrices of {Gaussian} Elimination and Related Decompositions", type = "Technical Report", number = "UMIACS-TR-95-91", institution = inst-UMIACS, address = inst-UMIACS:adr, day = "15", month = oct, year = "1998", bibdate = "Fri May 30 07:45:58 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/759", abstract = "It has become a commonplace that triangular systems are solved to higher accuracy than their condition would warrant. This observation is not true in general, and counterexamples are easy to construct. However, it is often true of the triangular matrices from pivoted LU or QR decompositions. It is shown that this fact is closely connected with the rank-revealing character of these decompositions.", acknowledgement = ack-nhfb, keywords = "Technical Report", } @TechReport{Stewart:1998:TSR, author = "G. W. Stewart", title = "Two Simple Residual Bounds for the Eigenvalues of {Hermitian} Matrices", number = "UMIACS-TR-89-123", institution = inst-UMIACS, address = inst-UMIACS:adr, day = "15", month = oct, year = "1998", bibdate = "Fri May 30 07:48:31 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://drum.lib.umd.edu/handle/1903/545", abstract = "Let $A$ be Hermitian and let the orthonormal columns of $X$ span an approximate invariant subspace of $X$. Then the residual $ R = A X - X M$ $ (M = X \ctp A X)$ will be small. The theorems of this paper bound the distance of the spectrum of $M$ from the spectrum of $A$ in terms of appropriate norms of $R$. Appeared in SIAM J. Mat. Anal. Appl. 12 (1991) 205--208. (Also cross-referenced as UMIACS-TR-89-123)", acknowledgement = ack-nhfb, } @Article{Kilmer:1999:IRM, author = "Misha Kilmer and G. W. Stewart", title = "Iterative Regularization and {MINRES}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "21", number = "2", pages = "613--628", year = "1999", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479898348623", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Oct 27 07:23:28 MDT 2000", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/2; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/34862", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J104", journal-URL = "http://epubs.siam.org/simax", } @Article{Stewart:1999:BRN, author = "G. W. Stewart", title = "Book Reviews: {{\em Numerical linear algebra}}, by {Lloyd N. Trefethen} and {David Bau, III}", journal = j-MATH-COMPUT, volume = "68", number = "225", pages = "??--??", month = jan, year = "1999", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Mon Jul 26 12:45:31 1999", bibsource = "http://www.ams.org/mcom/1999-68-225; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-00992-8&u=/mcom/1999-68-225/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", xxpages = "453--459", } @Article{Stewart:1999:FAE, author = "G. W. Stewart", title = "Four algorithms for the efficient computation of truncated pivoted {$ Q R $} approximations to a sparse matrix", journal = j-NUM-MATH, volume = "83", number = "2", pages = "313--323", month = aug, year = "1999", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon Oct 18 10:45:15 MDT 1999", bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t9000002.htm; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/9083002/90830313.htm; http://link.springer-ny.com/link/service/journals/00211/papers/9083002/90830313.pdf", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J103", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:1999:QAS, author = "G. W. Stewart", title = "The {QLP} Approximation to the Singular Value Decomposition", journal = j-SIAM-J-SCI-COMP, volume = "20", number = "4", pages = "1336--1348", month = jul, year = "1999", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/S1064827597319519", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Sat Jul 17 19:14:35 MDT 1999", bibsource = "http://epubs.siam.org/toc/sjoce3/20/4; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31951", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", GWS-number = "J102", journal-URL = "http://epubs.siam.org/sisc", } @Article{Holland:2000:WLC, author = "John H. Holland and Lashon B. Booker and Marco Colombetti and Marco Dorigo and David E. Goldberg and Stephanie Forrest and Rick L. Riolo and Robert E. Smith and Pier Luca Lanzi and Wolfgang Stolzmann and Stewart W. Wilson", title = "What Is a Learning Classifier System?", journal = j-LECT-NOTES-COMP-SCI, volume = "1813", pages = "3--??", year = "2000", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Fri Feb 1 09:16:30 MST 2002", bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t.htm; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/lncs2000.bib", URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1813/18130003.htm; http://link.springer-ny.com/link/service/series/0558/papers/1813/18130003.pdf", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Li:2000:NRP, author = "Ren-Cang Li and G. W. Stewart", title = "A new relative perturbation theorem for singular subspaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "313", number = "1--3", pages = "41--51", day = "1", month = jul, year = "2000", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Oct 9 10:54:41 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/130/25/27/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/130/25/27/article.pdf", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J106", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Stewart:2000:BRA, author = "G. W. Stewart", title = "Book review: {{\em ARPACK Users' Guide, Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods}}", journal = j-MATH-COMPUT, volume = "69", number = "231", pages = "1309--1311", month = jul, year = "2000", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed Nov 1 11:50:05 MST 2000", bibsource = "http://www.ams.org/mcom/2000-69-231; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib", URL = "http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01249-7/bookrev-S0025-5718-00-01249-7.html; http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01249-7/S0025-5718-00-01249-7.dvi; http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01249-7/S0025-5718-00-01249-7.pdf; http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01249-7/S0025-5718-00-01249-7.ps; http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01249-7/S0025-5718-00-01249-7.tex", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Stewart:2000:DAM, author = "G. W. Stewart", title = "The Decompositional Approach to Matrix Computation", journal = j-COMPUT-SCI-ENG, volume = "2", number = "1", pages = "50--59", month = jan # "\slash " # feb, year = "2000", CODEN = "CSENFA", DOI = "https://doi.org/10.1109/5992.814658", ISSN = "1521-9615 (print), 1558-366X (electronic)", ISSN-L = "1521-9615", bibdate = "Wed May 28 16:46:19 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/computscieng.bib", URL = "http://dlib.computer.org/cs/books/cs2000/pdf/c1050.pdf; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=814658; http://www.computer.org/cse/cs1999/c1050abs.htm", acknowledgement = ack-nhfb, author-affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", book-DOI = "https://doi.org/10.1109/5992.814658", fjournal = "Computing in Science and Engineering", GWS-number = "J105", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992", } @Article{Jia:2001:ARR, author = "Zhongxiao Jia and G. W. Stewart", title = "An analysis of the {Rayleigh--Ritz} method for approximating eigenspaces", journal = j-MATH-COMPUT, volume = "70", number = "234", pages = "637--647", month = apr, year = "2001", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed Apr 18 05:10:18 MDT 2001", bibsource = "http://www.ams.org/mcom/2001-70-234; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib", URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01208-4; http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01208-4/S0025-5718-00-01208-4.dvi; http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01208-4/S0025-5718-00-01208-4.pdf; http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01208-4/S0025-5718-00-01208-4.ps; http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01208-4/S0025-5718-00-01208-4.tex", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", GWS-number = "J107", journal-URL = "http://www.ams.org/mcom/", } @Article{Stewart:2001:EGM, author = "G. W. Stewart", title = "On the eigensystems of graded matrices", journal = j-NUM-MATH, volume = "90", number = "2", pages = "349--370", month = dec, year = "2001", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s002110100290", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sun Feb 3 10:07:58 MST 2002", bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090002.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath2000.bib", URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/1090002/10900349.htm; http://link.springer-ny.com/link/service/journals/00211/papers/1090002/10900349.pdf", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J109", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:2001:GST, author = "G. W. Stewart", title = "A generalization of {Saad}'s theorem on {Rayleigh--Ritz} approximations", journal = j-LINEAR-ALGEBRA-APPL, volume = "327", number = "1--3", pages = "115--119", day = "15", month = apr, year = "2001", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Apr 3 07:01:32 MDT 2001", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", URL = "http://www.elsevier.nl/gej%2Dng/10/30/19/152/25/35/abstract.html; http://www.elsevier.nl/gej%2Dng/10/30/19/152/25/35/article.pdf", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J108", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Stewart:2001:KSA, author = "G. W. Stewart", title = "A {Krylov--Schur} Algorithm for Large Eigenproblems", journal = j-SIAM-J-MAT-ANA-APPL, volume = "23", number = "3", pages = "601--614", year = "2001", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479800371529", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Feb 22 09:58:18 MST 2002", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/3; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/37152", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J111", journal-URL = "http://epubs.siam.org/simax", } @Book{Stewart:2001:MAV, author = "G. W. Stewart", title = "Matrix Algorithms. {Volume II}: Eigensystems", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xix + 469", year = "2001", ISBN = "0-89871-503-2 (paperback), 0-89871-805-8 (e-book)", ISBN-13 = "978-0-89871-503-3 (paperback), 978-0-89871-805-8 (e-book)", LCCN = "QA188 .S714 1998 v.2", bibdate = "Sun Jun 19 12:32:58 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/numana2000.bib", abstract = "This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats the derivation and implementation of the more important algorithms in detail. The notes and references sections contain pointers to other methods along with historical comments.", acknowledgement = ack-nhfb, GWS-number = "B8", subject = "Matrices", tableofcontents = "1. Eigensystems \\ 2. The $QR$ algorithm \\ 3. The symmetric eigenvalue problem \\ 4. Eigenspaces and their approximation \\ 5. Krylov sequence methods \\ 6. Alternatives \\ 7. Appendix : background", } @Article{Stewart:2002:AKS, author = "G. W. Stewart", title = "Addendum to {``A Krylov--Schur Algorithm for Large Eigenproblems''}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "24", number = "2", pages = "599--601", year = "2002", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479802403150", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Aug 15 05:45:45 MDT 2003", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/2; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/40315", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J113", journal-URL = "http://epubs.siam.org/simax", } @Article{Stewart:2002:ARQ, author = "G. W. Stewart", title = "Adjusting the {Rayleigh} Quotient in Semiorthogonal {Lanczos} Methods", journal = j-SIAM-J-SCI-COMP, volume = "24", number = "1", pages = "201--207", month = jan, year = "2002", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/S1064827501388984", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Tue Oct 22 18:24:38 MDT 2002", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/24/1; http://epubs.siam.org/toc/sjoce3/24/1; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/38898", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", GWS-number = "J112", journal-URL = "http://epubs.siam.org/sisc", } @Article{Stewart:2002:BEB, author = "G. W. Stewart", title = "Backward error bounds for approximate {Krylov} subspaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "340", number = "1--3", pages = "81--86", day = "1", month = jan, year = "2002", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Sat Feb 23 11:16:42 MST 2002", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", URL = "http://www.elsevier.com/gej-ng/10/30/19/172/27/32/abstract.html", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J110", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @TechReport{Stewart:2003:BOF, author = "G. W. Stewart", title = "Building an Old-Fashioned Sparse Solver", type = "Technical Report", number = "TR-4527", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "2003", bibdate = "Fri May 30 05:54:18 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "Also issued as University of Maryland Institute for Advanced Computer Studies UMIACS report TR-2003-95.", acknowledgement = ack-nhfb, GWS-number = "N37", } @Article{Stewart:2003:MLD, author = "G. W. Stewart", title = "Memory leaks in derived types revisited", journal = j-FORTRAN-FORUM, volume = "22", number = "3", pages = "25--27", month = dec, year = "2003", CODEN = "????", ISSN = "1061-7264 (print), 1931-1311 (electronic)", ISSN-L = "1061-7264", bibdate = "Mon Jan 5 17:53:11 MST 2004", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran-forum.bib", acknowledgement = ack-nhfb, fjournal = "ACM Fortran Forum", GWS-number = "J115", issue = "67", journal-URL = "http://portal.acm.org/toc.cfm?id=J286", } @Article{Stewart:2003:PMP, author = "G. W. Stewart", title = "On the powers of a matrix with perturbations", journal = j-NUM-MATH, volume = "96", number = "2", pages = "363--376", month = dec, year = "2003", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-003-0470-0", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Tue Jan 13 17:22:49 MST 2004", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/nummath2000.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", GWS-number = "J114", journal-URL = "http://link.springer.com/journal/211", } @Article{Stewart:2004:ELP, author = "G. W. Stewart", title = "An {Elsner}-like perturbation theorem for generalized eigenvalues", journal = j-LINEAR-ALGEBRA-APPL, volume = "390", number = "1", pages = "1--5", day = "1", month = oct, year = "2004", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Nov 9 07:02:36 MST 2004", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J116", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Berry:2005:ACS, author = "Michael W. Berry and Shakhina A. Pulatova and G. W. Stewart", title = "{Algorithm 844}: {Computing} sparse reduced-rank approximations to sparse matrices", journal = j-TOMS, volume = "31", number = "2", pages = "252--269", month = jun, year = "2005", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1067967.1067972", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Jun 21 16:55:57 MDT 2005", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix $A$. Unfortunately, the approximations based on traditional decompositions, like the singular value and $ Q R$ decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi-Gram--Schmidt-algorithm, to obtain two kinds of low-rank approximations. The first, the $ S P Q R$, approximation, is a pivoted, $Q$-less $ Q R$ approximation of the form $ (X R_{11}^{-1})(R_{11} R_{12}) $, where $X$ consists of columns of $A$. The second, the $ S C R$ approximation, is of the form the form $ A \approx X T Y T $, where $X$ and $Y$ consist of columns and rows $A$, and $T$ is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J118", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @Article{Stewart:2005:EAQ, author = "G. W. Stewart", title = "Error Analysis of the Quasi-{Gram--Schmidt} Algorithm", journal = j-SIAM-J-MAT-ANA-APPL, volume = "27", number = "2", pages = "493--506", month = apr, year = "2005", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/040607794", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Dec 29 16:33:54 MST 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/27/2; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/60779", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", GWS-number = "J117", journal-URL = "http://epubs.siam.org/simax", } @Article{Fassbender:2006:CVF, author = "Heike Fassbender and Michael Griebel and Olga Holtz and G. W. (Pete) Stewart and Christoph Zenger", title = "Curriculum vitae of {Friedrich Ludwig Bauer}", journal = j-LINEAR-ALGEBRA-APPL, volume = "417", number = "2--3", pages = "299--300", day = "1", month = sep, year = "2006", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2006.07.001", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "01A70", MRnumber = "2250311", bibdate = "Wed Mar 30 14:18:53 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", note = "Special Issue in honor of Friedrich Ludwig Bauer.", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", remark = "This short CV does NOT contain a list of Fritz Bauer's publications.", subject-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26 March 2015)", } @Article{Stewart:2006:NGH, author = "G. W. Stewart", title = "A note on generalized and hypergeneralized projectors", journal = j-LINEAR-ALGEBRA-APPL, volume = "412", number = "2--3", pages = "408--411", day = "15", month = jan, year = "2006", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Mar 13 16:56:11 MST 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", GWS-number = "J119", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Stewart:2008:BGS, author = "G. W. Stewart", title = "Block {Gram--Schmidt} Orthogonalization", journal = j-SIAM-J-SCI-COMP, volume = "31", number = "1", pages = "761--775", month = "????", year = "2008", CODEN = "SJOCE3", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Wed May 19 10:44:12 MDT 2010", bibsource = "http://epubs.siam.org/toc/sjoce3/31/1; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", abstract = "The classical Gram--Schmidt algorithm for computing the QR factorization of a matrix $X$ requires at least one pass over the current orthogonalized matrix $Q$ as each column of $X$ is added to the factorization. When $Q$ becomes so large that it must be maintained on a backing store, each pass involves the costly transfer of data from the backing store to main memory. However, if one orthogonalizes the columns of $X$ in blocks of $m$ columns, the number of passes is reduced by a factor of $ 1 / m$. Moreover, matrix-vector products are converted into matrix-matrix products, allowing level-3 BLAS cache performance. In this paper we derive such a block algorithm and give some experimental results that suggest it can be quite effective for large scale problems, even when the matrix $X$ is rank degenerate.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", GWS-number = "J121", journal-URL = "http://epubs.siam.org/sisc", keywords = "blocked algorithm, Gram--Schmidt algorithm, orthogonalization, QR factorization", } @Article{Lee:2009:AET, author = "Che-Rung Lee and G. W. Stewart", title = "{Algorithm 879}: {EIGENTEST} --- a test matrix generator for large-scale eigenproblems", journal = j-TOMS, volume = "35", number = "1", pages = "7:1--7:11", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377610", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran3.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat $A$ of order $n$ requires only $ O(n) $ storage for its representation. Auxiliary programs permit the computation of $ (A - s I) b $, $ (A - s I)^T b $, $ (A - s I)^{-1} b $, and $ (A - s I)^{-T} b $ in $ O(n) $ operations. A special routine computes specified eigenvectors of an eigenmat and the condition of its eigenvalue. Thus eigenmats are suitable for testing algorithms based on Krylov sequences, as well as others based on matrix-vector products. This article introduces the eigenmat and describes implementations in Fortran 77, Fortran 95, C, and Matlab.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Mathematical Software (TOMS)", GWS-number = "J120", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "eigensystem; test matrix generation", keywords = "Eigensystem, test matrix generation", } @TechReport{Stewart:2009:FMP, author = "G. W. Stewart", title = "{Flap}: {A} {Matlab} Package for Adjustable Precision Floating-Point Arithmetic", type = "Report", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "2009", bibdate = "Sun Jun 19 13:11:45 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib", URL = "http://www.cs.umd.edu/~stewart/flap/flap.html", abstract = "Flap is a package to implement floating-point arithmetic with adjustable precision. Specifically, operations are performed on Matlab doubles but are rounded to a user specified number of decimal digits after each operation. The number can be changed dynamically. Flap is intended to make it easy to generate examples of the effects of rounding error for classroom use.", acknowledgement = ack-nhfb, } @TechReport{Stewart:2009:UCC, author = "G. W. Stewart", title = "An Unreliable Convergence Criterion for {Arnoldi}'s Method", type = "Technical Report", number = "CMSC TR-4938", institution = inst-CS-U-MARYLAND, address = inst-CS-U-MARYLAND:adr, year = "2009", bibdate = "Fri May 30 07:30:55 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, } @TechReport{Stewart:2010:DF, author = "G. W. Stewart", title = "On Downdating {$ Q R $ } Factorizations", institution = "Institute for Advanced Computer Studies, University of Maryland", address = "College Park, MD, USA", pages = "1", year = "2010", bibdate = "Tue Mar 6 11:55:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-do, } @Article{Stewart:2010:SAM, author = "G. W. Stewart", title = "On the Semidefinite {$B$-Arnoldi} Method", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "3", pages = "1458--1468", month = "????", year = "2010", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/090759252", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Tue May 18 22:32:37 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://link.aip.org/link/?SML/31/1458/1", abstract = "The B-Arnoldi method is a variant of the ordinary Arnoldi method in which orthogonalization is done with respect to the inner product generated by a positive definite matrix $B$. It arises in connection with the generalized eigenvalue problem $ A x = \lambda B x$. When $B$ is semidefinite, the algorithm can proceed formally, with ``orthogonalization'' taking place in the semi-inner product generated by $B$. However, it has been observed that components of the Arnoldi vectors lying in the null space of $B$ can grow rapidly. In this paper we examine the source and consequences of this growth.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "Arnoldi's method, B-inner product, null-space component, semidefinite B", } @Unpublished{Stewart:2011:FHS, author = "G. W. Stewart", title = "{FREDHOLM}, {HILBERT}, {SCHMIDT}: Three Fundamental Papers on Integral Equations. {Translated} with commentary by {G. W. Stewart}", pages = "iv + 137", day = "15", month = dec, year = "2011", bibdate = "Tue Mar 6 11:55:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://www.umiacs.umd.edu/~stewart/FHS.pdf", abstract = "In the first decade of the twentieth century, Ivar Fredholm (1903), David Hilbert (1904), and Erhard Schmidt (1907) published three papers on integral equations that together advanced the topic from studies of special cases to a well developed general theory. This work presents English translations of these papers along with a commentary by the translator.", acknowledgement = ack-do, remark = "The Note to the Reader on page iii says: ``The downloaded paper is for personal use only. Please, no wholesale copying. At present I have no plans for further publication, but that may change.''", } @Article{Stewart:2011:NAO, author = "G. W. Stewart", title = "On the Numerical Analysis of Oblique Projectors", journal = j-SIAM-J-MAT-ANA-APPL, volume = "32", number = "1", pages = "309--348", month = "????", year = "2011", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/100792093", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Jun 9 09:09:08 MDT 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/1; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i1/p309_s1; http://link.aip.org/link/?SML/32/309/1", abstract = "An oblique projector is an idempotent matrix whose null space is oblique to its range, in contrast to an orthogonal projector, whose null space is orthogonal to its range. Oblique projectors arise naturally in many applications and have a substantial literature. Missing from that literature, however, are systematic expositions of their numerical properties, including their perturbation theory, their various representations, their behavior in the presence of rounding error, the computation of complementary projections, and updating algorithms. This article is intended to make a start at filling this gap. The first part of the article is devoted to the first four of the above topics, with particular attention given to complementation. In the second part, stable algorithms are derived for updating an XQRY representation of projectors, which was introduced in the first part.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "$B$-orthogonality, oblique projector, Perturbation theory, updating algorithms, XQRY form", onlinedate = "March 31, 2011", } @InProceedings{Stewart:2011:WTE, author = "G. W. Stewart", booktitle = "{Householder Symposium XVIII on Numerical Linear Algebra, June 12--17, 2011. Granlibakken Conference Center \& Lodge, Tahoe City, California}", title = "When Is Twice Enough? (The Oblique Case)", publisher = "????", address = "????", bookpages = "x + 272", pages = "220--221", year = "2011", bibdate = "Tue Mar 6 11:55:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://www.maths.manchester.ac.uk/~higham/conferences/householder/HH11_Abstracts.pdf", acknowledgement = ack-do, } @TechReport{Stewart:2012:SLB, author = "G. W. Stewart", title = "Smooth local bases for perturbed eigenspaces", institution = "Institute for Advanced Computer Studies, University of Maryland", address = "College Park, MD, USA", pages = "8", year = "2012", bibdate = "Tue Mar 6 11:55:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-do, } @Article{Lam:2013:DFP, author = "Michael O. Lam and Jeffrey K. Hollingsworth and G. W. Stewart", title = "Dynamic floating-point cancellation detection", journal = j-PARALLEL-COMPUTING, volume = "39", number = "3", pages = "146--155", month = mar, year = "2013", CODEN = "PACOEJ", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", MRclass = "65Y04 (65G50)", MRnumber = "3036891", bibdate = "Wed Mar 27 07:19:15 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib; http://www.sciencedirect.com/science/journal/01678191", URL = "http://www.sciencedirect.com/science/article/pii/S0167819112000622", acknowledgement = ack-nhfb, fjournal = "Parallel Computing", journal-URL = "http://www.sciencedirect.com/science/journal/01678191/", } @Article{Guglielmi:2015:EAC, author = "Nicola Guglielmi and Michael L. Overton and G. W. Stewart", title = "An Efficient Algorithm for Computing the Generalized Null Space Decomposition", journal = j-SIAM-J-MAT-ANA-APPL, volume = "36", number = "1", pages = "38--54", month = "????", year = "2015", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/140956737", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (65F30)", MRnumber = "3302594", MRreviewer = "Ana Marco", bibdate = "Wed Jun 10 14:55:05 MDT 2015", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/36/1; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2015", } @Article{Stewart:2016:CCR, author = "G. W. Stewart", title = "A Canonical {CS} Representation of a Pair of Subspaces", journal = j-SIAM-J-MAT-ANA-APPL, volume = "37", number = "2", pages = "539--549", year = "2016", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/15M1009573", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A21 65F15 65F30)", MRnumber = "3488164", bibdate = "Tue May 31 10:48:14 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/2; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2016", } @Unpublished{Stewart:2016:CJE, author = "G. W. Stewart", title = "{Camille Jordan} 1875: Essay on the Geometry of $n$ Dimensions", pages = "iv + 74", year = "2016", bibdate = "Tue Mar 6 11:55:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://www.umiacs.umd.edu/~stewart/Jord75.pdf", abstract = "In 1875 the French mathematician Camille Jordan published a paper on geometry in $n$ dimensions with the aim of generalizing results obtained for two and three dimensions. Although he largely succeeded, his paper is not much cited, principally because his approach of defining planes as the solution space of linear equations was superseded by vector space methods. Yet there is much to be learned from this paper. Here we give a partial translation from the original French along with a commentary", acknowledgement = ack-do, }

%%% ==================================================================== %%% Part 2 (of 2) --- publications about G. W. Stewart and his works %%% %%% Bibliography entries, sorted by year, and then by citation label, %%% with ``bibsort -byyear'':

@Article{Birkhoff:1980:BRC, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Computational analysis with the HP 25 pocket calculator}}, by Peter Henrici, John Wiley, New York, 1977, 280 pp.; \booktitle{Compact numerical methods for computers: linear algebra and function minimization}, by J. C. Nash, John Wiley \& Sons, New York, 1979, x + 227 pp.; \booktitle{LINPACK: User's guide}, by J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, Society for Industrial and Applied Mathematics, Philadelphia, 1979 368 pp.}", journal = j-BULL-AMS, volume = "2", number = "3", pages = "503--505", month = may, year = "1980", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0273-0979-1980-14785-0", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Nov 01 08:26:39 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "https://www.ams.org/journals/bull/1980-02-03/S0273-0979-1980-14785-0/S0273-0979-1980-14785-0.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", gb-number = "191b", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", subject-dates = "Peter Karl Henrici (13 September 1923--13 March 1987)", } @Article{Campbell:1981:RBU, author = "Stephen L. Campbell", title = "Review of {{\booktitle{Linpack User's Guide}} by J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart}", journal = j-LINEAR-ALGEBRA-APPL, volume = "39", number = "??", pages = "293--294", month = aug, year = "1981", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(81)90311-6", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Nov 30 13:48:48 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379581903116", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Parlett:1981:BRBb, author = "B. N. Parlett", title = "Book Review: {{\booktitle{{LINPACK} Users' Guide}} (J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W. Stewart)}", journal = j-SIAM-REVIEW, volume = "23", number = "1", pages = "126--128", month = "????", year = "1981", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1023033", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:53:16 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/23/1; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1981", } @Article{Plemmons:1981:RBM, author = "R. J. Plemmons", title = "Review of {{\booktitle{Sparse matrix proceedings 1978}}, edited by Iain S. Duff and G. W. Stewart}", journal = j-LINEAR-ALGEBRA-APPL, volume = "40", number = "??", pages = "275--278", month = oct, year = "1981", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(81)90158-0", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Nov 30 13:48:50 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379581901580", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Flamm:1982:RHE, author = "David S. Flamm and Robert A. Walker", title = "Remark on ``{Algorithm} 506: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]''", journal = j-TOMS, volume = "8", number = "2", pages = "219--220", month = jun, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355993.356002", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", note = "See \cite{Stewart:1976:AHE}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", } @Article{OLeary:1990:BSP, author = "Dianne P. O'Leary", title = "On Bounds For Scaled Projections and Pseudo-Inverses", journal = j-LINEAR-ALGEBRA-APPL, volume = "132", pages = "115--117", year = "1990", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(90)90056-I", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A60 (15A09 65F20)", MRnumber = "91f:15056", MRreviewer = "S. Lajos", bibdate = "Wed Jan 22 17:57:24 MST 1997", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", note = "See \cite{Stewart:1989:SPP}.", abstract = "Let $X$ be a matrix of full column rank, and let $D$ be a positive definite diagonal matrix. In a recent paper, Stewart considered the weighted pseudoinverse $ X \dagger D = (X T D X)^{-1} X T D$ and the associated oblique projection $ P D = X X \dagger D$, and gave bounds, independent of $D$, for the norms of these matrices. In this note, we answer a question he raised by showing that the bounds are computable.", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "la, projection, ginv", } @Article{Fraser:1995:BRBb, author = "Craig Fraser", title = "Book Review: {{\booktitle{Theoria combinationis observationum erroribus minimis obnoxiae}} [(Latin) [The theory of the combination of observations least subject to error]] by Carl Friedrich Gauss; G. W. Stewart}", journal = j-ISIS, volume = "86", number = "4", pages = "660--661", month = dec, year = "1995", CODEN = "ISISA4", ISSN = "0021-1753 (print), 1545-6994 (electronic)", ISSN-L = "0021-1753", bibdate = "Tue Jul 30 21:25:03 MDT 2013", bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211225; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/isis1990.bib", URL = "http://www.jstor.org/stable/235423", acknowledgement = ack-nhfb, fjournal = "Isis", journal-URL = "http://www.jstor.org/page/journal/isis/about.html", } @Article{Kincaid:1997:BRA, author = "David R. Kincaid", title = "Book Review: {{\booktitle{Afternotes on Numerical Analysis}}, by G. W. Stewart}", journal = j-SIAM-REVIEW, volume = "39", number = "1", pages = "153--153", month = mar, year = "1997", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Tue May 13 16:55:17 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kincaid-david-r.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib; http://www.siam.org/journals/sirev/sirev391.htm", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Serbin:1997:BRA, author = "Steven M. Serbin", title = "Book Reviews: {{\booktitle{Afternotes on numerical analysis}}, by G. W. Stewart}", journal = j-MATH-COMPUT, volume = "66", number = "219", pages = "1367--1374", month = jul, year = "1997", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Fri Jul 16 10:38:45 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{King:1999:BRA, author = "J. Thomas King", title = "Book Reviews: {{\booktitle{Afternotes goes to graduate school, lectures in advanced numerical analysis}}, by G. W. Stewart}", journal = j-MATH-COMPUT, volume = "68", number = "226", pages = "887--891", month = apr, year = "1999", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Mon Jul 26 12:48:16 1999", bibsource = "http://www.ams.org/mcom/1999-68-226; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01060-1&u=/mcom/1999-68-226/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Huckaby:2003:CSQ, author = "David A. Huckaby and Tony F. Chan", title = "On the Convergence of {Stewart}'s {QLP} Algorithm for Approximating the {SVD}", journal = j-NUMER-ALGORITHMS, volume = "32", number = "2--4", pages = "287--316", month = apr, year = "2003", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Mon Sep 29 08:37:11 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/45/10/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/45/10/fulltext.pdf", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Chen:2004:ARS, author = "Guizhi Chen and Zhongxiao Jia", title = "An analogue of the results of {Saad} and {Stewart} for harmonic {Ritz} vectors", journal = j-J-COMPUT-APPL-MATH, volume = "167", number = "2", pages = "493--498", day = "1", month = jun, year = "2004", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 12:59:58 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042703009403", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", } @Article{Priest:2004:ESC, author = "Douglas M. Priest", title = "Efficient scaling for complex division", journal = j-TOMS, volume = "30", number = "4", pages = "389--401", month = dec, year = "2004", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1039813.1039814", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Tue Apr 12 06:34:31 MDT 2005", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "We develop a simple method for scaling to avoid overflow and harmful underflow in complex division. The method guarantees that no overflow will occur unless at least one component of the quotient must overflow, otherwise the normwise error in the computed result is at most a few units in the last place. Moreover, the scaling requires only four floating point multiplications and a small amount of integer arithmetic to compute the scale factor. Thus, on many modern CPUs, our method is both safer and faster than Smith's widely used algorithm.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "complex division", } @Article{Huckaby:2005:SPQ, author = "D. A. Huckaby and T. F. Chan", title = "{Stewart}'s pivoted {QLP} decomposition for low-rank matrices", journal = j-NUM-LIN-ALG-APPL, volume = "12", number = "2--3", pages = "153--159", month = mar # "\slash " # apr, year = "2005", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.404", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", bibdate = "Sat May 14 10:12:15 MDT 2005", bibsource = "http://www.interscience.wiley.com/jpages/1070-5325; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numlinaa.bib; http://www3.interscience.wiley.com/journalfinder.html", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", onlinedate = "29 Sep 2004", } @Article{Schilders:2008:BMU, author = "W. H. A. Schilders and P. B. L. Meijer and E. Ciggaar", title = "Behavioural modelling using the {MOESP} algorithm, dynamic neural networks and the {Bartels--Stewart} algorithm", journal = j-APPL-NUM-MATH, volume = "58", number = "12", pages = "1972--1993", month = dec, year = "2008", CODEN = "ANMAEL", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", bibdate = "Tue Aug 24 11:17:22 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274/", } @InCollection{Duff:2010:BGW, author = "Iain S. Duff", title = "Biography of {G. W. Stewart}", crossref = "Kilmer:2010:GWS", pages = "3--9", year = "2010", DOI = "https://doi.org/10.1007/978-0-8176-4968-5_1", MRclass = "01A70", MRnumber = "2731850", bibdate = "Wed Apr 27 09:14:27 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "Contemp. Mathematicians", acknowledgement = ack-nhfb, }

%%% ==================================================================== %%% Cross-referenced entries must come last; entries are sorted by year, %%% and then by citation label, with `bibsort --byyear':

@Proceedings{Dejon:1969:CAF, editor = "Bruno Dejon and Peter Henrici", booktitle = "Constructive Aspects of the Fundamental Theorem of Algebra: proceedings of a symposium conducted at the {IBM Research Laboratory, Z{\"u}rich-R{\"u}schlikon, Switzerland, June 5--7, 1967}", title = "Constructive Aspects of the Fundamental Theorem of Algebra: proceedings of a symposium conducted at the {IBM Research Laboratory, Z{\"u}rich-R{\"u}schlikon, Switzerland, June 5--7, 1967}", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "337", year = "1969", ISBN = "0-471-20300-9", ISBN-13 = "978-0-471-20300-1", LCCN = "QA212 .C65", bibdate = "Sun Jan 27 19:57:13 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", ZMnumber = "0175.00104", acknowledgement = ack-nhfb, author-dates = "Peter Karl Henrici (13 September 1923--13 March 1987)", subject = "Equations, Roots of; Congresses; Fundamental theorem of algebra; Congresses", tableofcontents = "A never failing, fast convergent root-finding algorithm / B. Dejon and K. Nickel \\ Finding a zero by means of successive linear interpolation / T. J. Dekker \\ Remarks on the paper by Dekker / G. E. Forsythe \\ What is a satisfactory quadratic equation solver? / G. E. Forsythe \\ Mathematical and physical polynomials / L. Fox \\ A constructive form of the second Gauss proof of the Fundamental Theorem of Algebra / R. L. Goodstein \\ Uniformly convergent algorithms for the simultaneous approximation of all zeros of a polynomial / P. Henrici and I. Gargantini \\ On the notion of constructivity / H. Hermes \\ Bigradients, Hankel determinants, and the Pad{\'e} table / A. S. Householder and G. W. Stewart \\ An algorithm for an automatic general polynomial solver / M. A. Jenkins and J. F. Traub \\ Die numerische Bestimmung mehrfacher und nahe benachbarter polynomnullstellen nach einem verbesserten Bernoulli-Verfahren / I. Kupka \\ Search procedures for polynomial equation solving / D. H. Lehmer \\ A method for automatic solution of algebraic equations / A. M. Ostrowski \\ Iteration functions for solving polynomial matrix equations / M. Pavel-Parvu and A. Korganoff \\ Problematik der Nullstellenbestimmung bei polynomen / H. Rutishauser \\ Factorization of polynomials by generalized Newton procedures / J. Schroder \\ The fundamental theorem of algebra in recursive analysis / E. Specker", } @Proceedings{Rosenfeld:1974:IPP, editor = "Jack L. Rosenfeld", booktitle = "Information processing, 1974; Proceedings of {IFIP} Congress 74, Stockholm, Sweden, August 5--10, 1974", title = "Information processing, 1974; Proceedings of {IFIP} Congress 74, Stockholm, Sweden, August 5--10, 1974", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xxi + 1106", year = "1974", ISBN = "0-444-10689-8, 0-7204-2803-3", ISBN-13 = "978-0-444-10689-6, 978-0-7204-2803-2", LCCN = "QA 76 I615", bibdate = "Mon Jul 18 10:10:46 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, tableofcontents = "Vol. 1. Computer hardware and architecture \\ vol. 2. Software \\ vol. 3. Mathematical aspects of information processing \\ vol. 4. Technological and scientific applications. Applications in the social sciences and humanities \\ vol. 5. Systems for management and administration", } @Proceedings{Miller:1975:TNA, editor = "John J. H. Miller", booktitle = "{Topics in numerical analysis II: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1974}", title = "{Topics in numerical analysis II: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1974}", publisher = "Published for the Royal Irish Academy by Academic Press", address = "London, UK", pages = "xiv + 266", year = "1975", ISBN = "0-323-14134-X, 0-12-496952-6 (e-book), 0-323-14134-X (e-book)", ISBN-13 = "978-0-323-14134-5, 978-0-12-496952-0 (e-book), 978-0-323-14134-5 (e-book)", LCCN = "QA297 .R69", bibdate = "Wed May 28 17:28:41 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", URL = "http://catalog.hathitrust.org/api/volumes/oclc/6100019.html; http://www.sciencedirect.com/science/book/9780124969520", abstract = "Topics in Numerical Analysis II.", acknowledgement = ack-nhfb, subject = "Numerical analysis -- Congresses; Numerical analysis", tableofcontents = "Preface \\ Names and Addresses of Invited Speakers \\ Titles and Authors of Contributed Papers \\ Names and Addresses of Presenters of Contributed Papers \\ Table of Contents \\ Chapter 1. On a Discretization of $yn + (Sn(NUBk = 0))$ \\ Section 1 \\ Section 2 \\ Section 3 \\ Section 4 \\ Section 5 \\ References \\ Chapter 2. Some Applications of Approximation Theory to Numerical Analysis \\ Introduction \\ 1. Indirect Continuous Approximation to Solutions of Linear Functional Equations with Respect to a given Set of Functions \\ 2. Indirect Discrete Approximation to the Solution of a Functional Equation \\ 3. Discrete Approximation to Solutions of Boundary Value Problems \\ 4. Error Estimates for Discretization Methods for Data with Less Restrictive Structure \\ References \\ Chapter 3. Interior Regularity and Local Convergence of Galerkin Finite Element Approximations for Elliptic Equations \\ 1. Introduction \\ 2. Hypotheses \\ 3. Preliminaries \\ 4. Interior Regularity and Local Convergence \\ 5. Finite Differences \\ References \\ Chapter 4. Numerical Estimates for the Error of Gauss-Jacobi Quadrature Formulae \\ 1. Introduction \\ 2. The Numerical Estimation of the Error Term \\ 3. On the Error of Pad{\'e} Approximation \\ 4. On the Calculation of Elliptic Integrals \\ References \\ Chapter 5. Some Remarks on the Unified Treatment of Elementary Functions by Microprogramming \\ 1. Introduction \\ 2. Chen's Algorithms \\ 3. General Classification of Known Algorithms \\ 4. Perle's Application of CORDIC \\ 5. Remark on the Square Root through Hyperbolic CORDIC \\ References \\ Addenda \\ Chapter 6. Application of Finite Difference Methods to Exploration Seismology \\ Introduction \\ Formulation of Seismic Exploration Model \\ Finite-Difference Models \\ Grid Dispersion \\ Results \\ Edge Reflections \\ Conclusions \\ References \\ Chapter 7. Variable Coefficient Multistep Methods for Ordinary Differential Equations applied to Parabolic Partial Differential Equations \\ 1. Semi-discretization \\ 2. Variable Coefficient Multistep Methods (VCMM) \\ 3. Examples \\ Acknowledgment \\ References \\ Chapter 8. Realistic Estimates for Generic Constants in Multivariate Pointwise Approximation \\ 1. Introduction \\ 2. The General Problem of Error Estimation \\ 3. Taylor's Formula and Relevant Algebraic Topics \\ 4. Sharp Appraisals for Practical Error Coefficients of Chebyshev Type \\ 5. Two Examples of Application \\ References \\ Chapter 9. Matching of Essential Boundary Conditions in the Finite Element Method \\ 1. Introduction \\ 2. Blending Function Interpolants \\ 3. Transfinite Mappings \\ 4. Isoparametric Elements \\ 5. Direct Methods \\ References \\ Chapter 10. Collocation, Difference Equations, and Stitched Function Representations \\ Abstract \\ 1. Introduction \\ 2. Collocation by Piecewise Smooth Functions \\ 3. An $m$th Order Difference Approximation \\ 4. A Class of Intermediate Schemes \\ References \\ Chapter 11. A New Approach to Matrix Theory or Many Facets of the Matrix Decomposition Theorem", } @Proceedings{Bunch:1976:SMC, editor = "James R. Bunch and Donald J. Rose", booktitle = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", title = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xi + 453", year = "1976", ISBN = "0-12-141050-1", ISBN-13 = "978-0-12-141050-6", LCCN = "QA188 .S989 1975", bibdate = "Sat Oct 22 18:13:05 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, tableofcontents = "Contributors / / ix \\ Preface / / xi \\ I. Design and Analysis of Elimination Algorithms / / 1 \\ 1. Graph Theory and Gaussian Elimination / Robert Endre Tarjan / 3 \\ 2. Partitioning Using PAQ / Thomas D. Howell / 23 \\ 3. Block Methods for Solving Sparse Linear Systems / James R. Bunch / 39 \\ 4. A Recursive Analysis of Dissection Strategies / Donald J. Rose and Gregory F. Whitten / 59 \\ 5. Applications of an Element Model for Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and 4. H. Sherman / 85 \\ 6. An Optimization Problem Arising from Tearing Methods / Alberto Sangiovanni-Vincentelli / 97 \\ II. Eigenvalue Problems / / 111 \\ 1. A Bibliographical Tour of the Large, Sparse Generalized Eigenvalue Problem / G. W. Stewart / 113 \\ 2. How Far Should You Go With the Lanczos Process? / W. Kahan and B. N. Parlett / 131 \\ III. Optimization, Least Squares and Linear Programming / / 145 \\ 1. Optimization for Sparse Systems / T. L. Magnanti / 147 \\ 2. Methods for Sparse Linear Least Squares Problems / {AA}ke Bj{\"o}rck / 177 \\ 3. The Orthogonal Factorization of a Large Sparse Matrix / Philip E. Gill and Walter Murray / 201 \\ 4. A Fast, Stable Implementation of the Simplex Method Using Bartels-Golub Updating / Michael A. Saunders / 213 \\ 5. Using the Steepest-edge Simplex Algorithm to Solve Sparse Linear Programs / D. Goldfarb / 227 \\ IV. Mathematical Software / / 241 \\ 1. Sparse Matrix Software / W. Morven Gentleman and Alan George / 243 \\ 2. Considerations in the Design of Software for Sparse Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 263 \\ 3. Finding the Block Lower Triangular Form of a Sparse Matrix / Fred Gustavson / 275 \\ V. Matrix Methods for Partial Difference Equations / / 291 \\ 1. Marching Algorithms and Block Gaussian Elimination / Randolph E. Bank / 293 \\ 2. A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations / Paul Concus, Gene H. Golub, and Dianne P. O'Leary / 309 \\ 3. Preconditioned Conjugate Gradient Iteration Applied to Galerkin Methods for a Mildly-Nonlinear Dirichlet Problem / Jim Douglas, Jr. and Todd Dupont / 333 \\ 4. The Sparse Tableau Approach to Finite Element Assembly / Gary Hachtel / 349 \\ 5. A Capacitance Matrix Technique / B. L. Buzbee / 365 \\ 6. M-Matrix Theory and Recent Results in Numerical Linear Algebra / Richard S. Varga / 375 \\ VI. Applications / / 389 \\ 1. Sparse Matrix Problems in a Finite Element Open Ocean Model / Joel E. Hirsh and William L. Briggs / 391 \\ 2. Calculation of Normal Modes of Oceans Using a Lanczos Method / Alan K. Cline, Gene H. Golub, and George W. Platzman / 409 \\ 3. Application of Sparse Matrix Techniques to Reservoir Simulation / P. T. Woo, S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 427 \\ 4. On the Origins and Numerical Solution of Some Sparse Nonlinear Systems / T. A. Porsching / 439", } @Proceedings{Hoaglin:1976:CSS, editor = "David C. (David Caster) Hoaglin and Roy E. (Roy Elmer) Welsch", booktitle = "{Proceedings of the Ninth Interface Symposium on Computer Science and Statistics / Harvard University, Massachusetts Institute of Technology, April 1--2, 1976}", title = "{Proceedings of the Ninth Interface Symposium on Computer Science and Statistics / Harvard University, Massachusetts Institute of Technology, April 1--2, 1976}", publisher = "Prindle, Weber and Schmidt, Inc.", address = "Boston, MA, USA", pages = "x + 323", year = "1976", ISBN = "0-87150-237-2", ISBN-13 = "978-0-87150-237-7", LCCN = "QA276 C73 1976", bibdate = "Thu May 29 16:21:16 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, subject = "Proceedings.; Statistical Methods/ Probability.; Computer Programming.", } @Book{Rice:1977:MSS, editor = "John R. (John Rischard) Rice", booktitle = "{Mathematical Software Symposium, University of Wisconsin, Madison, 1977. Mathematical Software III: Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, March 28--30, 1977}", title = "{Mathematical Software Symposium, University of Wisconsin, Madison, 1977. Mathematical Software III: Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, March 28--30, 1977}", number = "39", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "ix + 388", year = "1977", ISBN = "0-12-587260-7 (hardcover)", ISBN-13 = "978-0-12-587260-7 (hardcover)", LCCN = "QA3 .U45 no. 39; QA297 .M36 1977", MRnumber = "68-03 01-06 68Nxx", bibdate = "Sat Oct 22 18:23:16 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "Publication of the Mathematics Research Center, the University of Wisconsin, Madison", URL = "http://zbmath.org/?q=an:0234.68003", ZMnumber = "0234.68003", acknowledgement = ack-nhfb, } @Proceedings{deBoor:1978:SRA, editor = "Carl de Boor and Gene H. Golub", booktitle = "{Symposium on Recent Advances in Numerical Analysis (1978: Madison, Wis.). Recent Advances in Numerical Analysis: Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, May 22--24, 1978}", title = "{Symposium on Recent Advances in Numerical Analysis (1978: Madison, Wis.). Recent Advances in Numerical Analysis: Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, May 22--24, 1978}", volume = "41", organization = "Army Mathematics Research Center", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "ix + 270", year = "1978", ISBN = "0-12-208360-1", ISBN-13 = "978-0-12-208360-0", LCCN = "QA3 .U45 no. 41; QA297 S994 1978", MRclass = "65-06", MRnumber = "80a:65016", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "Publication of the Mathematics Research Center, the University of Wisconsin, Madison", URL = "http://catalog.hathitrust.org/api/volumes/oclc/65991765.html; http://www.gbv.de/dms/hbz/toc/ht001227727.pdf", acknowledgement = ack-nhfb, keywords = "na; numerical analysis --- congresses; proceedings", remark = "See review in Mathematics of Computation, Vol. 38, No. 158 (Apr., 1982), p. 654.", tableofcontents = "Contributors / / vii \\ Preface / / ix \\ Positive Functions and Some Applications to Stability Questions for Numerical Methods / Germund Dahlquist / 1 \\ Constructive Polynomial Approximation in Sobolev Spaces / Todd Dupont and Ridgway Scott / 31 \\ Questions of Numerical Condition Related to Polynomials / Walter Gautschi / 45 \\ Global Homotopies and Newton Methods / Herbert B. Keller / 73 \\ Problems with Different Time Scales / Heinz-Otto Kreiss / 95 \\ Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations / Peter D. Lax / 107 \\ Finite Element Approximations to the One- Dimensional Stefan Problem / J. A. Nitsche / 119 \\ The Hodie Method and Its Performance for Solving Elliptic Partial Differential Equations / Robert E. Lynch and John R. Rice / 143 \\ Solving ODE's with Discrete Data in SPEAKEASY / L. F. Shampine / 177 \\ Perturbation Theory for the Generalized Eigenvalue Problem / G. W. Stewart / 193 \\ Some Remarks on Good, Simple, and Optimal Quadrature Formulas / H. F. Weinberger / 207 \\ Linear Differential Equations and Kronecker's Canonical Form / J. H. Wilkinson / 231 \\ Index / / 267", } @Proceedings{Duff:1979:SMP, editor = "Iain S. Duff and G. W. Stewart", booktitle = "{Sparse Matrix. Proceedings 1978: Symposium held in the Hyatt Regency, Knoxville, Tennessee on November 2--3, 1978}", title = "{Sparse Matrix. Proceedings 1978: Symposium held in the Hyatt Regency, Knoxville, Tennessee on November 2--3, 1978}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xvi + 334", year = "1979", ISBN = "0-89871-160-6", ISBN-13 = "978-0-89871-160-8", LCCN = "QA188 S9 1978", MRclass = "65-06", MRnumber = "81f:65003", bibdate = "Wed Jan 17 09:24:26 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", URL = "http://www.gbv.de/dms/hbz/toc/ht000381636.pdf", acknowledgement = ack-nhfb, GWS-number = "N11", tableofcontents = "Introduction / vii \\ Solution of Sparse Stiffness Matrices for Structural Systems / Edward L. Wilson / 1 \\ Linear Programming Problems Arising from Partial Differential Equations / Dianne P. O'Leary / 25 \\ Shifted Incomplete Cholesky Factorization / Thomas A. Manteuffel / 41 \\ Algorithmic Aspects of the Multi-Level Solution of Finite Element Equations / Randolph E. Bank and A. H. Sherman / 62 \\ LASCALA --- A Language for Large Scale Linear Algebra / A. W. Westerberg and T. J. Berna / 90 \\ Practical Comparisons of Codes for the Solution of Sparse Linear Systems / Iain S. Duff / 107 \\ Software for Sparse Gaussian Elimination with Limited Core Storage / S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 135 \\ A Quotient Graph Model for Symmetric Factorization / Alan George and Joseph W. H. Liu / 154 \\ The Use of Sparse Matrices for Image Reconstruction from Projections / Gabor T. Herman / 176 \\ Row-Generation Methods for Feasibility and Optimization Problems Involving Sparse Matrices and Their Applications \\ Yair Censor and Gabor T. Herman / 197 \\ Lanczos and the Computation in Specified Intervals of the Spectrum of Large, Sparse Real Symmetric Matrices \\ Jane Cullum and Ralph A. Willoughby / 220 \\ Systolic Arrays (for VLSI) / H. T. Kung and Charles E. Leiserson / 256 \\ A Basis Factorization Method for Block Triangular Linear Programs / Andre F. Perold and George B. Dantzig / 283 \\ On Combining the Schemes of Reid and Saunders for Sparse LP Bases / David M. Gay / 313", } @Proceedings{Kaagstrom:1983:MPP, editor = "Bo K{\aa}gstr{\"o}m and Axel Ruhe", booktitle = "{Matrix Pencils: Proceedings of a Conference Held at Pite Havsbad, Sweden, March 22--24, 1982}", title = "{Matrix Pencils: Proceedings of a Conference Held at Pite Havsbad, Sweden, March 22--24, 1982}", volume = "973", publisher = pub-SV, address = pub-SV:adr, pages = "xi + 293", year = "1983", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0062089", ISBN = "0-387-11983-3, 3-540-11983-3 (print), 3-540-39447-8 (e-book)", ISBN-13 = "978-0-387-11983-0, 978-3-540-11983-8 (print), 978-3-540-39447-1 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 973", bibdate = "Tue May 6 14:53:45 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/lnm1980.bib; z3950.loc.gov:7090/Voyager", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/BFb0062089; http://www.springerlink.com/content/978-3-540-39447-1", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/304", subject = "Eigenvalues; Congresses; Matrix pencils; Numerical analysis", tableofcontents = "A. General $(A-A B)$-Pencils \\ \\ A.1 Canonical Reductions --- Theory and Algorithms \\ \\ J. Demmel / The condition number of equivalence transformations that block diagonalize matrix pencils / 2 \\ V. N. Kublanovskaya / An approach to solving the spectral problem of $A - A B$ / 17 \\ B. Kagstr{\"o}m / On computing the Kronecker canonical form of regular $(A - A B)$-pencils / 30 \\ P. Van Dooren / Reducing subspaces --- definitions, properties, and algorithms / 58 \\ \\ A.2 Aspects from Differential Equations / / 74 \\ \\ C. W. Gear, L. R. Petzold / Differential/algebraic systems and matrix pencils / 75 \\ K-M. Liu, E. L. Ortiz / Approximation of eigenvalues defined by ordinary differential equations with the Tau method / 90 \\ \\ A.3 Algorithms for Large Sparse Unsymmetric $(A - A I)$-Problems / 103 \\ \\ A. Ruhe / The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems / 104 \\ Y. Saad / Projection methods for solving large sparse eigenvalue problems / 121 \\ \\ B. Symmetric $(A - A B)$-Pencils and Applications / / 145 \\ \\ L. Aasland, P. Bj{\o}rstad / The generalized eigenvalue problem in ship design and offshore industry --- a comparison of traditional methods with the Lanczos process / 146 \\ E. G. Carnoy, M. Geradin / On the practical use of the Lanczos algorithm in finite element applications to vibration and bifurcation problems / 156 \\ T. Ericsson / Implementation and applications of the spectral transformation Lanczos algorithm / 177 \\ D. J. Evans / Preconditioned iterative methods for the generalized eigenvalue problem / 189 \\ A. Jennings / On bounds for symmetric eigenvalue problems / 195 \\ \\ C. Generalized Singular Values and Data Analysis / / 206 \\ \\ G. W. Stewart / A method for computing the generalized singular value decomposition / 207 \\ J-G. Sun / Perturbation analysis for the generalized eigenvalue and the generalized singular value problem / 221 \\ C. Van Loan / A generalized SVD analysis of some weighting methods for equality constrained least squares / 245 \\ P-{\AA}. Wedin / On angles between subspaces / 263 \\ S. Wold, H. Martens, H. Wold / The multivariate calibration problem in chemistry solved by the PLS method / 286", } @Book{Cowell:1984:SDM, editor = "Wayne R. Cowell", booktitle = "Sources and Development of Mathematical Software", title = "Sources and Development of Mathematical Software", publisher = pub-PH, address = pub-PH:adr, pages = "xii + 404", year = "1984", ISBN = "0-13-823501-5", ISBN-13 = "978-0-13-823501-7", LCCN = "QA76.95 .S68 1984", bibdate = "Tue Dec 14 22:44:45 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", series = "Prentice-Hall Series in Computational Mathematics, Cleve Moler, Advisor", acknowledgement = ack-nhfb, tableofcontents = "Observations on the mathematical software effort / W. J. Cody \\ LINPACK: A package for solving linear systems / J. J. Dongarra and G. W. Stewart \\ FUNPACK: A package of special function routines / W. J. Cody \\ EISPACK: A package for solving matrix eigenvalue problems / J. J. Dongarra and C. B. Moler \\ The MINPACK project / J. More, D. Sorensen, B. Garbow, and K. Hillstrom \\ Software for ordinary differential equations / L. F. Shampine and H. A. Watts \\ Sources of information on quadrature software / D. Kahaner \\ A survey of sparse matrix software / Iain S. Duff \\ Mathematical software for elliptic boundary value problems \\ Ronald F. Boisvert and Roland A. Sweet \\ The IMSL Library / Thomas J. Aird \\ The SLATEC common mathematical library / Bill L. Buzbee \\ The Boeing mathematical software library / A. H. Erisman, K. W. Neves, and I. R. Philips \\ The PORT mathematical subroutine Library / Phyllis Fox \\ The evolving NAG library service / Brian Ford and James C. T. Pool", } @Proceedings{Iazeolla:1984:MCP, editor = "Giuseppe Iazeolla and Pierre Jacques Courtois and A. Hordijk", booktitle = "{Mathematical computer performance and reliability: proceedings of the International workshop: Pisa, Italy, September 26--30, 1983}", title = "{Mathematical computer performance and reliability: proceedings of the International workshop: Pisa, Italy, September 26--30, 1983}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "x + 429", year = "1984", ISBN = "0-444-86892-5", ISBN-13 = "978-0-444-86892-3", LCCN = "QA76.9.E94 M37 1984", bibdate = "Thu May 29 16:27:23 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://catalog.hathitrust.org/api/volumes/oclc/10505592.html; http://www.dandelon.com/servlet/download/attachments/dandelon/ids/DE004D409A71E004A5EA4C12579DE00471484.pdf", acknowledgement = ack-nhfb, subject = "Matematica applicata - Congressi - 1983; Elaborazione elettronica dei dati - Modelli matematici- Congressi - 1983; Congressi - Pisa - 1983", tableofcontents = "Part I: Queueing System Models \\ \\ 1.1. Decomposability in General Markovian Networks / S. Balsamo (University of Pisa, Dipartimento di Informatica, Italy) / 3 \\ \\ 1.2. On the Analysis of Two-Dimensional Queueing Problems / J. W. Cohen (University of Utrecht, Mathematical Institute, The Netherlands) / 17 \\ \\ 1.3. Diffusion Approximations for Computer/Communications Systems / E. G. Coffman and M. I. Reiman (Bell Labs, Murray Hill, USA) / 33 \\ \\ 1.4. On Functional Equations for One or Two Complex Variables Arising in the Analysis of Stochastic Models / \\ G. Fayolle (INRIA, Rocquencourt, France) / 55 \\ \\ 1.5. Insensitivity for Stochastic Networks / A. Hordijk (University of Leiden, Dept. of Mathematics and Computer Science, The Netherlands) / 77 \\ \\ 1.6. Aggregation and Disaggregation in Queueing Networks: The Principle of Product-Form Synthesis / S. Balsamo and G. Iazeolla (University of Pisa, Dipartimento di Informatica, Italy) / 95 \\ \\ 1.7. The Dependence of Sojourn Times in Closed Queueing Networks / F.P. Kelly (University of Cambridge, Statistical Laboratory, England) / 111 \\ \\ 1.8. On the Existence and Uniqueness of the Homogeneous Network / R. Marie and G. Rubino (IRISA/INRIA, Rennes, France) / 123 \\ \\ 1.9. Problems of Reducibility in Structured Markov Chains of M/G/l Type and Related Queueing Models in Communication Engineering / M. F. Neuts (University of Delaware, Dept. of Mathematics, USA) / 139 \\ \\ 1.10. Weak D-Markov Chain and its Application to a Queueing Network / Y. Takahashi (University of Tohoku, Dept. of Economics, Japan) / 153 \\ \\ 1.11. A Renewal Approximation for the Generalized Switched Poisson Process / P. Tran-Gia (University of Stuttgart, Inst. of Switching and Data Technics, W. Germany) / 167 \\ \\ 1.12. Multi-Armed Bandit Problems and Resource Sharing Systems / P. Varaiya and J. Walrand (University of California, Berkeley, Dept. of Computer Sciences, USA) / 181 \\ \\ Part II: Approximation Techniques \\ \\ 2.1. Iterative Aggregation/Disaggregation Methods / F. Chatelin (University of Grenoble, Lab. IMAG, France). . / 199 \\ \\ 2.2. Error Bounds for the Analysis by Decomposition of Non-Negative Matrices / P. J. Courtois and P. Semal (Philips Research, Brussels, Belgium) / 209 \\ \\ 2.3. A Perspective on Iterative Methods for the Approximate Analysis of Closed Queueing Networks / E. de Souza e Silva, S. S. Lavenberg and R. R. Muntz (Computer Science Department, UCLA, Los Angeles, USA) (IBM Research Center, Yorktown Heights, USA) / 225 \\ 2.4. Fixed-Point Approximations for Distributed Systems / I. Mitrani (University of Newcastle upon Tyne, Computing Lab., England) / 245 \\ \\ 2.5. An Aggregation Principle for Computing Invariant Probability Vectors for Semi-Markovian Models / R. Schassberger (Technical University of Berlin, Dept. of Mathematics, W. Germany) / 259 \\ \\ 2.6. Aggregation Methods for Large Markov Chains / P. J. Schweitzer (University of Rochester, Graduate School of Management, USA) / 275 \\ \\ 2.7. On the Structure of Nearly Uncoupled Markov Chains / G. W. Stewart (University of Maryland, Dept. of Computer Science, USA) / 287 \\ \\ 2.8. A Bound Problem in the Modeling of Computer Systems and Queueing Networks / C. P. Tan (University of Malaya, and Columbia University, Dept. of \\ Mathematical Statistics, USA) / 303 \\ \\ Part III: Performance and Reliability Models \\ \\ 3.1. Performance Analysis of the Checkpoint-Rollback-Recovery System via Diffusion Approximation / A. Duda (University of Paris-Sud, ISEM, France) / 315 \\ \\ 3.2. Modelling the Execution of Block Structured Processes with Hardware and Software Failures / E. Gelenbe* and I. Mitrani** (* University of Paris-Sud, ISEM, France) (** University of Newcastle upon Tyne, Computing Lab., England) / 329 \\ \\ 3.3. Trustable Evaluation of Computer Systems Dependability / J.-C. Laprie (LAAS, CNRS, France) / 341 \\ \\ 3.4. Performability Modeling of Distributed Real-Time Systems / J. F. Meyer (University of Michigan, Computing Research Lab., USA) / 361 \\ \\ 3.5. Some Results on Database Locking: Solutions, Computational Algorithms and Asymptotics / D. Mitra and P. J. Weinberger (Bell Labs, Murray Hill, USA) / 373 \\ \\ 3.6. A Golden Ratio Control Policy for a Communication Channel / A. Itai and Z. Rosberg (Technion, Computer Science Department, Israel) / 387 \\ \\ 3.7. Reliability Evaluation for Fault-Tolerant Systems / K. S. Trivedi (Duke University, Dept. of Computer Science, USA) / 403 \\ \\ Part IV: State of the Art and Future Directions \\ \\ Panel Discussion / / 417 \\ \\ Author Index / / 429", } @Proceedings{Allen:1986:CSS, editor = "David M. Allen", booktitle = "{Computer science and statistics: Proceedings of the Seventeenth Symposium on the Interface of Computer Sciences and Statistics, Radisson Plaza Hotel, Lexington, Kentucky, March 17--19, 1985}", title = "{Computer science and statistics: Proceedings of the Seventeenth Symposium on the Interface of Computer Sciences and Statistics, Radisson Plaza Hotel, Lexington, Kentucky, March 17--19, 1985}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xi + 342", year = "1986", ISBN = "0-444-70018-8 (paperback)", ISBN-13 = "978-0-444-70018-6 (paperback)", LCCN = "QA276.4 .S95 1985", MRclass = "62-06 (Proceedings of conferences (statistics)); 65C99 (Probabilistic methods, simulation and stochastic differential equations (numerical analysis)); 62-07 (Data analysis (statistics))", bibdate = "Thu May 29 16:50:58 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/bmdp.bib; https://www.math.utah.edu/pub/tex/bib/s-plus.bib; https://www.math.utah.edu/pub/tex/bib/sas.bib; https://www.math.utah.edu/pub/tex/bib/spss.bib", URL = "http://catalog.hathitrust.org/api/volumes/oclc/13455449.html; http://www.dtic.mil/dtic/tr/fulltext/u2/a166019.pdf; http://zbmath.org/?q=an:0647.62008", ZMnumber = "0647.62008", acknowledgement = ack-nhfb, meetingname = "Symposium on the Interface (17o. 1985. Lexington)", subject = "Mathematical statistics; Data processing; Congresses; calcul statistique; informatique statistique; syst{\`e}me interactif; langage statistique; m{\'e}thode num{\'e}rique; enseignement informatique; statistique; logiciel math{\'e}matique; poste travail; logiciel statistique; mod{\`e}le non lin{\'e}aire; statistique math{\'e}matique; analyse donn{\'e}e; infographie; intelligence artificielle; Informatique; Congr{\`e}s; Datenverarbeitung.; Statistik.; Kongress; Estad{\'i}stica matem{\'a}tica; Inform{\'a}tica; Congresos", } @Proceedings{Boardman:1986:CSS, editor = "Thomas J. Boardman and Irene M. Stefanski", booktitle = "{Computer science and statistics. Proceedings of the 18th Symposium on the Interface, Fort Collins, Colorado, March 1986}", title = "{Computer science and statistics. Proceedings of the 18th Symposium on the Interface, Fort Collins, Colorado, March 1986}", publisher = "American Statistical Association", address = "Washington, DC, USA", pages = "xiii + 466", year = "1986", LCCN = "QA 276.4 S95 1986; TL695 N67 1992", MRnumber = "62-06 68-06 68U99 65C99", bibdate = "Thu May 29 17:03:56 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://zbmath.org/?q=an:0638.62003", ZMnumber = "0638.62003", acknowledgement = ack-nhfb, xxISBN = "92-835-0689-8", xxISBN = "0-8186-0698-3", xxISBN-13 = "978-92-835-0689-8", xxISBN-13 = "978-0-8186-0698-4", xxnote = "Find correct ISBN: library catalogs have bad values??", } @Proceedings{George:1986:PCS, editor = "Alan George and G. W. (Gilbert W.) Stewart and Robert G. Voigt", booktitle = "Parallel computing: special volume", title = "Parallel computing: special volume", volume = "77", publisher = pub-ESP, address = pub-ESP:adr, pages = "357", month = may, year = "1986", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", LCCN = "QA184 L75 v. 77", bibdate = "Fri Jan 24 06:44:39 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", series = j-LINEAR-ALGEBRA-APPL, acknowledgement = ack-nhfb, keywords = "Algebras, Linear.; Parallel processing (Electronic computers)", } @Proceedings{Iserles:1987:SAN, editor = "A. Iserles and M. J. D. Powell", booktitle = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", title = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", volume = "9", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "x + 719", year = "1987", ISBN = "0-19-853614-3", ISBN-13 = "978-0-19-853614-7", LCCN = "QA297.J65 1986", bibdate = "Mon Sep 9 14:56:14 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", series = "The Institute of Mathematics and Its Applications conference series; new series", URL = "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf; http://zbmath.org/?q=an:0611.00024", ZMnumber = "0611.00024", acknowledgement = ack-nhfb, confdate = "14--18 April 1986", conflocation = "Birmingham, UK", confsponsor = "Inst. Math. Appl.; SIAM", pubcountry = "UK", tableofcontents = "Contributors / / xiii \\ 1. Eigenvalue problems / J. H. Wilkinson / 1 \\ 2. Numerical linear algebra in statistical computing / N. J. Higham and G. W. Stewart / 41 \\ 3. Sparse matrices / J. K. Reid / 59 \\ 4. Multivariate approximation / Carl de Boor / 87 \\ 5. Data approximation by splines in one and two independent variables / M. G. Cox / 111 \\ 6. Methods for best approximation and regression problems / G. A. Watson / 139 \\ 7. Branch cuts for complex elementary functions / W. Kahan / 165 \\ 8. Recent developments in linear and quadratic programming / R. Fletcher / 213 \\ 9. Solving systems of nonlinear equations by tensor methods / R. B. Schnabel and P. D. Frank / 245 \\ 10. Numerical methods for bifurcation problems / A. D. Jepson and A. Spence / 273 \\ 11. On the iterative solution of differential and integral equations using secant updating techniques / A. Griewank / 299 \\ 12. Methods for nonlinear constraints in optimization calculations / M. J. D. Powell / 325 \\ 13. The influence of vector and parallel processors on numerical analysis / I. S. Duff / 359 \\ 14. Developments in stability theory for ordinary differential equations / J. D. Lambert / 409 \\ 15. Stiff ODE initial value problems and their solution / A. R. Curtis / 433 \\ 16. Order stars and stability / G. Wanner / 451 \\ 17. The state of the art in the numerical treatment of integral equations / C. T. H. Baker / 473 \\ 18. Strongly elliptic boundary integral equations / W. L. Wendland / 511 \\ 19. Collocation methods for one-dimensional Fredholm and Volterra integral equations / H. Brunner / 563 \\ 20. Numerical methods for free and moving boundary problems / C. W. Cryer / 601 \\ 21. Multigrid methods for elliptic equations / J. Walsh / 623 \\ 22. Galerkin finite element methods and their generalizations / K. W. Morton / 645 \\ 23. Recent developments in the numerical solution of nonlinear conservation laws / S. Osher and P. K. Sweby / 681 \\ Index / 701", } @Proceedings{Edwards:1988:CPC, editor = "D. (David) Edwards and N. E. (Niels E.) Raun", booktitle = "{COMPSTAT: proceedings in computational statistics, 8th symposium held in Copenhagen 1988}", title = "{COMPSTAT: proceedings in computational statistics, 8th symposium held in Copenhagen 1988}", publisher = pub-PHYSICA-VERLAG, address = pub-PHYSICA-VERLAG:adr, bookpages = "xiv + 451", pages = "xiv + 451", year = "1988", ISBN = "3-7908-0411-8", ISBN-13 = "978-3-7908-0411-9", LCCN = "QA276.4 .C57 1988", bibdate = "Tue Jan 10 12:37:12 MST 2012", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://catalog.hathitrust.org/api/volumes/oclc/19564603.html; http://zbmath.org/?q=an:0732.00016", ZMnumber = "0732.00016", acknowledgement = ack-nhfb, remark = "Papers presented at COMPSTAT 1988, the 8th biannual Symposium in Computational Statistics held under the auspices of the International Association for Statistical Computing.", subject = "Statistics; Data processing; Congresses; Mathematical statistics", tableofcontents = "Keynote Papers \\ \\ Parallel Linear Algebra in Statistical Computations / G. W. Stewart / 3 \\ Three Examples of Computer-Intensive Statistical Inference / B. Efron. (See section `Late Arrivals' pp. 423--431) / \\ \\ Non-Parametric Estimation \\ \\ Efficient Nonparametric Smoothing in High Dimensions Using Interactive Graphical Techniques / W. H{\"a}rdle. (Invited paper) / 17 \\ A Boundary Modification of Kernel Function Smoothing, with Application to Insulin Absorption Kinetics. / P. Hougaard / 31 \\ A Roughness Penalty Regression Approach for Statistical Graphics / M. G. Schimek / 37 \\ \\ Projection Pursuit \\ Detecting Structures by Means of Projection Pursuit / 7.5. Yenyukov. (Invited paper) / 47 \\ Confidence Regions for Projection Pursuit Density Estimates / E. Elguero and S. Holmes-Junca / 59 \\ A Robustness Property of the Projection Pursuit Methods in Sampling from Separably Dependent Random Vectors / B. Baldessari and F. Gallo / 65 \\ \\ Graphical Techniques \\ Graphical Modelling with Large Numbers of Variables: An Application of Principal Components / J. Whittaker, A. Iliakopoulos, and P. W. F. Smith / 73 \\ Some Graphical Displays for Square Tables / A. de Falguerolles and J. R. Mathieu / 81 \\ Data Plotting Methods for Checking Multivariate Normality and Related Ideas / T. Isogai / 87 \\ Computer-aided Illustration of Regression Diagnostics / T. Nummi. M. Nurhonen, and S. Puntanen / 93 \\ Computer Guided Diagnostics / D. A. Belsley, A. Venetoulias, and R. E. Welsch / 99 \\ \\ Expert Systems \\ How should the Statistical Expert System and its User see Each Other? / J. A. Nelder. (Invited paper) / 107 \\ Towards a Probabilistic Analysis of MYCIN-like Expert Systems / P. H{\'a}jek / 117 \\ An Expert System Accepting Knowledge in a form of Statistical Data / R. Jirou{\v{s}}ek and O. K{\v{r}}i{\v{z}} / 123 \\ Building a Statistical Expert System with Knowledge Bases of Different Levels of Abstraction / KM. Wittkowski / 129 \\ An Expert System for the Interpretation of Results of Canonical Covariance Analysis / K. Momirovi{\'c}, J. Radakovi{\'c}, and V. Dobri{\'c} / 135 \\ Building a Statistical Knowledge Base: A Discussion of the Approach used in the Development of THESEUS, a Statistical Expert System / E. Bell and P. Watts / 143 \\ PRINCE: An Expert System for Nonlinear Principal Components Analysis / I. J. Duijsens, T. J. Duijkers, and G. M. van den Berg / 149 \\ Expert Systems for Non-Linear Modelling: Progress and Prospects / G. J. S. Ross / 155 \\ Inside a Statistical Expert System: Statistical Methods Employed in the ESTES System / P. Hietala / 163 \\ An Implementation of an EDA Expert System in Prolog Environment / P. Jirk{\r{u}} / 169 \\ Automatic Acquisition of Knowledge Base from Data without Expert: ESOD (Expert System from Observational Data) / J. Iv{\'a}nek and B. Stejskal / 175 \\ Experiments with Probabilistic Consultation Systems / S. Nordbotten / 181 \\ Statistical Consultants and Statistical Expert Systems / I. W. Molenaar / 187 \\ On Inference Process / T. Westerhoff and P. Naeve / 193 \\ Identification Keys, Diagnostic Tables and Expert Systems / R. W. Payne / 199 \\ \\ Languages and Packages \\ Adding new Statistical Techniques to Standard Software Systems: A Review / C. Payne, N. Cleave, and P. Brown '. / 207 \\ FUNIGIRLS: A Prototype Functional Programming Language for the Analysis of Generalized Linear Models / R. Gilchrist and A. Scallan / 213 \\ BLINWDR: An APL-function Library for Interactively Solving the Problem of Robust and Bounded Influence Regression / R. Dutter / 219 \\ \\ Computational Intensive Methods \\ Exact Non-Parametric Significance Tests / C. R. Mehta, N. R. Patel and P. Senchaudhuri / 227 \\ Resampling Tests of Statistical Hypotheses / A. Young / 233 \\ Clustering Based on Neural Network Processing / H.-M. Adorf and F. Murtagh / 239 \\ Decision Tree Classifier for Speech Recognition / A. M. Morin / 245 \\ \\ Algorithms \\ Efficient Sampling Algorithms and Balanced Samples / J. C. Deville, J. M. Grosbas, and N. Roth (Invited paper) / 255 \\ Recursive Partition in Biostatistics: Stability of Trees and Choice of the Most Stable Classification / A. Ciampi and J. Thiffault / 267 \\ Generating Rules by Means of Regression Analysis / C. Berzuini / 273 \\ A New Algorithm for Matched Case-Control Studies with Applications to Additive Models / T. Hastie and D. Pregibon / 279 \\ An Algorithm for the Approximation of N-Dimensional Distributions / J. Gordesch / 285 \\ Further Recursive Algorithms for Multidimensional Table Computation / B. P. Murphy and G. Bartlett / 291 \\ \\ Statistical Methods \\ Nonlinear Regression: Methodological and Software Aspects / A. Mess{\'e}an. (Invited paper) / 299 \\ Comparing Sensitivity of Models to Missing Data in the GMANOVA / E. P. Liski and T. Nummi / 311 \\ A Modelling Approach to Multiple Correspondence Analysis / M. Green / 317 \\ Multidimensional Scaling on the Sphere / M. A. A. Cox and T. F. Cox / 323 \\ A Monte Carlo Evaluation of the Methods for Estimating the Parameters of the Generalized Lambda Distribution / M. C. Okur / 329 \\ Statistical Guidance for Model Modification in Covariance Structure Analysis / T. C. Luijben and A. Boomsma / 335 \\ Similarities Functions / G.le Calv{\'e}s / 341 \\ Robust Bayesian Regression Analysis with HPD-Regions / K. Felsenstein and K. Potzelberger / 349 \\ \\ Time Series \\ Estimation of ARMA Process Parameters and Noise Variance by Means of a Non-Linear Filtering Algorithm / M. P. Mu{\~n}oz-Gracia, J. Pages-Fita and M. Marti-Recober / 357 \\ Autoregressive Models with Latent Variables / P. H. C. Eilers / 363 \\ An Algorithm for Time Series Decomposition Using State Space Models with Singular Transition Matrix / E. Alvoni / 369 \\ \\ Statistical Data Bases and Survey Processing \\ New Perspectives in Computer Assisted Survey Processing / W. J. Keller and J. G. Bethlehem. (Invited paper) / 377 \\ Multiple Imputation for Data-Base Construction / D. B. Rubin. (Invited paper) / 389 \\ GRASP: A Complete Graphical Conceptual Language for Definition and Manipulation of Statistical Databases / T. Catarci and G. Santucci / 401 \\ \\ Experimental Design \\ New Algorithmic and Software Tools for D-Optimal Design Computation in Nonlinear Regression / J. P. Vila / 409 \\ \\ Econometric Computing \\ Model-Building on Micro Computers: Sapreadsheets or Specific Software / J.-L. Brillet / 417 \\ \\ Late Arrivals \\ Three Examples of Computer-Intensive Statistical Inference / B. Efron / 423 \\ New Computer Procedures for Generating Optimal Mixture Designs on Finite Design Spaces / H. A. Yonchev / 433 \\ Screening Based Exclusively on Experts Opinions / J. {\'C}wik and E. Pleszczy{\'n}iska / 439 \\ \\ Address list of Authors / / 445", } @Proceedings{Sharda:1989:IRC, editor = "R. Sharda and B. L. Golden and E. Wasil and O. Balci and G. W. Stewart", booktitle = "Impacts of Recent Computer Advances on Operations Research", title = "Impacts of Recent Computer Advances on Operations Research", volume = "9", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xii + 585", year = "1989", ISBN = "0-444-01492-6", ISBN-13 = "978-0-444-01492-4", LCCN = "T57.6 .I4831 1989", bibdate = "Wed May 28 17:52:37 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", series = "Publications in Operations Research", URL = "http://zbmath.org/?q=an:0727.90047", ZMnumber = "0727.90047", acknowledgement = ack-nhfb, subject = "Operations research; Data processing", tableofcontents = "\\ I. Plenary papers \\ \\ G. B. Dantzig / Decomposition techniques for large-scale electric power systems planning under uncertainty / 3--22 \\ \\ II. Parallel algorithms for mathematical programming \\ \\ R. S. Barr, M. G. Christiansen / A parallel auction algorithm: A case study in the use of parallel object-oriented programming, 23--32 \\ J. O. Berkey, P. Y. Wang / A comparative study of some parallel bin packing algorithms / 33--43 \\ T. E. Gerasch, P. Y. Wang, S. T. Weidman / SIMD knapsack approximation algorithms / 44-- 56 \\ A. R. Joshi, D.-S. Chen / A vectorized dual algorithm for generalized network problem / 57--70 \\ H. S. Mahmassani, K. C. Mouskos / Vectorization of transportation network equilibrium assignment codes / 71--81 \\ G. L. Schultz, R. R. Meyer / A flexible parallel algorithm for block-constrained optimization problems / 82--91 \\ R. Hunter Mladineo / Supercomputers and global optimization / 92--105 \\ J. M. Mulvey, H. Vladimirou / Evaluation of a parallel hedging algorithm for stochastic network programming / 106--119 \\ D. M. Nicol / Parallel solution of dynamic programming equation using optimistic evaluation / 120--130 \\ P. M. Pardalos, G. P. Rodgers / Parallel branch and bound algorithms for unconstrained quadratic zero-one programming / 131--143 \\ G. Plateau, C. Roucairol / A supercomputer algorithm for the 0--1 multiknapsack problem / 144--157 \\ M. J. Saltzman, R. Subramanian, R. E. Marsten / Implementing an interior point LP algorithm on a supercomputer / 158--168 \\ C. Phillips, S. A. Zenios / Experiences with large scale network optimization on the connection machine / 169--182 \\ \\ III. Graphics in optimization \\ \\ I. Lustig / Application of interactive computer graphics to linear programming / 183--189 \\ C. L. Monma, D. F. Shallcross / A PC-based interactive network design system for fiber optic communication networks / 190--204 \\ \\ IV. Microcomputers in operations research \\ \\ E. Gelman, M. A. Pollatschek / Personal computer version of nearly triangular Leontief LP solution / 205--216 \\ T. P. Harrison, J. L. Martin / Optimizing exchange agreements in the refining industry / 217-- 225 \\ J. K. Ho / Nonprocedural implementation of mathematical programming algorithms / 226--237 \\ R. Terry, D. DeBald, R. Chikkala / Closed queueing network analysis of indirect labor requirements / 238--247 \\ M. L. Villanueva, N. A. Wittpenn, C. B. Austin, E. Baker / A microcomputer-based marine geographic information system with marketing application / 248--262 \\ E. Wasil, B. Golden, R. Sharda / Mathematical programming software for the microcomputer: Recent advances, comparisons and trends / 263--272 \\ E. Wasil, A. Assad / Project management software for the microcomputer: Recent advances and future directions / 273--288 \\ \\ V. Artificial intelligence and expert systems \\ \\ G. Anandalingam, R. Mathieu, C. L. Pittard, N. Sinha / Artificial intelligence based approaches for solving hierarchical optimization problems / 289--301 \\ J. W. Denton, G. R. Madey / Impact of neurocomputing on operations research / 302--312 \\ H. J. Greenberg / Neural networks for an intelligent mathematical programming system / 313-- 320 \\ M. R. Hilliard, G. E. Liepins, M. Palmer, G. Rangarajan / The computer as a partner in algorithmic design: Automated discovery of parameters for a multi-objective scheduling heuristic / 321--331 \\ J.- Y. Potvin, S. F. Smith / Flexible systems for the design of heuristic algorithms in complex OR domains / 332--346 \\ \\ VI. Vehicle routing and scheduling applications \\ \\ D. Jovanovic, P. T. Harker / SCAN: A decision support system for railroad scheduling / 347--360 \\ K. E. Nygard, P. Juell, K. Nagesh / An interactive decision support system for vehicle routing / 361--372 \\ J. R. Schaffer, P. K. Pearl / Vehicle routing and scheduling for home delivery / 373--384 \\ \\ VII. Simulation \\ \\ O. Balci, R. E. Nance / Simulation model development: The multidimensionality of the computing technology pull / 385--395 \\ R. K. Kincaid, K. W. Miller, S. K. Park / Locating P mobile servers on a congested network: A simulation analysis / 396--406 \\ R. L. Moose, R. E. Nance / The design and development of an analyzer for discrete event model specifications / 407--421 \\ R. J. Paul / Visual simulation: Seeing is believing? 422--432 \\ M. B. Silberholz, B. L. Golden, E. K. Baker / Simulating a marine container terminal on the Macintosh II / 433 \\ \\ VIII. Model development and analysis systems \\ \\ G. H. Bradley / Mathematical programming modeling project - overview / 447--462 \\ R. G. Brown, J. W. Chinneck, G. M. Karam / Optimization with constraint programming systems / 463--473 \\ M. Grauer, S. Albers, M. Frommberger / Concept and first experiences with an object-oriented interface for mathematical programming / 474--483 \\ G. Mitra / Tools for modelling support and construction of optimization applications / 484--496 \\ A. D. Waren, M. Pechura, L. S. Lasdon / The GRG2 model builder / 497--506 \\ S. Zenios, S. S. Nielsen, M. Pinar / On the use of advance architecture computers via high-level modelling languages / 507 \\ \\ IX. Telecommunications \\ \\ A. J. Perticone, J. P. Jarvis, D. R. Shier / Evaluation and design of voice telecommunications network / 521--532 \\ \\ X. Numerical analysis \\ \\ R. Baker Kearfott / Interval arithmetic methods for nonlinear systems and nonlinear optimization: An outline and status / 533--542 \\ A. P. Morgan / Polynomial continuation / 543--554 \\ L. T. Watson / Modern homotopy methods in optimization / 555--566", } @Proceedings{Wouk:1989:PPM, editor = "Arthur Wouk", booktitle = "{Parallel processing and medium-scale multiprocessors [Proceedings of the workshop, held in Stanford, California, January 1986]}", title = "{Parallel processing and medium-scale multiprocessors [Proceedings of the workshop, held in Stanford, California, January 1986]}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xi + 207", year = "1989", ISBN = "0-89871-238-6", ISBN-13 = "978-0-89871-238-4", LCCN = "QA76.5 .W665 1986", MRnumber = "68-06 68N25 68W30", bibdate = "Thu May 29 18:03:16 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://books.google.com/books?id=O3GOAAAAIAAJ; http://catalog.hathitrust.org/api/volumes/oclc/19630560.html; http://zbmath.org/?q=an:0681.68004", ZMnumber = "0681.68004", acknowledgement = ack-nhfb, meetingname = "Workshop on Parallel Processing and Medium-scale Multiprocessors (1986 : Stanford, Calif.)", remark = "Proceedings of the Workshop on Parallel Processing and Medium-Scale Multiprocessors, Stanford, California, January, 1986. This workshop was sponsored by the Mathematical Sciences Division of the United States Army Research Office and the Department of Computer Science.", subject = "Parallel processing (Electronic computers); Multiprocessors; multit{\^a}che; hypercube; multiprocesseur; parall{\'e}lisme; traitement parall{\`e}le; Multiprocesseurs.; Multiprocessors.; Parallel processing (Electronic computers)", } @Proceedings{Brown:1990:SAM, editor = "Philip J. Brown and Wayne A. Fuller", booktitle = "{Statistical analysis of measurement error models and applications: proceedings of the AMS-IMS-SIAM joint summer research conference held June 10-16, 1989, with support from the National Science Foundation and the U.S. Army Research Office}", title = "{Statistical analysis of measurement error models and applications: proceedings of the AMS-IMS-SIAM joint summer research conference held June 10-16, 1989, with support from the National Science Foundation and the U.S. Army Research Office}", volume = "112", publisher = pub-AMS, address = pub-AMS:adr, pages = "xii + 248", year = "1990", ISBN = "0-8218-5117-9, 0-8218-7700-3 (e-book)", ISBN-13 = "978-0-8218-5117-3, 978-0-8218-7700-5 (e-book)", ISSN = "0271-4132 (print), 1098-3627 (electronic)", LCCN = "QA275 .A47 1989", bibdate = "Wed May 28 17:40:15 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", series = "Contemporary Mathematics", URL = "http://www.ams.org/conm/112/", acknowledgement = ack-nhfb, mynote = "Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference", remark = "The AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Statistical Analysis of Measurement Error Models and Applications was held at Humboldt State University, Arcata, California.", tableofcontents = "Some history of functional and structural relationships / Peter Sprent \\ \path=https://doi.org/10.1090/conm/112/1087095= \\ Errors-in-variables regression problems in epidemiology / Alice S. Whittemore \\ \path=https://doi.org/10.1090/conm/112/1087096= \\ Models with latent variables: LISREL versus PLS / Hans Schneeweiss \\ \path=https://doi.org/10.1090/conm/112/1087097= \\ Prediction of true values for the measurement error model / Wayne A. Fuller \\ \path=https://doi.org/10.1090/conm/112/1087098= \\ Analysis of residuals from measurement error models / Stephen M. Miller \\ \path=https://doi.org/10.1090/conm/112/1087099= \\ Errors-in-variables estimation in the presence of serially correlated observations / John L. Eltinge \\ \path=https://doi.org/10.1090/conm/112/1087100= \\ Improvements of the naive approach to estimation in nonlinear errors-in-variables regression models / Leon Jay Gleser \\ \path=https://doi.org/10.1090/conm/112/1087101= \\ Structural logistic regression measurement error models / Leonard A. Stefanski and Raymond J. Carroll \\ \path=https://doi.org/10.1090/conm/112/1087102= \\ Measurement error model estimation using iteratively weighted least squares / Daniel W. Schafer \\ \path=https://doi.org/10.1090/conm/112/1087103= \\ Problematic points in nonlinear calibration / Philip J. Brown and Samuel D. Oman \\ \path=https://doi.org/10.1090/conm/112/1087104= \\ Instrumental variable estimation of the nonlinear measurement error model / Yasuo Amemiya \\ \path=https://doi.org/10.1090/conm/112/1087105= \\ A likelihood ratio test for error covariance specification in nonlinear measurement error models / Daniel J. Schnell \\ \path=https://doi.org/10.1090/conm/112/1087106= \\ Plotting techniques for errors-in-variables problems / Cliff H. Spiegelman \\ \path=https://doi.org/10.1090/conm/112/1087107= \\ Perturbation theory and least squares with errors in the variables / G. W. Stewart \\ \path=https://doi.org/10.1090/conm/112/1087108= \\ Orthogonal distance regression / Paul T. Boggs and Janet E. Rogers \\ \path=https://doi.org/10.1090/conm/112/1087109= \\ Computing error bounds for regression problems / Nicholas J. Higham \\ \path=https://doi.org/10.1090/conm/112/1087110= \\ Asymptotic robustness of normal theory methods for the analysis of latent curves / M. W. Browne \\ \path=https://doi.org/10.1090/conm/112/1087111= \\ Bounded influence errors-in-variables regression / Chi Lun Cheng and John W. Van Ness \\ \path=https://doi.org/10.1090/conm/112/1087112= \\ Bounded influence estimation in the errors-in-variables model / V{\'i}ctor J. Yohai and Ruben H. Zamar \\ \path=https://doi.org/10.1090/conm/112/1087113=", } @Proceedings{Cox:1990:RNC, editor = "M. G. Cox and S. Hammarling", booktitle = "Reliable numerical computation", title = "Reliable numerical computation", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xvi + 339", year = "1990", ISBN = "0-19-853564-3", ISBN-13 = "978-0-19-853564-5", LCCN = "QA297 .R435 1990", MRclass = "65-06", MRnumber = "91k:65011", bibdate = "Fri Dec 20 18:34:52 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", note = "Based on papers from a conference in honour of the late James Hardy Wilkinson (died Sunday 5th October 1986) held at National Physical Laboratory, Teddington, Middlesex, UK, 8th--10th July 1987.", price = "US\$75.00", abstract = "Published to honor the late Jim Wilkinson, the respected pioneer in numerical analysis, this book includes contributions from his colleagues and collaborators, leading experts in their own right. The breadth of Wilkinson's research is reflected in the topics covered, which include linear algebra, error analysis and computer arithmetic algorithms, and mathematical software. An invaluable reference, the book is completely up-to-date with the latest developments on the Lanczos algorithm, QR-factorizations, error propagation models, parameter estimation problems, sparse systems, and shape-preserving splines. Reflecting the current growth and vitality of this field, the volume is an essential reference for all numerical analysts.", acknowledgement = ack-nhfb, tableofcontents = "List of contributors / / xv \\ Prologue. Reflections on Jim Wilkinson / Gene Golub / 1 \\ 1. Misconvergence in the Lanczos algorithm / Beresford Parlett / 7 \\ 2. The Lanczos algorithm for a pure imaginary Hermitian matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\ 3. Nearest defective matrices and the geometry of ill-conditioning / James Demmel / 35 \\ 4. Computational aspects of the Jordan canonical form / Theo Beelen and Paul Van Dooren / 57 \\ 5. Some aspects of generalized QR factorizations / C. C. Paige / 73 \\ 6. The multifrontal method in a parallel environment / I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K. Reid / 93 \\ 7. A Schur-complement method for sparse quadratic programming / Philip E. Gill, Walter Murray, Michael A. Saunders, and Margaret H. Wright / 113 \\ 8. A probabilistic round-off error propagation model. Application to the eigenvalue problem / Francoise Chatelin and Marie Christine Brunet / 139 \\ 9. Analysis of the Cholesky decomposition of a semi-definite matrix / Nicholas J. Higham / 161 \\ 10. On the conditioning of parameter estimation problems / James M. Varah / 187 \\ 11. Rounding errors in algebraic process-in level-index arithmetic / F. W J. Olver / 197 \\ 12. Experiments in tearing large sparse systems / Mario Arioli and lain S. Duff / 207 \\ 13. The least-squares solution of linear equations with block-angular observation matrix / M. G. Cox / 227 \\ 14. An iterative method for solving linear inequalities / G. W Stewart / 241 \\ 15. Iterative refinement and reliable computing / {\AA}ke Bj{\"o}rck / 249 \\ 16. Software for shape-preserving spline interpolation / Christian H. Reinsch / 267 \\ 17. Experiences with some software engineering practices in numerical software / D. A. H. Jacobs and G. Markham / 277 \\ 18. Evolution of numerical software for dense linear algebra / Jack Dongarra and Sven Hammarling / 297 \\ Epilogue. Jim Wilkinson: some after-dinner sentiments / L. Fox / 329", } @Proceedings{Stewart:1990:NSM, editor = "W. J. Stewart", booktitle = "Numerical Solutions of {Markov} Chains", title = "Numerical Solutions of {Markov} Chains", publisher = pub-DEKKER, address = pub-DEKKER:adr, pages = "????", year = "1990", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Thu May 29 18:13:39 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, } @Proceedings{Chen:1991:CRT, editor = "Ray R. Chen", booktitle = "{Conference record of the Twenty-fifth Asilomar Conference on Signals, Systems and Computers: November 4--6, 1991, Pacific Grove, California}", title = "{Conference record of the Twenty-fifth Asilomar Conference on Signals, Systems and Computers: November 4--6, 1991, Pacific Grove, California}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xx + 1269 + 5", year = "1991", ISBN = "0-8186-2470-1 (paperback), 0-8186-2471-X (microfiche), 0-8186-2472-8 (hardcover)", ISBN-13 = "978-0-8186-2470-4 (paperback), 978-0-8186-2471-1 (microfiche), 978-0-8186-2472-8 (hardcover)", LCCN = "TK 5102.5 A78 1991", bibdate = "Thu Apr 27 08:38:04 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bell-brad.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "IEEE catalog number 91CH31120. IEEE Computer Society Press order number 2470.", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=382", acknowledgement = ack-nhfb, } @Proceedings{IEEE:1991:ICA, editor = "{IEEE}", booktitle = "{1991 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-91: May 14--17, 1991, The Sheraton Centre Hotel and Towers, Toronto, Ontario, Canada}", title = "{1991 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-91: May 14--17, 1991, The Sheraton Centre Hotel and Towers, Toronto, Ontario, Canada}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "3732 (5 volumes)", year = "1991", ISBN = "0-7803-0003-3 (paperback), 0-7803-0004-1 (hardcover), 0-7803-0005-X (microfiche)", ISBN-13 = "978-0-7803-0003-3 (paperback), 978-0-7803-0004-0 (hardcover), 978-0-7803-0005-7 (microfiche)", LCCN = "TA365 I58 1991; TK7882.S65 I16 1991", bibdate = "Wed May 28 16:58:34 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=540", acknowledgement = ack-nhfb, tableofcontents = "vol. 1. S1: Speech processing 1 \\ vol. 2. S2, VLSI, U: Speech processing 2, VLSI, Underwater signal processing \\ vol. 3. D: Digital signal processing \\ vol. 4. M: Multidimensional signal processing \\ vol. 5. EA: Spectral estimation, Audio and electroacoustics", } @Proceedings{Vaccaro:1991:SSP, editor = "Richard J. Vaccaro", booktitle = "{SVD and signal processing, II: algorithms, analysis, and applications}", title = "{SVD and signal processing, II: algorithms, analysis, and applications}", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "xv + 512", year = "1991", ISBN = "0-444-88896-9", ISBN-13 = "978-0-444-88896-9", LCCN = "TK5102.5 .S93 1991", bibdate = "Thu May 29 18:20:53 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", URL = "http://catalog.hathitrust.org/api/volumes/oclc/22911621.html", abstract = "This volume is an outgrowth of the 2nd International Workshop on SVD and Signal Processing which was held in Kingston, Rhode Island, 25--27 June, 1990. The singular value decomposition (SVD) has been applied to signal processing problems since the late 1970's, although it has been known in various forms for over 100 years. SVD filtering has been shown to give better results at lower signal-to-noise ratios than classical techniques based on linear filtering. This explains in part the recent interest in SVD techniques for signal processing. This book is a compilation of papers that examine in detail the singular decomposition of a matrix and its application to problems in signal processing. Algorithms and implementation architectures for computing the SVD are discussed, and analysis techniques for predicting and understanding the performance of SVD-based algorithms are given. The volume will provide both a stimulus for future research in this field as well as useful reference material for many years to come.", acknowledgement = ack-nhfb, remark = "An outgrowth of the 2nd International Workshop on SVD and Signal Processing, held at the University of Rhode Island, June 25--27, 1990, sponsored by the URI College of Engineering.", subject = "Signal processing; Digital techniques; Decomposition (Mathematics)", tableofcontents = "Part I. Survey Papers \\ \\ The SVD and reduced-rank signal processing / L. L. Scharf / 13--17 \\ Second Order Perturbation Calculation / / 18--?? \\ Parallel implementations of the SVD using implicit CORDIC arithmetic / J-M. Delosme / 33--56 \\ Neural networks for extracting pure/constrained/oriented principal components / S. Y. Kung et al. / \\ Generalizations of the OSVD: structure, properties and applications / B. de Moor / \\ Perturbation theory for the singular value decomposition / G. W. Stewart / \\ \\ Part II. Algorithms and Architectures \\ \\ An accurate product SVD algorithm / A. W. Bojanczyk et al. / \\ The hyperbolic singular value decomposition and applications / R. Onn et al. / \\ Adaptive SVD algorithm with application to narrow-band signal tracking / W. Ferzali, J. G. Proakis / \\ Chebyshev acceleration techniques for solving slowly varying total least squares problems / S. van huffel / \\ Combined Jacobi-type algorithms in signal processing / M. Moonan et al. / \\ A modified non-symmetric Lanczos algorithm and applications / D. Boley, G. Golub / \\ Parallel one sided Euler-Jacobi method for symmetric eigendecomposition and SVD / A. W. Bojanczyk et al. / \\ Using UNITY to implement SVD on the connection machine / M. Kleyn, I. Chakravarty / \\ A CORDIC processor array for the SVD of a complex matrix / J. R. Cavallaro, A. C. Elster / \\ \\ Part III. Analysis of SVD-Based Algorithms \\ \\ Analytical performance prediction of subspace-based algorithms for DOA estimation / Fu Li, R. J. Vaccaro / \\ Spatial smoothing and MUSIC: Further results / B. D. Rao, K. V. S. Hari / \\ A performance analysis of adaptive algorithms in the presence of calibration errors / D. R. Farrier, D. J. Jeffries / \\ Second order perturbation calculation of state space estimation / W. W. F. Pijnappel et al. / \\ The threshold effect in signal processing algorithms which use an estimated subspace / D. W. Tufts et al. / \\ \\ Part IV \\ \\ Applications to signal modeling and detection OSVD and QSVD in signal separation / D. Callaerts et al. / \\ Enhanced sinusoidal and exponential data modeling / J. A. Cadzow, D. M. Wilkes / \\ Enhancements to SVD-Based detection / J. H. Cozzens, M. J. Sousa / \\ Resolution of closely spaced coherent plane waves via SVD / H. Krim et al. / \\ Transient parameter estimation by an SVD-based Wigner distribution / M. F. Griffin, A. M. Finn / \\ Signal/noise subspace decomposition for random transient detection / N. M. Marinovich, L. M. Roytman / \\ Comparisons of truncated QR and SVD methods for AR spectral estimations / S. F. Hsieh et al. / \\ Using singular value decomposition to recover periodic waveforms in noise and with residual carrier / B. Rice / \\ Other Applications. SVD-based low-rank approximations of rational models / A-J. van der Veen, E. F. Deprettere / \\ Computing the singular values and vectors of a Hankel operator / H. Ozbay / \\ SVD analysis of probability matrices / J. A. Ramos / \\ Fast matrix-vector multiplication using displacement rank approximation via an SVD / J. M. Speiser et al. / \\ A new use of singular value decomposition in bioelectric imaging of the brain / D. J. Major, R. J. Sidman /", } @Proceedings{IEEE:1992:III, editor = "IEEE", booktitle = "{ICASSP-92 / 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, March 23--26, 1992, the San Francisco Marriott, San Francisco, California}", title = "{ICASSP-92 / 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, March 23--26, 1992, the San Francisco Marriott, San Francisco, California}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "640 (vol. 1), 572 (vol. 2), 596 (vol. 3), 716 (vol. 4), 696 (vol. 5)", year = "1992", ISBN = "0-7803-0533-7 (hardcover), 0-7803-0532-9 (paperback), 0-7803-0534-5 (microfiche)", ISBN-13 = "978-0-7803-0533-5 (hardcover), 978-0-7803-0532-8 (paperback), 978-0-7803-0534-2 (microfiche)", LCCN = "TK 7882 S65 I16 1992", bibdate = "Sun Apr 07 09:26:57 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib", note = "Five volumes. IEEE catalog number 92CH3103-9", acknowledgement = ack-nhfb, tableofcontents = "vol. 1. S1: Speech processing 1 \\ vol. 2. S2, ANU: Speech processing 2, audio, neural networks, underwater acoustics \\ vol. 3. M: Multidimensional signal processing \\ vol. 4. D1: Digital signal processing \\ vol. 5. D2EV: Digital signal processing 2, estimation, VSLI", } @Proceedings{Meyer:1993:LAM, editor = "C. D. (Carl Dean) Meyer and Robert J. Plemmons", booktitle = "{Linear algebra, Markov chains, and queueing models: [\ldots{} some of the lectures given at the Workshop Linear Algebra, Markov Chains, and Queueing Models held January 13--17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications]}", title = "{Linear algebra, Markov chains, and queueing models: [\ldots{} some of the lectures given at the Workshop Linear Algebra, Markov Chains, and Queueing Models held January 13--17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications]}", volume = "48", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 294", year = "1993", ISBN = "0-387-94085-5 (New York), 3-540-94085-5 (Berlin)", ISBN-13 = "978-0-387-94085-4 (New York), 978-3-540-94085-2 (Berlin)", LCCN = "QA184 .L545 1993", bibdate = "Wed May 28 17:58:34 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", series = "The IMA volumes in mathematics and its applications", URL = "http://catalog.hathitrust.org/api/volumes/oclc/28182134.html; http://www.gbv.de/dms/ilmenau/toc/126000387.PDF; http://zbmath.org/?q=an:0779.00020", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Congresses; Markov processes; Queuing theory", tableofcontents = "Error bounds for the computation of null vectors with applications to Markov chains / Jesse L. Barlow \\ The influence of nonnormality on matrix computations / Fran{\c{c}}oise Chatelin \\ Componentwise error analysis for stationary iterative methods / Nicholas J. Higham and Philip A. Knight \\ The character of a finite Markov chain / Carl D. Meyer \\ Gaussian elimination, perturbation theory, and Markov chains / G. W. Stewart \\ Algorithms for periodic Markov chains / Fran{\c{c}}ois Bonhoure, Yves Dallery, and William J. Stewart \\ Iterative methods for queueing networks with irregular state-spaces / Raymond H. Chan \\ Analysis of $p$-cyclic iterations for Markov chains / Apostolos Hadjidimos and Robert J. Plemmons \\ Iterative methods for finding the stationary vector for Markov chains / Dianne P. O'Leary \\ Local convergence of (exact and inexact) iterative aggregation / Daniel B. Szyld \\ Automated generation and analysis of Markov reward models using stochastic reward nets / Gianfranco Ciardo \ldots{} [et al.] \\ Means and variances in Markov reward systems / Winfried K. Grassman \\ A direct algorithm for computing the stationary distribution of a $p$-cyclic Markov chain / Daniel P. Heyman \\ Approximate analysis of a discrete-time queueing model of the shared buffer ATM switch / S. Hong, H. G. Perros, and H. Yamashita \\ Algorithms for infinite Markov chains with repeating columns / Guy Latouche \\ Cray-2 memory organization and interprocessor memory contention / Robert W. Numrich", } @Proceedings{Moonen:1993:LAL, editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De Moor}", booktitle = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", title = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", volume = "232", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "ix + 435", year = "1993", ISBN = "0-7923-2151-0", ISBN-13 = "978-0-7923-2151-4", LCCN = "QA185.D37 L56 1993", MRclass = "65-06 (65Fxx 65Y05)", MRnumber = "94e:65009", bibdate = "Mon Jan 15 17:53:04 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "NATO ASI series. Series E, Applied sciences", URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html; http://www.gbv.de/dms/hbz/toc/ht004938330.pdf; http://zbmath.org/?q=an:0810.00029", ZMnumber = "0810.00029", abstract = "In recent years there has been great interest in large scale and real-time matrix computations; these computations arise in a variety of fields, such as computer graphics, imaging, speech and image processing, telecommunication, biomedical signal processing, optimization and so on. This volume, which is an outgrowth of a NATO ASI, held at Leuven, Belgium, August 1992, gives an account of recent research advances in numerical techniques used in large scale and real-time computations and their implementation on high performance computers.", acknowledgement = ack-nhfb, tableofcontents = "Preface / / xi \\ Invited Lectures / / 1 \\ Large scale structural analysis on massively parallel computers / P. E. Bj{\o}rstad and J. Cook / 3 \\ Data-parallel BLAS as a basis for LAPACK on massively parallel computers / P. E. Bj{\o}rstad and T. S{\o}revik / 13 \\ a Large-scale nonlinear constrained optimization / A. R. Conn, N. Gould and Ph. L. Toint / 21 \\ Trading off parallelism and numerical stability / J. W. Demmel / 49 \\ Subband filtering: CORDIC modulation and systolic quadrature mirror filter tree / E. F. Deprettere / 69 \\ A parallel image rendering algorithm and architecture based on ray tracing and radiosity shading / E. F. Deprettere and L.-S. Shen / 91 \\ Reduction and approximation of linear computational circuits / P. Dewilde and A.-J. van der Veen / 109 \\ The look-ahead Lanczos process for large nonsymmetric matrices and related algorithms / R. W. Freund / 137 \\ Case studies of real-time processing in robotics / W. M. Gentleman / 165 \\ Adaptive signal processing with emphasis on QRD-least squares lattice / S. Haykin / 183 \\ A direct method for reordering eigenvalues in the generalized real Schur form of a regular matrix pair (A, B) / B. K{\aa}gstr{\"o}m / 195 \\ Block shift invariance and efficient system identification algorithms / N. Kalouptsidis / 219 \\ Computing the singular value decomposition on a fat-tree architecture / T. J. Lee, F. T. Luk and D. L. Boley / 231 \\ A new matrix decomposition for signal processing / F. T. Luk and S. Qiao / 241 \\ The linear algebra of perfect reconstruction filtering / M. Stewart and G. Cybenko / 249 \\ Determining rank in the presence of error / G. W. Stewart / 275 \\ Approximation with Kronecker products / C. F. Van Loan and N. Pitsianis / 293 \\ Some linear algebra issues in large-scale optimization / M. H. Wright / 315 \\ Contributed Lectures / / 339 \\ Direct and inverse unitary eigenproblems in signal processing: an overview / G. S. Ammar, W. B. Gragg and L. Reichel / 341 \\ Block implementations of the symmetric QR and Jacobi algorithms / P. Arbenz and M. Oettli / 345 \\ Linear algebra for large-scale information retrieval applications / M. W. Berry / 347 \\ Matched filter vs. least-squares approximation / L. H. J. Bierens / 349 \\ Reordering diagonal blocks in real Schur form / A. W. Bojanczyk and P. Van Dooren / 351 \\ Placing zeroes and the Kronecker canonical form / D. L. Boley and P. Van Dooren / 353 \\ Analysis of the recursive least squares lattice algorithm / J. R. Bunch and R. C. LeBorne / 355 \\ Adaptive Chebyshev iteration based on modified moments / D. Calvetti, G. H. Golub and L. Reichel / 357 \\ Continuous realization methods and their applications / M. T. Chu / 359 \\ Asymptotic behavior of orthogonal polynomials / T. Dehn / 361 \\ CADCS and parallel computing / F. Dumortier, A. Van Cauwenberghe and L. Boullart / 363 \\ Eigenvalue roulette and random test matrices / A. Edelman / 365 \\ On numerical methods for unitary eigenvalue problems / H. Fa{\sas}bender / 369 \\ Accurate singular values and differential qd algorithms / K. V. Fernando and B. N. Parlett / 371 \\ Orthogonal projection and total least squares / R. D. Fierro and J. R. Bunch / 375 \\ Gauss quadratures associated with the Arnoldi process and the Lanczos algorithm / R. W. Freund and M. Hochbruck / 377 \\ An implementation of the QMR method based on coupled two-term recurrences / R. W. Freund and N. M. Nachtigal / 381 \\ Computationally efficient homotopies for the H 2 model order reduction problem / Y. Ge, L. T. Watson, E. G. Collins, Jr. and L. D. Davis / 385 \\ A fast algorithm for $QR$ decomposition of Toeplitz matrices / G. O. Glentis / 387 \\ Unitary Hessenberg methods for Toeplitz approximations and applications / Ch. He and A. Bunse-Gerstner / 389 \\ Perturbation theory and backward error for $A X - X B = C$ / N. J. Higham / 391 \\ Fast transforms and elliptic problems / T. Huckle / 393 \\ An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices / F. Jarre / 395 \\ The lattice-ladder with generalized forgetting / J. Kadlec / 397 \\ Solving a least squares problem with boundary constraints / L. Kaufman / 399 \\ Estimating the extremal eigenvalues and condition number by the Lanczos algorithm with a random start / J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\ A generalized ADI iterative method / N. Levenberg and L. Reichel / 403 \\ Quaternions and the symmetric eigenvalue problem / N. Mackey / 405 \\ Application of the Gauss-Seidel iteration to the RLS algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407 \\ Ranks of submatrices of a matrix and its inverse / C. C. Paige and M. Wei / 409 \\ A QRD-based least-squares algorithm for multipulse antenna array signal processing / I. K. Proudler / 411 \\ On displacement structures for covariance matrices and lossless functions / P. A. Regalia and F. Desbouvries / 413 \\ Application of vector extrapolation and conjugate gradient type methods to the semiconductor device problem / W. H. A. Schilders / 415 \\ Accurate symmetric eigenreduction by a Jacobi method / I. Slapni{\v{c}}ar / 417 \\ The order-recursive Chandrasekhar equations for fast square-root Kalman filtering / D. T. M. Slock / 419 \\ Hybrid iterative methods based on Faber polynomials / G. Starke / 421 \\ Aspects of implementing a 'C' matrix library / D. E. Stewart / 423 \\ Intermediate fill-in in sparse QR decomposition / M. T{\r{u}}ma / 425 \\ Shifting strategies for the parallel QR algorithm / D. S. Watkins / 427 \\ List of Participants / / 429 \\ Authors Index / / 437", } @Proceedings{Brown:1994:PCL, editor = "J. David Brown and Moody T. Chu and Donald C. Ellison and Robert J. Plemmons", booktitle = "{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}", title = "{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}", volume = "73", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "lxv + 644", year = "1994", ISBN = "0-89871-339-0", ISBN-13 = "978-0-89871-339-8", LCCN = "QC19.2 .C67 1993", bibdate = "Wed Jun 8 14:42:43 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager", series = "Proceedings in Applied Mathematics", acknowledgement = ack-nhfb, meetingname = "Cornelius Lanczos International Centenary Conference (1993:Raleigh, NC)", subject = "Mathematical physics; Congresses; Astrophysics; Mathematics; Lanczos, Cornelius; Physicists; Hungary; Biography; Mathematicians", subject-dates = "1893--1974", tableofcontents = "The Life and Works of Cornelius Lanczos \\ \\ A Photographic Essay / / xvii \\ Cornelius Lanczos: A Biographical Essay / Barbara Gellai / xxi \\ Cornelius Lanczos (1893-1974), and the Hungarian Phenomenon in Science and Mathematics / Peter D. Lax / xlix \\ The Roots of Cornelius Lanczos / George Marx / liii \\ Reminiscences of Cornelius Lanczos / Jon Todd / lviii \\ Published Papers and Books of Cornelius Lanczos / / lx \\ \\ Plenary Presentations: Computational Mathematics \\ \\ Lanczos and the FFT: A Discovery Before its Time / James W. Cooley / 3 \\ Lanczos Algorithms for Large Scale Symmetric and Nonsymmetric Matrix Eigenvalue Problems / Jane K. Cullum / 11 \\ The Look-Ahead Lanczos Process for Nonsymmetric Matrices and its Applications / Roland W Freund / 33 \\ The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic / Anne Greenbaum / 49 \\ The Lanczos Process and Pade Approximation / Martin H. Gutknecht / 61 \\ The Tau Method and the Numerical Solution of Differential Equations: Past Research and Recent Research / Eduardo L. Ortiz / 77 \\ Krylov Subspace Processes, Krylov Subspace Methods, and Iteration Polynomials / C. C. Paige / 83 \\ Do We Fully Understand the Symmetric Lanczos Algorithm Yet? / Beresford N. Parlett / 93 \\ On Generalized Band Matrices and Their Inverses / P{\'a}l R{\'o}sa, Francesco Romani, and Roberto Bevilacqua / 109 \\ Theoretical Error Bounds and General Analysis of a Few Lanczos-Type Algorithms / Youcef Saad / 123 \\ Lanczos and Linear Systems / G. W. Stewart / 135 \\ \\ Plenary Presentations: Theoretical Physics and Astrophysics \\ \\ Integration on the Space of Connections Modulo Gauge Transformations / Abbay Ashtekar, Donald Marolf, and Jose Mourdo / 143 \\ Quasiclassical Domains in a Quantum Universe / James B. Hartle / 161 \\ Gauge Invariant Energy-Momentum Tensor in Spinar Electrodynamics / D. Petiot and Y. Takahashi / 173 \\ $\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi Piran / 187 \\ Lanczos's Early Contributions to Relativity and His Relationship with Einstein / John Stachel / 201 \\ Topological Roots of Black Hole Entropy / Claudio Teitelboim / 223 \\ Variational Principles, Local Symmetries, and Black Hole Entropy / Robert M. Wald / 231 \\ \\ Mathematics Minisymposia \\ \\ Eigenvalue Computations: Theory and Algorithms / / 241 \\ Eigenvalue Computations: Applications / / 249 \\ Moments in Numerical Analysis / / 265 \\ Iterative Methods for Linear Systems / / 277 \\ Least Squares / / 301 \\ Software for Lanczos-based Algorithms / / 311 \\ Tau Method / / 335 \\ Chebyshev Polynomials / / 357 \\ Lanczos Methods in Control and Signal Processing / / 375 \\ Development of the FFT / / 393 \\ The FFT in Signal Processing / / 399 \\ Wavelets / / 411 \\ \\ Physics Minisymposia \\ \\ Computational Magnetohydrodynamics in Astrophysics / / 431 \\ Numerical Simulations of Collisionless Space Plasmas / / 453 \\ Detection of Gravitational Radiation from Astrophysical Sources / / 477 \\ Lanczos $H$-tensor / / 489 \\ Cosmic Censorship / / 513 \\ Cauchy Problem of General Relativity / / 527 \\ Black Hole Evaporation and Thermodynamics / / 543 \\ The Problem of Time in Quantum Gravity / / 555 \\ New Variables and Loop Quantization / / 571 \\ Decoherence and the Foundations of Quantum Mechanics / / 589 \\ Open Questions in Particle Theory / / 603 \\ Supercollider Physics / / 621 \\ Symplectic Methods in Physics / / 633", } @Proceedings{Golub:1994:RAI, editor = "Gene Golub and Anne Greenbaum and Mitchell Luskin", booktitle = "{Recent advances in iterative methods: [papers from the IMA Workshop on Iterative Methods for Sparse and Structured Problems, held in Minneapolis, Minnesota, February 24--March 1, 1992]}", title = "{Recent advances in iterative methods: [papers from the IMA Workshop on Iterative Methods for Sparse and Structured Problems, held in Minneapolis, Minnesota, February 24--March 1, 1992]}", volume = "60", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 225", year = "1994", ISBN = "0-387-94252-1 (New York), 3-540-94252-1 (Berlin)", ISBN-13 = "978-0-387-94252-0 (New York), 978-3-540-94252-8 (Berlin)", LCCN = "QA297.8 .R43 1994", MRclass = "65-06", MRnumber = "95m:65001", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib", series = "The IMA Volumes in Mathematics and its Applications", URL = "http://zbmath.org/?q=an:0790.00015", ZMnumber = "0790.00015", acknowledgement = ack-nhfb, tableofcontents = "Some themes in Gene H. Golub's work on iterative methods / Dianne P. O'Leary / 1 / \\ Computing the sparse singular value decomposition via SVDPACK / Michael W. Berry / 13 \\ Gaussian quadrature applied to adaptive Chebyshev iteration / D. Calvetti, G. H. Golub, and L. Reichel / 31 \\ Ordering effects on relaxation methods applied to the discrete convection-diffusion equation / Howard C. Elman and Michael P. Chernesky / 45 \\ On the error computation for polynomial based iteration methods / Bernd Fischer and Gene H. Golub / 59 \\ Transpose-free quasi-minimal residual methods for non-Hermitian linear systems / Roland W. Freund / 69 \\ Matrices that generate the same Krylov residual spaces / Anne Greenbaum and Zdenek Strakos / 95 \\ Incomplete block factorizations as preconditioners for sparse SPD matrices / L. Yu. Kolotilina and A. Yu Yeremin / 119 \\ How fast can iterative methods be? / Olavi Nevanlinna / 135 \\ Rational Krylov algorithms for nonsymmetric eigenvalue problems / Axel Ruhe / 149 \\ Highly parallel preconditioners for general sparse matrices / Youcef Saad / 165 \\ A two-stage iteration for solving nearly completely decomposable Markov chains / G. W. Stewart, W. J. Stewart and D. F. McAllister / 201 \\ Minimum residual modifications to Bi-CG and to the preconditioner / Henk A. Van der Vorst / 217", } @Proceedings{Griffiths:1994:NAP, editor = "D. F. (David Francis) Griffiths and G. A. (G. Alistair) Watson", booktitle = "{Numerical analysis 1993: proceedings of the 15th Dundee Conference, June--July 1993}", title = "{Numerical analysis 1993: proceedings of the 15th Dundee Conference, June--July 1993}", volume = "303", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "275", year = "1994", ISBN = "0-582-22568-X", ISBN-13 = "978-0-582-22568-8", ISSN = "0269-3674", LCCN = "QA297 .D85 1993", bibdate = "Mon Jan 2 16:37:00 MST 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; library.ox.ac.uk:210/ADVANCE", series = "Pitman research notes in mathematics series", acknowledgement = ack-nhfb, meetingname = "Dundee Biennial Conference on Numerical Analysis (15th: 1993)", remark = "The 15th Dundee Biennial Conference on Numerical Analysis was held at the University of Dundee during the 4 days June 29--July 2, 1993.", subject = "Numerical analysis; Congresses", tableofcontents = "J. W. Harrett \& Wenbin Liu: Finite Element Approximation of Degenerate Quasilinear Elliptic and Parabolic Problems / 1 \\ R. K. Beatson \& M. J. D. Powell: An Iterative Method for Thin Plate Spline Interpolation that Employs Approximations to Lagrange Functions / 17 \\ I. S. Duff: The Solution of Augmented Systems / 10 \\ C. M. Elliott \& A. R. Gardiner: One Dimensional Phase Field Computations / 56 \\ J. de Frutos \& J. M. Sanz-Serna: Erring and being Conservative / 75 \\ P. E. Gill, W. Murray, D. B. Poncele{\'o}n \& M. A. Saunders: Solving Reduced KKT Systems in Barrier Methods for Linear Programming / 89 \\ G. H. Golub \& Gerard Meurant: Matrices, Moments, and Quadrature / 105 \\ J. Groeneweg \& M. N. Spijker: On the Error due to the Stopping of the Newton Iteration in Implicit Linear Multistep Methods / 157 \\ D. J. Higham: The Dynamics of a Discretised Nonlinear Delay Differential Equation / 167 \\ A. R. Humphries, D. A. Jones \& A. M. Stuart: Approximation of Dissipative Partial Differential Equations over Long Time Intervals / 180 \\ N. K. Nichols: Differential--Algebraic Equations and Control System Design / 208 \\ G. W. Stewart: $UTV$ Decompositions / 225 \\ M. J. Todd: A Lower Bound on the Number of Iterations of an Interior-Point Algorithm for Linear Programming / 237 \\ P. Townsend \& M. F. Webster: Computational Analysis in Rheological Flow Problems / 260 \\ List of Contributed Talks / / 267", } @Proceedings{Stewart:1995:CMC, editor = "William J. Stewart", booktitle = "{Computations with Markov chains: proceedings of the 2nd International Workshop on the Numerical Solution of Markov Chains}", title = "{Computations with Markov chains: proceedings of the 2nd International Workshop on the Numerical Solution of Markov Chains}", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "xvi + 600", year = "1995", ISBN = "0-7923-9550-6", ISBN-13 = "978-0-7923-9550-8", LCCN = "QA274.7 .I595 1995", bibdate = "Thu May 29 19:15:04 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", URL = "http://zbmath.org/?q=an:0940.00042", ZMnumber = "0940.00042", acknowledgement = ack-nhfb, meetingname = "International Workshop on the Numerical Solution of Markov Chains (2nd : 1995 : Raleigh, NC)", remark = "Papers from the workshop held Jan. 16-18, 1995, in Raleigh, NC", subject = "Markov processes; Congresses", tableofcontents = "1. Detecting Block GI/M/1 and Block M/G/1 Matrices from Model Specifications / S. Berson and R. Muntz / 1 \\ 2. On Cyclic Reduction Applied to a Class of Toeplitz-like Matrices Arising in Queueing Problems / D. Bini and B. Meini / 21 \\ 3. A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue / G. Latouche and P. J. Schweitzer / 39 \\ 4. Preconditioned Krylov subspace methods for the numerical solution of Markov chains / Y. Saad / 49 \\ 5. A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains / M. Benzi, F. Sgallari and G. Spaletta / 65 \\ 6. Iterative Methods for Queueing Models with Batch Arrivals / R. H. Chun and W.-K. Ching / 81 \\ 7. Transient Colutions of Markov Processes by Krylov Subspaces / R. B. Sidje and B. Philippe / 95 \\ 8. Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains / A. Rindos, S. Woolet, I. Viniotis and K. Trivedi / 121 \\ Time-Dependent behavior of Redundant Systems with Deterministic Repair / / 135 \\ What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses / / 151 \\ Immediate Events in Markov Chains / / 163 \\ Compositional Markovian Modelling Using A Process Algebra / / 177 \\ Equivalence Relations for Stochastic Automata Networks / / 197 \\ Graphs and Stochastic Automata Networks / / 217 \\ Analyzing Sample Path Data from Markov Chain Sampling Experiments / / 237 \\ Resource Sharing Models with State-Dependent Arrivals of Batches / / 255 \\ Implementable Policies: Discounted Cost Case / / 283 \\ Two Bounding Schemes for the Steady-State Solution of Markov Chains / / 307 \\ The Power-Series Algorithm for Markovian Queueing Networks / / 321 \\ Discrete-Time Markovian Stochastic Petri Nets / / 339 \\ Concurrent Generalized Petri Nets / / 359 \\ Exploiting Isomorphisms and Special Structures in the Analysis of Markov Regenerative Stochastic Petri Nets / / 383 \\ Numerical solution of large finite Markov chains by algebraic multigrid techniques / / 403 \\ On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains / / 425 \\ A Computationally Efficient Algorithm for Characterizing the Superposition of Multiple Heterogeneous Interrupted Bernoulli Processes / / 443 \\ Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and its Queueing Applications / / 463 \\ Efficient Solutions for a Class of Non-Markovian Models / / 483 \\ Markovian Arrival and Service Communication Systems: Spectral Expansions, Separability and Kronecker-Product Forms / / 507 \\ Empirical Comparison of Uniformization Methods for Continuous-Time Markov Chains / / 547 \\ Numerical Methods for M/G/1 Type Queues / / 571 \\ Closing the Gap between Classical and Tensor Based Iteration Techniques / / 582 \\ Adaptive Relaxation for the Steady-State Analysis of Markov Chains / / 585 \\ State Space Decomposition for Large Markov Chains / / 587 \\ Aggregation/Disaggregation Method on Parallel Computer / / 591 \\ Parallel Implementation of the GTH Algorithm for Markov Chains / / 594 \\ A Parallel Implementation of the Block-GTH algorithm / / 597 \\ Approximate Computation of Sojourn Time Distribution in Open Queueing Networks / / 599", } @Proceedings{vanHuffel:1997:RAT, editor = "Sabine van Huffel", booktitle = "{Recent advances in total least squares techniques and errors-in-variables modeling}", title = "{Recent advances in total least squares techniques and errors-in-variables modeling}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxii + 377", year = "1997", ISBN = "0-89871-393-5", ISBN-13 = "978-0-89871-393-0", LCCN = "QA275 .R4 1997", bibdate = "Thu May 29 19:17:47 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; z3950.loc.gov:7090/Voyager", note = "Proceedings of the Second International Workshop on Total Least Squares and Errors-in-Variables Modeling, Leuven, Belgium, August 21--24, 1996.", URL = "http://zbmath.org/?q=an:0861.00018", ZMnumber = "0861.00018", acknowledgement = ack-nhfb, subject = "Least squares; Congresses; Error analysis (Mathematics)", } @Proceedings{ACM:1998:AWJ, editor = "{ACM}", booktitle = "ACM 1998 Workshop on Java for High-Performance Network Computing, February 28 and March 1, 1998", title = "{ACM} 1998 Workshop on Java for High-Performance Network Computing, February 28 and March 1, 1998", publisher = pub-ACM, address = pub-ACM:adr, pages = "????", year = "1998", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Tue Feb 26 08:15:29 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "Possibly unpublished, except electronically.", URL = "http://www.cs.ucsb.edu/conferences/java98/program.html", acknowledgement = ack-nhfb, } @Proceedings{IEEE:2002:IIC, editor = "{IEEE}", booktitle = "{2002 IEEE international conference on acoustics, speech and signal processing: proceedings, May 13-17, 2002, Renaissance Orlando Resort, Orlando, Florida, USA}", title = "{2002 IEEE international conference on acoustics, speech and signal processing: proceedings, May 13-17, 2002, Renaissance Orlando Resort, Orlando, Florida, USA}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "civ + 4194 (4 volumes)", year = "2002", ISBN = "0-7803-7402-9 (paperback)", ISBN-13 = "978-0-7803-7402-7 (paperback)", LCCN = "TA365 I11 2002; TK7882.S65 I61 2002", bibdate = "Wed May 28 17:21:25 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", note = "IEEE catalog number 02CH37334C", acknowledgement = ack-nhfb, subject = "Speech processing systems; Signal processing systems; Electro-acoustics; Underwater acoustics; Integrated circuits; Very large scale integration; DSP; signal multidimensionnel; traitement parole; traitement signal biom{\'e}dical; syst{\`e}me embarqu{\'e}; architecture traitement signal; multim{\'e}dia; temps r{\'e}el; filigrane; indexation video; analyse image; authentification; codage vid{\'e}o; codage image; algorithme traitement image; Traitement du signal; Congr{\`e}s; Traitement automatique de la parole; {\'E}lectroacoustique; Acoustique sous-marine; Circuits int{\'e}gr{\'e}s {\`a} tr{\`e}s grande {\'e}chelle; DSP; signal multidimensionnel; traitement parole; traitement signal biom{\'e}dical; syst{\`e}me embarqu{\'e}; architecture traitement signal; multim{\'e}dia; temps r{\'e}el; filigrane; indexation video; analyse image; authentification; codage vid{\'e}o; codage image; algorithme traitement image.", tableofcontents = "Vol. 1, Speech processing, neural networks for signal processing \\ Vol. 2, Signal processing theory and methods, audio and electro-acoustics, multimedia signal processing \\ Vol. 3, Signal processing for communications, sensor array and multichannel signal processing, design and implementation of signal processing systems \\ Vol. 4, Image and multidimensional signal processing, industry technology tracks, special sessions, signal processing education, student forum (all areas)", } @Book{Kilmer:2010:GWS, editor = "Misha Elena Kilmer and Dianne P. O'Leary", booktitle = "{G. W. Stewart}: selected works with commentaries", title = "{G. W. Stewart}: selected works with commentaries", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xii + 729", year = "2010", DOI = "https://doi.org/10.1007/978-0-8176-4968-5", ISBN = "0-8176-4967-0 (hardcover), 0-8176-4968-9 (e-book)", ISBN-13 = "978-0-8176-4967-8 (hardcover), 978-0-8176-4968-5 (e-book)", LCCN = "QA188 .S74 2010", bibdate = "Wed May 28 12:51:20 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Contemporary mathematicians", URL = "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=64586; http://rave.ohiolink.edu/ebooks/ebc/978081764968; http://site.ebrary.com/id/1042123", abstract = "Published in honor of his 70th birthday, this volume explores and celebrates the work of G. W. (Pete) Stewart, a world-renowned expert in computational linear algebra. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. \booktitle{G. W. Stewart: Selected Works with Commentaries} will appeal to graduate students, practitioners.", acknowledgement = ack-nhfb, subject = "Stewart, G. W (Gilbert W.); Perturbation (Mathematics); Matrices", tableofcontents = "Cover \\ G. W. Stewart \\ Contents \\ Foreword \\ List of Contributors \\ Part I: G. W. Stewart \\ 1. Biography of G. W. Stewart \\ 2. Publications, Honors, and Students \\ 2.1 Publications of G. W. Stewart \\ 2.2 Major Honors of G. W. Stewart \\ 2.3 Ph.D. Students of G. W. Stewart \\ Part II: Commentaries \\ 3. Introduction to the Commentaries \\ 4. Matrix Decompositions: Linpack and Beyond \\ 4.1 The Linpack Project \\ 4.2 Some Algorithmic Insights \\ 4.3 The Triangular Matrices of Gaussian Elimination and Related Decompositions \\ 4.4 Solving Sylvester Equations \\ 4.5 Perturbation Bounds for Matrix Factorizations \\ 4.6 Rank Degeneracy \\ 4.7 Pivoted $QR$ as an Alternative to SVD \\ 4.8 Summary \\ 5. Updating and Downdating Matrix Decompositions \\ 5.1 Solving Nonlinear Systems of Equations \\ 5.2 More General Update Formulas for $QR$ \\ 5.3 Effects of Rounding Error on Downdating Cholesky Factorizations \\ 5.4 Stability of a Sequence of Updates and Downdates \\ 5.5 An Updating Algorithm for Subspace Tracking \\ 5.6 From the $URV$ to the $ULV$ \\ 5.7 Impact \\ 6. Least Squares, Projections, and Pseudoinverses \\ 6.1 Continuity of the Pseudoinverse \\ 6.2 Perturbation Theory \\ 6.3 Weighted Pseudoinverses \\ 6.4 Impact \\ 7. The Eigenproblem and Invariant Subspaces: Perturbation Theory \\ 7.1 Perturbation of Eigenvalues of General Matrices \\ 7.2 Further Results for Hermitian Matrices \\ 7.3 Stochastic Matrices \\ 7.4 Graded Matrices \\ 7.5 Rayleigh / Ritz Approximations \\ 7.6 Powers of Matrices \\ 7.7 Impact \\ 8. The SVD, Eigenproblem, and Invariant Subspaces: Algorithms \\ 8.1 Who Invented Subspace Iteration? \\ 8.2 Extracting Invariant Subspaces \\ 8.3 Approximating the SVD \\ 8.4 Impact \\ 9. The Generalized Eigenproblem \\ 9.1 Perturbation Theory \\ 9.2 The $QZ$ Algorithm \\ 9.3 Gershgorin's Theorem \\ 9.4 Definite Pairs \\ 10. Krylov Subspace Methods for the Eigenproblem \\ 10.1 A Krylov / Schur Algorithm \\ 10.2 Backward Error Analysis of Krylov Subspace Methods \\ 10.3 Adjusting the Rayleigh Quotient in Lanczos Methods \\ 10.4 Impact \\ 11. Other Contributions \\ References \\ Index \\ Part III: Reprints \\ 12 Papers on Matrix Decompositions \\ 12.1 [GWS-B / 2] (with J. J. Dongarra, J. R. Bunch, and C. B. Moler) Introduction from Linpack Users Guide \\ 12.2 [GWS-J / 17] (with R. H. Bartels), ''Algorithm 432: Solution of the Matrix Equation $AX + XB = C$'' \\ 12.3 [GWS-J / 32] ''The Economical Storage of Plane Rotations'' \\ 12.4 [GWS-J / 34] ''Perturbation Bounds for the $QR$ Factorization of a Matrix'' \\ 12.5 [GWS-J / 42] (with A. K. Cline, C. B. Moler, and J. H. Wilkinson), ''An Estimate for the Condition Number of a Matrix'' \\ 12.6 [GWS-J / 49] ''Rank Degeneracy'' \\ 12.7 [GWS-J / 78] ''On the Perturbation of $LU$, Cholesky, and $QR$ Factorizations'' \\ 12.8 [GWS-J / 89] ''On Graded $QR$ Decompositions of Products of Matrices'' \\ 12.9 [GWS-J / 92] ''On the Perturbation of $LU$ and Cholesky Factors'' \\ 12.10 [GWS-J / 94] ''The Triangular Matrices of Gaussian Elimination and Related Decompositions'' \\ 12.11 [GWS-J / 103] ''Four Algorithms for the the [sic] Efficient Computation of Truncated Pivoted $QR$ Approximations to a Sparse Matrix'' \\ 12.12 GWS-J / 118 (with M. W. Berry and S. A. Pulatova) ''Algorithm 844: Computing Sparse Reduced-Rank Approximations to Sparse Matrices'' \\ 13 Papers on Updating and Downdating Matrix Decompositions \\ 14 Papers on Least Squares, Projections, and Generalized Inverses \\ 15 Papers on the Eigenproblem and Invariant Subspaces: Perturbation Theory \\ 16 Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms \\ 17 Papers on the Generalized Eigenproblem \\ 18 Papers on Krylov Subspace Methods for the Eigenproblem", }

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