%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.06",
%%%     date            = "31 March 2008",
%%%     time            = "17:00:13 MDT",
%%%     filename        = "parlett-beresford-n.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             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "27303 5429 22977 236074",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "BibTeX; bibliography",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of
%%%                        Beresford Neill Parlett, B.A. (Oxford, 1955),
%%%                        Ph.D. (Stanford, 1962), Professor Emeritus of
%%%                        Computer Science, and Professor Emeritus of
%%%                        Mathematics, University of California,
%%%                        Berkeley.  The companion LaTeX file
%%%                        parlett-beresford-n.ltx can be used to
%%%                        typeset this bibliography.
%%%
%%%                        Beresford N. Parlett's personal Web site is
%%%
%%%                            http://math.berkeley.edu/~parlett/
%%%
%%%                        This bibliography contains a few additional
%%%                        entries that refer to the work of Beresford
%%%                        N. Parlett in their titles.
%%%
%%%                        At version 1.06, the year coverage looked
%%%                        like this:
%%%
%%%                             1962 (   1)    1978 (   4)    1994 (   9)
%%%                             1963 (   0)    1979 (   2)    1995 (   8)
%%%                             1964 (   4)    1980 (   6)    1996 (   8)
%%%                             1965 (   2)    1981 (   8)    1997 (   5)
%%%                             1966 (   6)    1982 (   9)    1998 (   2)
%%%                             1967 (   4)    1983 (   7)    1999 (   0)
%%%                             1968 (   1)    1984 (   7)    2000 (   7)
%%%                             1969 (   3)    1985 (   8)    2001 (   0)
%%%                             1970 (   2)    1986 (   4)    2002 (   4)
%%%                             1971 (   3)    1987 (   8)    2003 (   4)
%%%                             1972 (   2)    1988 (   7)    2004 (   4)
%%%                             1973 (   3)    1989 (   2)    2005 (   5)
%%%                             1974 (   3)    1990 (   9)    2006 (   1)
%%%                             1975 (   3)    1991 (   5)    2007 (   0)
%%%                             1976 (   5)    1992 (  10)    2008 (   1)
%%%                             1977 (   9)    1993 (   5)
%%%
%%%                             Article:         95
%%%                             Book:             7
%%%                             InCollection:     1
%%%                             InProceedings:   25
%%%                             Misc:             2
%%%                             PhdThesis:        1
%%%                             Proceedings:     24
%%%                             TechReport:      55
%%%
%%%                             Total entries:  210
%%%
%%%                        Data for this bibliography have been
%%%                        collected from the University of Utah
%%%                        Mathematics Department bibliography archives,
%%%                        the TeX User Group bibliography archives, the
%%%                        Karlsruhe Computer Science bibliography
%%%                        archives, from the European Mathematical
%%%                        Society Zentralblatt fuer Mathematik
%%%                        database, from the American Mathematical
%%%                        Society MathSciNet database, from the
%%%                        publication list at Beresford N. Parlett's
%%%                        personal Web site, and from several online
%%%                        library catalogs, including those of the
%%%                        British Library, the Karlsruhe Virtual
%%%                        Library catalog, the Oxford University
%%%                        Library, and the US Library of Congress.
%%%
%%%                        This file is available as part of the BibNet
%%%                        Project.  The master copy is available for
%%%                        public access on ftp.math.utah.edu in the
%%%                        directory tree /pub/bibnet/authors.  It is
%%%                        mirrored to netlib.bell-labs.com in the directory
%%%                        tree /netlib/bibnet/authors, from which it is
%%%                        available via anonymous ftp and the Netlib
%%%                        service.
%%%
%%%                        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{
    "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi"
}

%%% ====================================================================
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@String{inst-CPAM-UCB           = "Center for Pure and Applied Mathematics,
                                  University of California, Berkeley"}

@String{inst-CPAM-UCB:adr       = "Berkeley, CA, USA"}

@String{inst-ERL-CE-UCB         = "Electronics Research Laboratory,
                                  College of Engineering, University of
                                  California, Berkeley"}
@String{inst-ERL-CE-UCB:adr     = "Berkeley, CA, USA"}

@String{inst-UT-CS              = "Department of Computer Science,
                                  University of Tennessee, Knoxville"}
@String{inst-UT-CS:adr          = "Knoxville, TN 37996, USA"}

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

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BULL-AMS-NS           = "Bulletin of the American Mathematical
                                  Society (New Series)"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMP-PHYS-COMM        = "Computer Physics Communications"}

@String{j-COMP-STRUCTURES       = "Computers and Structures"}

@String{j-COMPUT-SCI-ENG        = "Computing in Science and Engineering"}

@String{j-FOUND-COMPUT-MATH     = "Foundations of Computational Mathematics.
                                  The Journal of the Society for the Foundations
                                  of Computational Mathematics"}

@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization
                                   and Computer Graphics"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
                                  Computing (IJHSC)"}

@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical
                                  Methods in Engineering"}

@String{j-J-COMP-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-COMPUT-PHYS         = "Journal of computational physics"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-J-NUM-LIN-ALG-APPL    = "Journal of Numerical linear algebra with
                                  applications"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-NUM-LIN-ALG-APPL      = "Numerical Linear Algebra with Applications"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-PARALLEL-ALGORITHMS-APPL = "Parallel Algorithms and Applications"}

@String{j-PARALLEL-COMPUTING    = "Parallel Computing"}

@String{j-SIAM-J-ALG-DISC-METH  = "SIAM Journal on Algebraic and Discrete
                                  Methods"}

@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-REVIEW           = "SIAM Review"}

@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-THEOR-POPUL-BIOL      = "Theoretical Population Biology"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-Z-ANGE-MATH-MECH      = "Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, 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-BIRKHAUSER-BOSTON   = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-DUNOD               = "Dunod"}
@String{pub-DUNOD:adr           = "Paris, France"}

@String{pub-EDITORIAL-MIR       = "Editorial Mir"}
@String{pub-EDITORIAL-MIR:adr   = "Moscow, USSR"}

@String{pub-ELSEVIER            = "Elsevier"}
@String{pub-ELSEVIER:adr        = "Amsterdam, The Netherlands"}

@String{pub-ELSEVIER-SCIENCE    = "Elsevier Science, Inc."}
@String{pub-ELSEVIER-SCIENCE:adr = "Amsterdam, The Netherlands"}

@String{pub-GRUYTER             = "Walter de Gruyter"}
@String{pub-GRUYTER:adr         = "Berlin, Germany"}

@String{pub-LONGMAN             = "Longman Scientific and Technical"}
@String{pub-LONGMAN:adr         = "Harlow, Essex, UK"}

@String{pub-MIT                 = "MIT Press"}
@String{pub-MIT:adr             = "Cambridge, MA, USA"}

@String{pub-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ 07458, USA"}

@String{pub-PLENUM              = "Plenum Press"}
@String{pub-PLENUM:adr          = "New York, NY, USA; London, UK"}

@String{pub-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-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA; London, UK; Sydney, Australia"}

%%% ====================================================================
%%% Bibliography entries, sorted by ascending year with
%%% "bibsort -byyear":

@PhdThesis{Parlett:1962:BML,
  author =       "Beresford Neill Parlett",
  title =        "{I}. Bundles of matrices and the linear independence
                 of their minors; {II}. Applications of {Laguerre}'s
                 method to the matrix eigenvalue problem",
  type =         "{Ph.D.} dissertation",
  school =       "Department of Mathematics, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 118",
  year =         "1962",
  bibdate =      "Fri Nov 11 05:07:47 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=32898;
                 http://wwwlib.umi.com/dxweb/details?doc_no=5023767",
  acknowledgement = ack-nhfb,
  advisor =      "George E. Forsythe",
}

@Article{Forsythe:1964:TPA,
  author =       "George E. Forsythe",
  title =        "Tests of {Parlett}'s {ALGOL} Eigenvalue Procedure $Eig
                 3$ (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "87",
  pages =        "486--487",
  month =        jul,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1964:DUM,
  author =       "Beresford Parlett",
  title =        "The development and use of methods of {LR} type",
  journal =      j-SIAM-REVIEW,
  volume =       "6",
  number =       "3",
  pages =        "275--295",
  year =         "1964",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  MRclass =      "65.35",
  MRnumber =     "MR0172450 (30 \#2669)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  fjournal =     "SIAM Review",
  ZMnumber =     "0242.65039",
}

@Article{Parlett:1964:LMA,
  author =       "Beresford N. Parlett",
  title =        "{Laguerre}'s Method Applied to the Matrix Eigenvalue
                 Problem",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "87",
  pages =        "464--485",
  month =        jul,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65.40",
  MRnumber =     "MR0165668 (29 \#2948)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  keywords =     "numerical analysis",
  kwds =         "nla, eig, Laguerre's method, polynomial",
  ZMnumber =     "0124.33004",
}

@Article{Parlett:1964:NBA,
  author =       "Beresford Parlett",
  title =        "A Note on {La Budde}'s Algorithm (in {Technical Notes
                 and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "87",
  pages =        "505--506",
  month =        jul,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65.35",
  MRnumber =     "MR0165671 (29 \#2951)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F99 Numerical linear algebra",
  fjournal =     "Mathematics of Computation",
  ZMnumber =     "0208.39902",
}

@Article{Parlett:1965:CA,
  author =       "Beresford Parlett",
  title =        "Convergence of the {$QR$} algorithm",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "187--193",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  MRclass =      "65.40",
  MRnumber =     "MR0176600 (31 \#872)",
  MRreviewer =   "E. R. Hansen",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "See correction \cite{Parlett:1967:CCA}.",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  keywords =     "numerical analysis",
  ZMnumber =     "0132.36301",
}

@Article{Parlett:1965:MEP,
  author =       "Beresford Parlett",
  title =        "Matrix Eigenvalue Problems",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "72",
  number =       "2, part II",
  pages =        "59--66",
  year =         "1965",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890",
  MRclass =      "65.40",
  MRnumber =     "MR0172452 (30 \#2671)",
  MRreviewer =   "P. J. Davis",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Mathematical Monthly",
  keywords =     "numerical analysis",
  ZMnumber =     "0123.11302",
}

@Article{Buchanan:1966:UCM,
  author =       "M. L. Buchanan and B. N. Parlett",
  title =        "The uniform convergence of matrix powers",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "51--54",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  MRclass =      "65.40",
  MRnumber =     "MR0205434 (34 \#5262)",
  MRreviewer =   "H.-O. Kreiss",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  keywords =     "linear algebra, forms",
  ZMnumber =     "0143.05104",
}

@Article{Parlett:1966:ADD,
  author =       "Beresford Parlett",
  title =        "Accuracy and dissipation in difference schemes",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "19",
  number =       "1",
  pages =        "111--123",
  year =         "1966",
  CODEN =        "CPAMAT, CPMAMV",
  ISSN =         "0010-3640",
  MRclass =      "65.65",
  MRnumber =     "MR0196957 (33 \#5141)",
  MRreviewer =   "H.-O. Kreiss",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics",
  keywords =     "numerical analysis",
  ZMnumber =     "0173.44703",
}

@Article{Parlett:1966:CQR,
  author =       "Beresford Parlett",
  title =        "Convergence of the {Q-R} algorithm for {Hessenberg}
                 matrices",
  journal =      j-CACM,
  volume =       "9",
  number =       "7",
  pages =        "475--475",
  month =        jul,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  bibdate =      "Fri Nov 25 18:20:07 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1966:SIM,
  author =       "Beresford N. Parlett",
  title =        "Singular and Invariant Matrices Under the ${QR}$
                 Transformation (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "611--615",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65.35",
  MRnumber =     "MR0213005 (35 \#3870)",
  MRreviewer =   "N. Gastinel",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F30 Other matrix algorithms",
  fjournal =     "Mathematics of Computation",
  kwds =         "nla, eig, QR algorithm",
  ZMnumber =     "0238.65018",
}

@Article{Rust:1966:SAC,
  author =       "B. Rust and W. R. Burrus and C. Schneeberger",
  title =        "A simple algorithm for computing the generalized
                 inverse of a matrix",
  journal =      j-CACM,
  volume =       "9",
  number =       "5",
  pages =        "381--385, 387",
  month =        may,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782",
  MRclass =      "65.35",
  MRnumber =     "33\#3448",
  bibdate =      "Tue May 28 07:33:09 1996",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib",
  abstract =     "The generalized inverse of a matrix is important in
                 analysis because it provides an extension of the
                 concept of an inverse which applies to all matrices. It
                 also has many applications in numerical analysis, but
                 it is not widely used because the existing algorithms
                 are fairly complicated and require considerable storage
                 space. A simple extension has been found to the
                 conventional orthogonalization method for inverting
                 non-singular matrices, which gives the generalized
                 inverse with little extra effort and with no additional
                 storage requirements. The algorithm gives the
                 generalized inverse for any $m$ by n matrix $A$,
                 including the special case when $m + n$ and $A$ is
                 non-singular and the case when $m > n$ and
                 $\mbox{rank}(A) = n$. In the first case the algorithm
                 gives the ordinary inverse of $A$. In the second case
                 the algorithm yields the ordinary least squares
                 transformation matrix $\mbox{INV}(A'A)A'$ and has the
                 advantage of avoiding the loss of significance which
                 results in forming the product $A'A$ explicitly.",
  acknowledgement = ack-nhfb,
  kwds =         "nla, ginv",
  reviewer =     "B. N. Parlett",
}

@Article{Varah:1966:CPA,
  author =       "J. M. Varah",
  title =        "Certification of {Parlett}'s {ALGOL} Eigenvalue
                 Procedure $\operatorname{Eig}$ 3 (in {Technical Notes
                 and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "95",
  pages =        "437--438",
  month =        jul,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parlett:1967:A,
  author =       "B. N. Parlett",
  title =        "The {$LU$} and {$QR$} algorithms",
  crossref =     "Ralston:1967:MMD",
  pages =        "116--130",
  year =         "1967",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1967:CCA,
  author =       "Beresford Parlett",
  title =        "Correction to: ``{Convergence of the {$QR$}
                 algorithm}''",
  journal =      j-NUM-MATH,
  volume =       "10",
  pages =        "163--164",
  year =         "1967",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  MRclass =      "65.35",
  MRnumber =     "MR0214278 (35 \#5129)",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "See \cite{Parlett:1965:CA}.",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  keywords =     "numerical analysis",
  ZMnumber =     "0171.36004",
}

@Article{Parlett:1967:CDH,
  author =       "Beresford Parlett",
  title =        "Canonical Decomposition of {Hessenberg} Matrices (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "223--227",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "15.30 (65.00)",
  MRnumber =     "MR0228519 (37 \#4099)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  keywords =     "numerical analysis",
  ZMnumber =     "0159.20501",
}

@Article{Parlett:1968:GCB,
  author =       "Beresford N. Parlett",
  title =        "Global Convergence of the Basic {QR} Algorithm on
                 {Hessenberg} Matrices",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "104",
  pages =        "803--817",
  month =        oct,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65.35",
  MRnumber =     "MR0247759 (40 \#1020)",
  MRreviewer =   "J. Vandergraft",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  keywords =     "numerical analysis",
  kwds =         "nla, eig, QR algorithm, Hessenberg matrix",
  ZMnumber =     "0184.37602",
}

@Article{Parlett:1969:BMC,
  author =       "B. N. Parlett and C. Reinsch",
  title =        "Balancing a matrix for calculation of eigenvalues and
                 eigenvectors",
  journal =      j-NUM-MATH,
  volume =       "13",
  pages =        "293--304",
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 Theory/Matrix.bib",
  note =         "Also in \cite[pp. 315--326]{Wilkinson:1971:LA}.",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  keywords =     "eig; nla; numerical analysis; scaling; software",
  xxpages =      "292--304",
  ZMnumber =     "0184.37703",
}

@InProceedings{Parlett:1969:CPA,
  author =       "B. N. Parlett and W. Kahan",
  title =        "On the convergence of a practical {$QR$} algorithm.
                 ({With} discussion)",
  crossref =     "Morrell:1969:IPP",
  volume =       "1",
  pages =        "114--118",
  year =         "1969",
  MRclass =      "65.40",
  MRnumber =     "MR0255035 (40 \#8242)",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis",
  ZMnumber =     "0195.45002",
}

@Article{Parlett:1970:EPP,
  author =       "Beresford Parlett",
  title =        "Ergodic properties of populations. {I}. {The} one sex
                 model",
  journal =      j-THEOR-POPUL-BIOL,
  volume =       "1",
  number =       "??",
  pages =        "191--207",
  year =         "1970",
  CODEN =        "TLPBAQ",
  ISSN =         "0040-5809",
  MRclass =      "92A15",
  MRnumber =     "MR0325180 (48 \#3529)",
  MRreviewer =   "N. Keyfitz",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*92D25 Population dynamics",
  fjournal =     "Theoretical Population Biology. An International
                 Journal",
  ZMnumber =     "0239.92007",
}

@Article{Parlett:1970:SSL,
  author =       "B. Parlett and J. K. Reid",
  title =        "On the Solution of a System of Linear Equations whose
                 Matrix is Symmetric but not Definite",
  journal =      j-BIT,
  volume =       "10",
  number =       "3",
  pages =        "386--397",
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/bit.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bunch:1971:DMS,
  author =       "James R. Bunch and Beresford N. Parlett",
  title =        "Direct Methods for Solving Symmetric Indefinite
                 Systems of Linear Equations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "8",
  number =       "4",
  pages =        "639--655",
  month =        dec,
  year =         "1971",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F05",
  MRnumber =     "MR0305564 (46 \#4694)",
  MRreviewer =   "John Todd",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  keywords =     "numerical analysis",
  remark =       "Zentralblatt MATH database records this as number 3,
                 1970.",
  ZMnumber =     "0199.49802",
}

@Article{Parlett:1971:AAR,
  author =       "Beresford N. Parlett",
  title =        "Analysis of Algorithms for Reflections in Bisectors",
  journal =      j-SIAM-REVIEW,
  volume =       "13",
  number =       "2",
  pages =        "197--208",
  year =         "1971",
  CODEN =        "SIREAD",
  ISSN =         "1095-7200",
  MRclass =      "65.80",
  MRnumber =     "MR0290608 (44 \#7788)",
  MRreviewer =   "G. Fairweather",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F99 Numerical linear algebra 65G99 Error analysis
                 65Y20 Complexity and performance of numerical
                 algorithms",
  fjournal =     "SIAM Review",
  ZMnumber =     "0217.52606",
}

@InProceedings{Parlett:1972:CTM,
  author =       "B. Parlett",
  title =        "Can there be a marriage function?",
  crossref =     "Greville:1972:PDP",
  pages =        "107--135",
  year =         "1972",
  MRclass =      "92A15",
  MRnumber =     "MR0446591 (56 \#4916)",
  MRreviewer =   "R. Fischler",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1973:GTP,
  author =       "B. N. Parlett and W. G. {Poole, Jr.}",
  title =        "A Geometric Theory for the ${QR}$, ${LU}$ and Power
                 Iterations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "10",
  number =       "2",
  pages =        "389--412",
  month =        apr,
  year =         "1973",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "MR0336979 (49 \#1752)",
  MRreviewer =   "J. Vandergraft",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  note =         "Collection of articles dedicated to the memory of
                 George E. Forsythe",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  ZMnumber =     "0227.65027",
  ZMnumber =     "0253.65018",
}

@Article{Parlett:1973:NHM,
  author =       "Beresford Parlett",
  title =        "Normal {Hessenberg} and moment matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "6",
  number =       "??",
  pages =        "37--43",
  year =         "1973",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F15",
  MRnumber =     "MR0324887 (48 \#3236)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*15A57 Other types of matrices 65F30 Other matrix
                 algorithms",
  ZMnumber =     "0251.15022",
}

@Article{Parlett:1973:PGM,
  author =       "B. N. Parlett",
  title =        "Pr{\'e}sentation g{\'e}om{\'e}trique des m{\'e}thodes
                 de calcul des valeurs propres. ({French}) [{Geometric}
                 presentation of methods for calculation of
                 eigenvalues]",
  journal =      j-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "223--233",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "MR0329229 (48 \#7571)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  corpsource =   "Univ. California, Berkeley, CA, USA",
  fjournal =     "Numerische Mathematik",
  keywords =     "calculation; convergence; convergence of numerical
                 methods; eigenvalues; eigenvalues and eigenfunctions;
                 eigenvectors; geometric presentation; matrices; matrix
                 algebra; methods",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0255.65020",
}

@TechReport{Kahan:1974:ALA,
  author =       "W. Kahan and B. N. Parlett",
  title =        "An Analysis of {Lanczos} Algorithms for Symmetric
                 Matrices",
  number =       "ERL-M467",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  year =         "1974",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1974:CFT,
  author =       "Beresford N. Parlett",
  title =        "Computation of Functions of Triangular Matrices",
  type =         "Memorandum",
  number =       "ERL-M481",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "18",
  month =        nov,
  year =         "1974",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1974:RQI,
  author =       "B. N. Parlett",
  title =        "The {Rayleigh} Quotient Iteration and Some
                 Generalizations for Nonnormal Matrices",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "679--693",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65F15",
  MRnumber =     "MR0405823 (53 \#9615)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc",
  corpsource =   "Univ. California, Berkeley, CA, USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "eigenvector; generalizations; iterative methods; local
                 convergence; matrices; matrix algebra; nonnormal;
                 Rayleigh Quotient Iteration",
  kwds =         "nla, eig, Rayleigh quotient, nonnormal matrix",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0293.65023",
}

@TechReport{Chan:1975:PCC,
  author =       "Sai-Pak Chan and R. Feldman and Beresford N. Parlett",
  title =        "A program to compute the condition numbers of matrix
                 eigenvalues without computing eigenvectors",
  type =         "Memorandum",
  number =       "ERL-M517",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "44",
  year =         "1975",
  bibdate =      "Fri Nov 11 05:22:23 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1975:ICC,
  author =       "B. N. Parlett and Y. Wang",
  title =        "The Influence of the Compiler on the Cost of
                 Mathematical Software{}\emdash in Particular on the
                 Cost of Triangular Factorization",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "35--46",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib;
                 http://doi.acm.org/10.1145/355626.355633",
  acknowledgement = ack-nhfb,
  classmath =    "*68N01 General",
  keywords =     "cs; lud; nla; software",
  ZMnumber =     "0312.68017",
}

@TechReport{Parlett:1975:PCR,
  author =       "Beresford N. Parlett and R. Feldman",
  title =        "A program to compute the real {Schur} Form of a real
                 square matrix",
  type =         "Memorandum",
  number =       "ERL-M526",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "28",
  year =         "1975",
  bibdate =      "Fri Nov 11 05:21:27 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bunch:1976:DSM,
  author =       "James R. Bunch and Linda Kaufman and Beresford N.
                 Parlett",
  title =        "Decomposition of a Symmetric Matrix",
  journal =      j-NUM-MATH,
  volume =       "27",
  number =       "1",
  pages =        "95--109",
  year =         "1976",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
  classmath =    "*65F35 Matrix norms, etc. (numerical linear algebra)
                 68W99 None of the above, but in this section",
  corpsource =   "Dept. of Math., Univ. of California, San Diego, CA,
                 USA",
  keywords =     "Cholesky; indefinite system; inertia; linear
                 equations; linear system; lud; matrix algebra; nla;
                 permutation matrix; symmetric matrix; triangular
                 factorisation",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0342.65026",
}

@InProceedings{Kahan:1976:HFS,
  author =       "W. Kahan and B. N. Parlett",
  title =        "How far should you go with the {Lanczos} process?",
  crossref =     "Bunch:1976:SSM",
  pages =        "131--144",
  year =         "1976",
  MRclass =      "65F15",
  MRnumber =     "MR0458836 (56 \#17036)",
  MRreviewer =   "Michael S. Martin",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc",
  ZMnumber =     "0345.65017",
}

@Article{Parlett:1976:RAE,
  author =       "B. N. Parlett",
  title =        "A Recurrence Among the Elements of Functions of
                 Triangular Matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "14",
  number =       "2",
  pages =        "117--121",
  year =         "1976",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F30",
  MRnumber =     "MR0448846 (56 \#7151)",
  MRreviewer =   "C. G. Cullen",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1970.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F99 Numerical linear algebra 15A15 Special matrix
                 functions",
  keywords =     "nla, matrix function, triangular matrix",
  ZMnumber =     "0353.65027",
}

@TechReport{Parlett:1976:RES,
  author =       "Beresford N. Parlett",
  title =        "Roundoff error in the solution of finite element
                 systems",
  type =         "Report",
  number =       "????",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "21",
  year =         "1976",
  bibdate =      "Fri Nov 11 05:48:59 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chan:1977:APC,
  author =       "S. P. Chan and R. Feldman and B. N. Parlett",
  title =        "{Algorithm 517}: {A} Program for Computing the
                 Condition Numbers of Matrix Eigenvalues Without
                 Computing Eigenvectors [{F2}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "186--203",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sat Aug 27 22:34:22 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/toms.bib;
                 http://doi.acm.org/10.1145/355732.355741",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65F35
                 Matrix norms, etc. (numerical linear algebra)",
  keywords =     "condition estimation; eig; nla; nonsymmetric matrix;
                 pert; software",
  ZMnumber =     "0353.65026",
}

@TechReport{Hoffman:1977:NPG,
  author =       "W. Hoffman and Beresford N. Parlett",
  title =        "A new proof of global convergence for the tridiagonal
                 {QL} algorithm",
  type =         "Memorandum",
  number =       "UCB/ERL M77/48",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "18",
  day =          "7",
  month =        jul,
  year =         "1977",
  bibdate =      "Fri Nov 11 05:18:34 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1977:CYC,
  author =       "W. M. Kahan and B. N. Parlett",
  title =        "Can You Count on Your Calculator?",
  type =         "Memorandum",
  number =       "UCB/ERL M77/21",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "ii + 28",
  day =          "6",
  month =        apr,
  year =         "1977",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  note =         "German Transl. Published In: Jahrbuch {\"U}berblicke
                 Mathematik 1978, Ed. by B. Fuchssteiner and others,
                 Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
                 199--216, 1978",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-jr,
}

@Article{Parlett:1977:ICC,
  author =       "B. N. Parlett and Y. Wang",
  title =        "The influence of the compiler on the cost of
                 mathematical software---in particular on the cost of
                 triangular factorization",
  journal =      j-TOMS,
  volume =       "1",
  pages =        "35--46",
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1977:LAI,
  author =       "B. N. Parlett and D. S. Scott",
  title =        "The {Lanczos} algorithm with implicit deflation",
  type =         "Memorandum",
  number =       "UCB/ERL M77/70",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "29",
  day =          "2",
  month =        dec,
  year =         "1977",
  bibdate =      "Fri Nov 11 05:16:39 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1977:PNA,
  author =       "Beresford N. Parlett",
  title =        "Progress in numerical analysis",
  type =         "Memorandum",
  number =       "UCB/ERL M77/26",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "30",
  day =          "13",
  month =        apr,
  year =         "1977",
  bibdate =      "Fri Nov 11 05:19:27 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1977:PSD,
  author =       "Beresford N. Parlett",
  title =        "A program to swap diagonal blocks",
  type =         "Memorandum",
  number =       "UCB/ERL M77/66",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "30",
  day =          "3",
  month =        nov,
  year =         "1977",
  bibdate =      "Fri Nov 11 05:17:40 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parlett:1977:RES,
  author =       "Beresford Parlett",
  title =        "Roundoff error in the solution of finite element
                 systems",
  crossref =     "Bathe:1977:FCA",
  pages =        "632--654",
  year =         "1977",
  MRclass =      "65G05 (65N30)",
  MRnumber =     "MR0488692 (58 \#8211)",
  MRreviewer =   "Peter Lancaster",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hoffmann:1978:NPG,
  author =       "W. Hoffmann and B. N. Parlett",
  title =        "A new proof of global convergence for the tridiagonal
                 {QL} algorithm",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "15",
  number =       "5",
  pages =        "929--937",
  month =        oct,
  year =         "1978",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "MR507555 (80a:65075)",
  MRreviewer =   "S. F. McCormick",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  keywords =     "Eigenpairs of Matrices; Global Convergence; Ql
                 Algorithm; Wilkinson'S Shift",
  ZMnumber =     "0402.65019",
}

@TechReport{Kahan:1978:HFS,
  author =       "W. Kahan and B. N. Parlett",
  title =        "How far should you go with the {Lanczos} process?",
  type =         "Memorandum",
  number =       "UCB/ERL M78/48",
  institution =  inst-ERL-CE-UCB,
  address =      inst-ERL-CE-UCB:adr,
  pages =        "16",
  year =         "1978",
  bibdate =      "Fri Nov 11 05:15:08 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1978:KSI,
  author =       "W. Kahan and B. N. Parlett",
  title =        "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
                 (German) [Can you count on your calculator?]",
  journal =      "{Jahrbuch {\"U}berblicke Mathematik}",
  volume =       "??",
  pages =        "199--216",
  year =         "1978",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65Y99 Computer aspects of numerical algorithms 65D20
                 Computation of special functions 00A99 Miscellaneous
                 topics in general mathematics",
  keywords =     "Automated Algorithms; Error of Computation; Pocket
                 Calculator",
  language =     "German",
  ZMnumber =     "0397.65081",
}

@Article{Parlett:1978:PNA,
  author =       "Beresford N. Parlett",
  title =        "Progress in numerical analysis",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "3",
  pages =        "443--456",
  year =         "1978",
  CODEN =        "SIREAD",
  ISSN =         "1095-7200",
  MRclass =      "65-02",
  MRnumber =     "MR0494816 (58 \#13601)",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65-02 Research monographs (numerical analysis) 68Nxx
                 Software 00A06 Mathematics for non-mathematicians",
  fjournal =     "SIAM Review",
  keywords =     "Iterative Methods for Linear Equations; Library
                 Functions; Matrix Computations; Minimization; Numerical
                 Methods; Ordinary Differential Equations; Packages;
                 Program Libraries; Programming Languages; Progress in
                 Numerical Analysis; Quadrature; Small Matrix
                 Computations; Stored Matrices; Theoretical Treatment",
  ZMnumber =     "0408.65002",
}

@Article{Parlett:1979:LAS,
  author =       "B. N. Parlett and D. S. Scott",
  title =        "The {L{\'a}nczos} Algorithm with Selective
                 Orthogonalization",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "217--238",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65F15",
  MRnumber =     "MR514820 (80c:65090)",
  MRreviewer =   "Colette Lebaud",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65F25
                 Orthogonalization (numerical linear algebra)",
  corpsource =   "Univ. California, Berkeley, CA, USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "eigenvalues; eigenvalues and eigenfunctions;
                 eigenvectors; Eigenvectors; extreme; Extreme
                 Eigenvalues of a Large Symmetric Matrix; independence;
                 Lanczos algorithm; Lanczos Process; large symmetric
                 matrix; linear; Modification; selective
                 orthogonalization; Selective Orthogonalization",
  kwds =         "nla, eig, Lanczos Algorithm, orthogonalization",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0405.65015",
}

@Article{Rice:1979:NCN,
  author =       "J. R. Rice and C. W. Gear and J. Ortega and B. Parlett
                 and M. Schultz and L. F. Shampine and P. Wolfe and J.
                 F. Traub",
  title =        "Numerical computation: its nature and research
                 directions",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "1--48",
  month =        feb,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778",
  bibdate =      "Tue Apr 12 07:50:06 MDT 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 http://portal.acm.org/",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C1180 (Optimisation techniques); C4140 (Linear
                 algebra); C4170 (Differential equations)",
  corpsource =   "Purdue Univ., Lafayette, IN, USA",
  keywords =     "curves; graphics; linear algebra; mathematical
                 software; nonlinear equations; numerical computation;
                 optimisation; optimization; ordinary differential
                 equations; partial differential equations; surfaces",
  treatment =    "G General Review",
}

@TechReport{Nour-Omid:1980:LVS,
  author =       "Bahram Nour-Omid and Beresford N. Parlett and Robert
                 L. Taylor",
  title =        "{Lanczos} versus subspace iteration for solution of
                 eigenvalue problems",
  type =         "Report",
  number =       "UC SESM 80-8",
  institution =  "Structural Engineering Laboratory, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "16",
  year =         "1980",
  bibdate =      "Fri Nov 11 05:12:33 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parlett:1980:HSK,
  author =       "B. N. Parlett",
  title =        "How to solve {$(K - \lambda M)z = 0$} for large {$K$}
                 and {$M$}",
  crossref =     "Absi:1980:NME",
  year =         "1980",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  keywords =     "comparison; Lanczos algorithm; large eigenvalue
                 problems; numerical example; subspace iteration
                 method",
  ZMnumber =     "0455.65027",
}

@InProceedings{Parlett:1980:HSL,
  author =       "B. N. Parlett",
  title =        "How to solve {$(K-\lambda M)z=0$} for large {$K$} and
                 {$M$}",
  crossref =     "Absi:1980:NME",
  volume =       "1",
  pages =        "97--106",
  year =         "1980",
  MRclass =      "65F15",
  MRnumber =     "MR660669 (83g:65044)",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1980:NLA,
  author =       "B. N. Parlett",
  title =        "A new look at the {Lanczos} algorithm for solving
                 symmetric systems of linear equations",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "29",
  pages =        "323--346",
  year =         "1980",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F10",
  MRnumber =     "MR562767 (83e:65064)",
  bibdate =      "Wed Jan 22 17:57:24 MST 1997",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1980.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F10 Iterative methods for linear systems 65-04
                 Machine computation, programs (numerical analysis)
                 65F15 Eigenvalues (numerical linear algebra)",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "nla, Lanczos algorithm, symmetric matrix, linear
                 system",
  keywords =     "conjugate gradient algorithm; implementation; Lanczos
                 algorithm; large sparse symmetric matrix; selective
                 orthogonalization; tridiagonalization",
  ZMnumber =     "0431.65016",
}

@Book{Parlett:1980:SEP,
  author =       "Beresford N. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 348",
  year =         "1980",
  ISBN =         "0-13-880047-2",
  ISBN-13 =      "978-0-13-880047-5",
  LCCN =         "QA188 .P3",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR570116 (81j:65063)",
  MRreviewer =   "Robert Todd Gregory",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "Prentice-Hall Series in Computational Mathematics",
  series =       "Series in Computational Mathematics",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/all_brec.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc. 15A57 Other types of
                 matrices 15-02 Research monographs (linear algebra)
                 65-02 Research monographs (numerical analysis) 15A23
                 Factorization of matrices 65F25 Orthogonalization
                 (numerical linear algebra)",
  keywords =     "bandmatrices; bounds for eigenvalues; eigenvalues;
                 generalized eigenvalue problem; Krylov sequences;
                 localization of eigenvalues; orthogonal
                 transformations; tridiagonal matrices; vector
                 iteration",
  ZMnumber =     "0431.65017",
}

@Article{Berman:1981:DSO,
  author =       "A. Berman and B. N. Parlett and R. J. Plemmons",
  title =        "Diagonal scaling to an orthogonal matrix",
  journal =      j-SIAM-J-ALG-DISC-METH,
  volume =       "2",
  number =       "1",
  pages =        "57--65",
  month =        mar,
  year =         "1981",
  CODEN =        "SJAMDU",
  ISSN =         "0196-5212",
  MRclass =      "65F35 (15A21)",
  MRnumber =     "MR604511 (82d:65040)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/siamjalgdiscmeth.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C4170 (Differential
                 equations)",
  classmath =    "*65F35 Matrix norms, etc. (numerical linear algebra)
                 35L45 First order hyperbolic systems, initial value
                 problems",
  corpsource =   "Dept. of Math., Technion-Israel Inst. of Technol.,
                 Haifa, Israel",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Algebraic and Discrete Methods",
  keywords =     "algorithm; diagonal matrix; diagonal scaling; energy
                 conserving norm; Hadamard quotient; hyperbolic
                 equations; matrix algebra; orthogonal matrix; partial
                 differential equation; partial differential equations;
                 positive matrix; scaling factors",
  treatment =    "A Application; T Theoretical or Mathematical",
  ZMnumber =     "0498.65024",
}

@TechReport{Parlett:1981:ACT,
  author =       "Beresford N. Parlett",
  title =        "Analytic complexity theory and the solution of {$AX =
                 b$}",
  type =         "Technical Report",
  number =       "PAM-40",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1981:FSF,
  author =       "Beresford N. Parlett and B. Nour-Omid and M. R. Li",
  title =        "A fast solver free of fill-in for finite element
                 problems",
  type =         "Technical Report",
  number =       "PAM-42",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1981:HSK,
  author =       "Beresford N. Parlett",
  title =        "How to solve {$(K-\lambda M)z = 0$} for large {$K$}
                 and {$M$}",
  type =         "Technical Report",
  number =       "PAM-39",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1981:LAL,
  author =       "Beresford N. Parlett and D. Taylor",
  title =        "A look-ahead {Lanczos} algorithm for unsymmetric
                 matrices",
  type =         "Technical Report",
  number =       "PAM-43",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1981:MSD,
  author =       "Beresford N. Parlett and T. L. Landis",
  title =        "Methods for scaling to doubly stochastic form",
  type =         "Technical Report",
  number =       "PAM-44",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1981:PNA,
  author =       "Beresford Parlett",
  title =        "Progress in numerical analysis",
  journal =      "Yingyong Shuxue yu Jisuan Shuxue",
  volume =       "3",
  pages =        "1--10",
  year =         "1981",
  MRclass =      "65-02",
  MRnumber =     "MR656304 (83d:65005)",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "Translated from the English by Wu Mu",
  acknowledgement = ack-nhfb,
  fjournal =     "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics
                 and Computational Mathematics",
}

@Article{Parlett:1981:TPL,
  author =       "B. N. Parlett and J. K. Reid",
  title =        "Tracking the Progress of the {Lanczos} Algorithm for
                 Large Symmetric Eigenproblems",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "1",
  number =       "2",
  pages =        "135--155",
  year =         "1981",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "MR616327 (82e:65039)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 MathSciNet database",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65Y99
                 Computer aspects of numerical algorithms",
  fjournal =     "IMA (Institute of Mathematics and its Applications).
                 Journal of Numerical Analysis",
  keywords =     "interpolation procedures; Lanczos algorithm; large
                 symmetric matrix",
  ZMnumber =     "0474.65022",
}

@Article{Kahan:1982:RBA,
  author =       "W. Kahan and B. N. Parlett and E. Jiang",
  title =        "Residual Bounds on Approximate Eigensystems of
                 Nonnormal Matrices",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "470--484",
  month =        jun,
  year =         "1982",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F15 (65F35)",
  MRnumber =     "MR656463 (83h:65050)",
  MRreviewer =   "William W. Hager",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@Article{Li:1982:FSF,
  author =       "M. R. Li and B. Nour-Omid and B. N. Parlett",
  title =        "A Fast Solver Free of Fill-in for Finite-element
                 Problems",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "19",
  number =       "6",
  pages =        "1233--1242",
  month =        dec,
  year =         "1982",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F10 (65F05 65N30)",
  MRnumber =     "MR679662 (84b:65031)",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@TechReport{Parlett:1982:AUE,
  author =       "Beresford N. Parlett and B. Nour-Omid",
  title =        "An algorithm to update eigenvalues of a growing
                 symmetric tridiagonal matrix",
  type =         "Technical Report",
  number =       "PAM-104",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        oct,
  year =         "1982",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1982:ELE,
  author =       "B. N. Parlett and H. Simon and L. M. Stringer",
  title =        "On Estimating the Largest Eigenvalue with the
                 {L{\'a}nczos} Algorithm",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "157",
  pages =        "153--165",
  month =        jan,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65F15",
  MRnumber =     "MR637293 (82m:65033)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0210 (Algebra); B0290H (Linear algebra); C1110
                 (Algebra); C4140 (Linear algebra)",
  corpsource =   "Dept. of Math., Univ. of California, Berkeley, CA,
                 USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "definite matrix; eigenvalue; eigenvalues and
                 eigenfunctions; Lanczos algorithm; large matrices;
                 matrix algebra; methods; misconvergence; numerical;
                 positive",
  kwds =         "nla, eig, Lanczos algorithm",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Parlett:1982:EP,
  author =       "Beresford N. Parlett and B. Nour-Omid",
  title =        "Element preconditioning",
  type =         "Technical Report",
  number =       "PAM-103",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        oct,
  year =         "1982",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1982:MSD,
  author =       "B. N. Parlett and T. L. Landis",
  title =        "Methods for Scaling to Doubly Stochastic Form",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "48",
  number =       "??",
  pages =        "53--79",
  year =         "1982",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "15A12 (15A51 65F35)",
  MRnumber =     "MR683210 (84b:15007)",
  MRreviewer =   "Ray C. Shiflett",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1980.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*15A12 Conditioning of matrices 65F35 Matrix norms,
                 etc. (numerical linear algebra) 15A51 Stochastic
                 matrices",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "convergence theorem; doubly stochastic matrices; nla,
                 eig, nonnegative matrix, doubly stochastic matrix;
                 scaling",
  xxtitle =      "Methods for Scaling to Double Stochastic Form",
  ZMnumber =     "0508.15003",
}

@InProceedings{Parlett:1982:TMS,
  author =       "B. N. Parlett",
  title =        "Two monitoring schemes for the {Lanczos} algorithm",
  crossref =     "Glowinski:1982:CMA",
  year =         "1982",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F10 Iterative methods for linear systems 65F15
                 Eigenvalues (numerical linear algebra) 65F25
                 Orthogonalization (numerical linear algebra)",
  keywords =     "Lanczos algorithm; monitoring schemes; symmetric
                 matrices",
  ZMnumber =     "0499.65017",
}

@Article{Parlett:1982:WFT,
  author =       "B. N. Parlett",
  title =        "{Winograd}'s {Fourier} transform via circulants",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "45",
  number =       "??",
  pages =        "137--155",
  year =         "1982",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65T05 (68C25)",
  MRnumber =     "MR660985 (83f:65222)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1980.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65T40 Trigonometric approximation and interpolation
                 65F30 Other matrix algorithms 15A23 Factorization of
                 matrices 42A15 Trigonometric interpolation",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "associated circulant matrices; discrete Fourier
                 transform; eigenvalue-eigenvector decomposition; na,
                 nla, eig, fft, fast algorithm, circulant matrix; real
                 arithmetic; Winograd's algorithm",
  ZMnumber =     "0515.65099",
}

@TechReport{McCurdy:1983:ACD,
  author =       "A. McCurdy and K. C. Ng and Beresford N. Parlett",
  title =        "Accurate computation of divided differences of the
                 exponential function",
  type =         "Technical Report",
  number =       "PAM-160",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  acknowledgement = ack-nhfb,
}

@Article{Nour-Omid:1983:LVS,
  author =       "Bahram Nour-Omid and Beresford N. Parlett and Robert
                 L. Taylor",
  title =        "{Lanczos} versus subspace iteration for solution of
                 eigenvalue problems",
  journal =      j-INT-J-NUMER-METHODS-ENG,
  volume =       "19",
  number =       "??",
  pages =        "859--871",
  year =         "1983",
  CODEN =        "IJNMBH",
  ISSN =         "0029-5981",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 74S05
                 Finite element methods",
  keywords =     "comparison of methods; Lanczos algorithm; large eigen
                 problems; subspace iteration",
  ZMnumber =     "0521.65024",
}

@Article{Nour-Omid:1983:NLM,
  author =       "Bahram Nour-Omid and Beresford N. Parlett and Robert
                 L. Taylor",
  title =        "A {Newton--Lanczos} method for solution of nonlinear
                 finite element equations",
  journal =      j-COMP-STRUCTURES,
  volume =       "16",
  number =       "??",
  pages =        "241--252",
  year =         "1983",
  CODEN =        "CMSTCJ",
  ISSN =         "0045-7949",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*74S05 Finite element methods 65H10 Systems of
                 nonlinear equations (numerical methods)",
  keywords =     "asymptotic cost estimates; initial-boundary value
                 problems; Lanczos algorithm; linearized set of
                 equations; local convergence characteristics; modified
                 Newton method; Newton's method; Newton--Lanczos method;
                 partial reorthogonalization; quasi-Newton; rate of
                 convergence; selective orthogonalization; varied from
                 superlinear to quadratic by controlling certain
                 tolerance",
  ZMnumber =     "0499.73058",
}

@TechReport{Parlett:1983:EMS,
  author =       "Beresford N. Parlett and H. Wu and W. D. Wu",
  title =        "Eigenvector matrices of symmetric tridiagonals",
  type =         "Technical Report",
  number =       "PAM-174",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        aug,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Book{Parlett:1983:SPS,
  author =       "Beresford N. Parlett",
  title =        "Simmetrichnaya problema sobstvennykh znachenii.
                 Chislennye metody ({Russian}) [The symmetric eigenvalue
                 problem. Numerical methods]",
  publisher =    pub-EDITORIAL-MIR,
  address =      pub-EDITORIAL-MIR:adr,
  pages =        "384",
  year =         "1983",
  MRclass =      "65-02 (15A18 65F15)",
  MRnumber =     "MR702348 (85b:65003)",
  MRreviewer =   "K. Moszy{\'n}ski",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "Translated from the English by Kh. D. Ikranov and Yu.
                 A. Kuznetsov.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc. 15-02 Research monographs
                 (linear algebra) 65-02 Research monographs (numerical
                 analysis) 15A23 Factorization of matrices 15A57 Other
                 types of matrices 65F25 Orthogonalization (numerical
                 linear algebra)",
  keywords =     "bandmatrices; bounds for eigenvalues; eigenvalues;
                 generalized eigenvalue problem; Krylov sequences;
                 localization of eigenvalues; orthogonal
                 transformations; tridiagonal matrices; vector
                 iteration",
  language =     "Russian",
  ZMnumber =     "0524.65023",
}

@TechReport{Parlett:1983:SSE,
  author =       "Beresford N. Parlett",
  title =        "The software scene in the extraction of eigenvalues
                 from sparse matrices",
  type =         "Technical Report",
  number =       "PAM-132",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        mar,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1983:URE,
  author =       "Beresford N. Parlett and B. Nour-Omid",
  title =        "The use of refined error bound when updating
                 eigenvalues of tridiagonals",
  type =         "Technical Report",
  number =       "PAM-175",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        sep,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{McCurdy:1984:ACD,
  author =       "A. McCurdy and K. C. Ng and B. N. Parlett",
  title =        "Accurate Computation of Divided Differences of the
                 Exponential Function",
  journal =      j-MATH-COMPUT,
  volume =       "43",
  number =       "168",
  pages =        "501--528",
  month =        oct,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65D20 (33A10 65G05)",
  MRnumber =     "MR758198 (86e:65029)",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@TechReport{Nour-Omid:1984:HIS,
  author =       "N. Nour-Omid and B. N. Parlett",
  title =        "How to implement the spectral transformation",
  type =         "Technical Report",
  number =       "PAM-224",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  pages =        "????",
  year =         "1984",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1984:ECM,
  author =       "Beresford N. Parlett and B. Nour-Omid and J. Natvig",
  title =        "Effect of the {CYBER 205} on methods for computing
                 natural frequencies of structures",
  type =         "Technical Report",
  number =       "PAM-218",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        apr,
  year =         "1984",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1984:EMS,
  author =       "B. N. Parlett and W. D. Wu",
  title =        "Eigenvector matrices of symmetric tridiagonals",
  journal =      j-NUM-MATH,
  volume =       "44",
  number =       "1",
  pages =        "103--110",
  month =        jun,
  year =         "1984",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  MRclass =      "65F15",
  MRnumber =     "MR745089 (85h:65083)",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0210 (Algebra); C1110 (Algebra)",
  corpsource =   "Maths. Dept., Univ. of California, Berkeley, CA, USA",
  fjournal =     "Numerische Mathematik",
  keywords =     "eigenvalues and eigenfunctions; eigenvector matrix;
                 matrix algebra; symmetric tridiagonals",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Parlett:1984:LAL,
  author =       "B. N. Parlett and D. R. Taylor and Z. S. Liu",
  title =        "The look ahead {L{\'a}nczos} algorithm for large
                 unsymmetric eigenproblems",
  crossref =     "Glowinski:1984:CMA",
  pages =        "87--96",
  year =         "1984",
  MRclass =      "65F15",
  MRnumber =     "MR806772 (86k:65028)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  abstract =     "A modification of the Lanczos algorithm for solving
                 eigenproblems for large unsymmetric matrices is
                 proposed. The algorithm is based on the idea of the
                 pivoting strategy introduced in the paper of {\it J. R.
                 Bunch} and {\it B. N. Parlett} [SIAM J. Numer. Anal. 8,
                 639-655 (1971; Zbl 0199.498)], which reduces the
                 occurrence of breakdown of the algorithm. Some details
                 of the modified algorithm are discussed",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  keywords =     "breakdown; Lanczos algorithm; large unsymmetric
                 matrices; pivoting strategy",
  reviewer =     "T. Reginska",
  ZMnumber =     "0564.65021",
}

@Article{Parlett:1984:SSE,
  author =       "B. N. Parlett",
  title =        "The Software Scene in the Extraction of Eigenvalues
                 from Sparse Matrices",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "5",
  number =       "3",
  pages =        "590--604",
  month =        sep,
  year =         "1984",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F15 (65F50)",
  MRnumber =     "MR754487 (85i:65048)",
  MRreviewer =   "David R. Kincaid",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/fortran2.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C7310 (Mathematics
                 computing)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15-04
                 Machine computation, programs (linear algebra) 65F50
                 Sparse matrices 68N99 Software",
  conflocation = "Fairfield Glade, TN, USA; 25-27 Oct. 1982",
  conftitle =    "Sparse Matrix Symposium",
  corpsource =   "Dept. of Math., California Univ., Berkeley, CA, USA",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Scientific and Statistical Computing",
  keywords =     "dense matrices; efficiency; eigenvalue programs;
                 eigenvalues; eigenvalues and eigenfunctions; EISPACK;
                 FORTRAN subroutines; Lanczos; Lanczos algorithm; matrix
                 algebra; reliability; software; software packages;
                 sparse matrices; subspace iteration; survey on
                 available software; users",
  reviewer =     "F. M{\'o}ricz",
  sponsororg =   "Army Res. Office; Office of Naval Res.; Oak Ridge Nat.
                 Lab",
  treatment =    "P Practical",
  ZMnumber =     "0573.65025",
}

@Book{Cullum:1985:LAL,
  author =       "Jane K. Cullum and Ralph A. Willoughby",
  title =        "{Lanczos} Algorithms for Large Symmetric Eigenvalue
                 Computations, Volume {I} Theory",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xiv + 273",
  year =         "1985",
  ISBN =         "0-8176-3058-9",
  ISBN-13 =      "978-0-8176-3058-4",
  bibdate =      "Mon Mar 6 15:34:09 GMT 1995",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
  mynote =       "Only skimmed. Tiny typeface. Emphasizes `local
                 orthogonality is enough' approach, as opposed to
                 Parlett \cite{Parlett:1980:SEP}'s `global orthogonality
                 is crucial'. They summarize Paige's error analysis but
                 don't (?) given any of their own.",
}

@Article{Nour-Omid:1985:EPU,
  author =       "B. Nour-Omid and B. N. Parlett",
  title =        "Element preconditioning using splitting techniques",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "6",
  number =       "3",
  pages =        "761--770",
  month =        jul,
  year =         "1985",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F10 (49D07 65N20)",
  MRnumber =     "MR791197 (86h:65046)",
  MRreviewer =   "Beny Neta",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 Parallel/mgnet.bib; Parallel/Multi.grid.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  abstract =     "For large sparse linear systems $Ax=b$ arising in the
                 solution of partial differential equations via the
                 finite element method, preconditioning of the conjugate
                 gradient method is considered. Splitting techniques are
                 used for the preconditioning. The resulting method is
                 examined and it's behaviour tested on a model
                 problem.",
  acknowledgement = ack-nhfb,
  classification = "B0290P (Differential equations); C4170 (Differential
                 equations)",
  classmath =    "*65F10 Iterative methods for linear systems 65N30
                 Finite numerical methods (BVP of PDE) 65F35 Matrix
                 norms, etc. (numerical linear algebra) 35J25 Second
                 order elliptic equations, boundary value problems",
  corpsource =   "Center for Pure and Appl. Math., California Univ.,
                 Berkeley, CA, USA",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Scientific and Statistical Computing",
  keywords =     "assembly process; boundary-value problems; code;
                 conjugate gradient algorithm; conjugate gradient
                 method; element preconditioning; elliptic boundary
                 value problems; finite element analysis; finite element
                 method; large sparse linear systems; large symmetric
                 systems; numerical example; preconditioning; Splitting;
                 splitting techniques",
  reviewer =     "V. Mehrmann",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0582.65019",
}

@TechReport{Parlett:1985:CSI,
  author =       "Beresford N. Parlett and Y. Saad",
  title =        "Complex shift and invert strategies for real
                 matrices",
  type =         "Research report",
  number =       "RR-424",
  institution =  "Department of Computer Science, Yale University",
  address =      "New Haven, CT, USA",
  pages =        "17",
  year =         "1985",
  bibdate =      "Fri Nov 11 05:42:25 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1985:DAA,
  author =       "Beresford N. Parlett and K. C. Ng",
  title =        "Development of an accurate algorithm for
                 {$\exp(Bt)$}",
  type =         "Technical Report",
  number =       "PAM-294",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        aug,
  year =         "1985",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parlett:1985:ILA,
  author =       "B. Parlett and B. Nour-Omid and J. Jatvig",
  title =        "Implementation of {Lanczos} Algorithms on Vector
                 Computers",
  crossref =     "Numrich:1985:SA",
  pages =        "1--18",
  year =         "1985",
  bibdate =      "Thu Nov 10 18:36:35 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/ovr.bib",
  acknowledgement = ack-nhfb,
}

@Article{Parlett:1985:LAL,
  author =       "Beresford N. Parlett and Derek R. Taylor and Zhishun
                 A. Liu",
  title =        "A look-ahead {L{\'a}nczos} algorithm for unsymmetric
                 matrices",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "105--124",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65F15",
  MRnumber =     "MR771034 (86f:65072)",
  MRreviewer =   "Youcef Saad",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Parallel/par.lin.alg.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  abstract =     "The Lanczos algorithm for nonsymmetric matrices is
                 studied. It is shown how breakdown caused by a pair of
                 corresponding basis vectors being orthogonal can be
                 remedied by computing further vectors in the Krylov
                 sequences. This corresponds to performing $2\times 2$
                 pivots when factorizing the moment matrix, which may be
                 indefinite for nonsymmetric eigenproblems. It is stated
                 that when $2\times 2$ pivots are insufficient to
                 continue the process, all eigenvalues have converged.
                 Results of a few numerical tests are reported.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  fjournal =     "Mathematics of Computation",
  keywords =     "eigenvalues and eigenfunctions; instability; Krylov
                 sequences; Lanczos algorithm; look-ahead Lanczos
                 algorithm; matrix; matrix algebra; moment; nonsymmetric
                 eigenproblems; numerical tests; plasma; triangular
                 factorization; tridiagonal matrix; unsymmetric
                 matrices",
  reviewer =     "A. Ruhe",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0564.65022",
}

@Article{Parlett:1985:URE,
  author =       "B. N. Parlett and B. Nour-Omid",
  title =        "The Use of a Refined Error Bound When Updating
                 Eigenvalues of Tridiagonals",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "68",
  number =       "??",
  pages =        "179--219",
  year =         "1985",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F15 (65-04)",
  MRnumber =     "MR794821 (86j:65046)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/gvl.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1980.bib",
  abstract =     "For computing some eigenvalues of a given symmetric
                 matrix $A$ the Lanczos algorithm is used. It provides a
                 nested sequence of tridiagonal matrices $T\sb j$, whose
                 eigenvalues approximate those of A. The eigenvalues of
                 $T\sb j$ tend to stagnate quite early (as functions of
                 j). An algorithm (ANALYZE T) is described, which is a
                 part of the inner loops of the Lanczos algorithm, and
                 which monitors the convergence behaviour of the Ritz
                 values. It helps, e.g., to avoid the so-called
                 misconvergence.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 15-04
                 Machine computation, programs (linear algebra)",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "convergence; eigenvalues; Lanczos algorithm;
                 misconvergence; nested sequence of tridiagonal
                 matrices; nla, eig, pert, tridiagonal matrix; Ritz
                 values",
  reviewer =     "L. Elsner",
  xxpages =      "179--220",
  ZMnumber =     "0629.65037",
}

@Article{Natvig:1986:ECC,
  author =       "J. Natvig and B. Nour-Omid and B. N. Parlett",
  title =        "Effect of the {CYBER 205} on the choice of method for
                 solving the eigenvalue problem {$(A - \lambda M)x =
                 0$}",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "15",
  number =       "2",
  pages =        "137--159",
  year =         "1986",
  CODEN =        "JCAMDI",
  DOI =          "http://dx.doi.org/10.1016/0377-0427(86)90023-3",
  ISSN =         "0377-0427",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  abstract =     "For the eigenvalue problem $Ax=\lambda Mx$, $A$, $B$
                 large, sparse, symmetric matrices, two methods,
                 subspace iteration and Lanczos method, are compared
                 when running on typical examples from structural
                 dynamic analysis (order of $A$, $B$ up to 8000) on a
                 Cyber 205. A fixed number of eigenpairs is calculated.
                 As on serial computers it turns out on this vector
                 computer that the Lanczos algorithm is considerably
                 faster. However, on problems with substantial overhead
                 in reading\slash writing, a block Lanczos method is
                 preferable.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65F50
                 Sparse matrices",
  keywords =     "comparison of methods; eigenvalue problem; Lanczos
                 method; large, sparse, symmetric matrices; subspace
                 iteration; vector computer; vectorization",
  reviewer =     "L. Elsner",
  ZMnumber =     "0635.65032",
}

@InProceedings{Parlett:1986:ACM,
  author =       "B. N. Parlett and K. C. Ng",
  title =        "Accurate computation of the matrix exponential",
  crossref =     "Glowinski:1986:CMA",
  pages =        "107--116",
  year =         "1986",
  MRclass =      "65F30",
  MRnumber =     "MR905289 (89f:65048)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  abstract =     "This document describes a program to compute the
                 exponential of a given $n\times n$ matrix B multiplied
                 by a scalar $\tau$ that is to be thought of as
                 representing time. Our primary goal has been to achieve
                 as much accuracy as working precision permits without
                 resorting to simulated higher precision. The final
                 product is more complicated than we anticipated at the
                 outset. How these complications came to be accepted is
                 the theme of this story. The cases we consider may be
                 of interest to those who wish to use the matrix
                 exponential in their work. We hasten to add that the
                 code acts simply on simple cases.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F30 Other matrix algorithms 15-04 Machine
                 computation, programs (linear algebra) 15A60 Appl. of
                 functional analysis to matrix theory",
  keywords =     "accuracy; accurate computation; matrix exponential;
                 program; working precision",
  ZMnumber =     "0677.65040",
}

@InProceedings{Schreiber:1986:BRC,
  author =       "Robert S. Schreiber and Beresford N. Parlett",
  title =        "Block reflectors: Computation and applications",
  crossref =     "Glowinski:1982:CMA",
  pages =        "71--79",
  year =         "1986",
  MRclass =      "65F30 (65W05)",
  MRnumber =     "MR905287 (88h:65090)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  abstract =     "A block reflector is an orthogonal, symmetric matrix
                 that reverses a subspace whose dimension may be greater
                 than one. We shall develop the properties of block
                 reflectors and give an algorithm for computing a block
                 reflector that introduces a block of zero into a
                 matrix. We consider the compact representation of block
                 reflectors, some applications, and their use in
                 parallel computers.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F30 Other matrix algorithms 65Y05 Parallel
                 computation (numerical methods)",
  keywords =     "algorithm; block reflector; orthogonal, symmetric
                 matrix; parallel computers",
  ZMnumber =     "0677.65039",
}

@Article{Nour-Omid:1987:HIS,
  author =       "Bahram Nour-Omid and Beresford N. Parlett and Thomas
                 Ericsson and Paul S. Jensen",
  title =        "How to Implement the Spectral Transformation",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "178",
  pages =        "663--673",
  month =        apr,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718",
  MRclass =      "65F15",
  MRnumber =     "MR878698 (88f:65062)",
  MRreviewer =   "William W. Hager",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  corpsource =   "Lockheed Palo Alto, Res. Lab., CA, USA",
  fjournal =     "Mathematics of Computation",
  keywords =     "algebra; Cholesky factor; eigenpairs; eigenvalue;
                 eigenvalue equations; eigenvalues and eigenfunctions;
                 factorization; inverse; iteration; iterative methods;
                 Lanczos algorithm; linear; matrix; numerical methods;
                 reductions; Ritz vectors; spectral transformation;
                 symmetric matrices; transformation step",
  reviewer =     "L. Boubel{\'\i}kov{\'a}",
  treatment =    "T Theoretical or Mathematical",
  ZMnumber =     "0638.65026",
}

@TechReport{Parlett:1987:BRT,
  author =       "Beresford N. Parlett and Robert Schreiber",
  title =        "Block reflectors: theory and computation",
  type =         "Technical Report",
  number =       "PAM-378",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        may,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1987:CJH,
  author =       "Beresford N. Parlett",
  title =        "A contribution of {J. H. Wilkinson} to numerical
                 analysis",
  type =         "Technical Report",
  number =       "PAM-372",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        apr,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1987:CLC,
  author =       "Beresford N. Parlett and B. Nour-Omid and A. Raefsky",
  title =        "Comparison of {Lanczos} with conjugate gradient using
                 element preconditioning",
  type =         "Technical Report",
  number =       "PAM-363",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        feb,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1987:CSI,
  author =       "Beresford N. Parlett and Youcef Saad",
  title =        "Complex Shift and Invert Strategies for Real
                 Matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "88/89",
  number =       "??",
  pages =        "575--595",
  year =         "1987",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F05",
  MRnumber =     "MR882464 (88d:65056)",
  MRreviewer =   "H. R. Schwarz",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/linala1980.bib",
  abstract =     "Algorithms for the nonsymmetric eigenvalue problem
                 $(F-\lambda M)X=0$ with real matrices are studied. It
                 is shown that the symmetry around the real axis can be
                 exploited in algorithms based on inverse iteration.
                 Algorithm are developed which use either the real or
                 the imaginary part of $(F-\lambda M)\sp{-1}M$, obtained
                 by a complex banded Gaussian elimination. Numerical
                 results are given for an example arising from a
                 brusselator model of a tubular chemical reactor.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 80A32
                 Chemically reacting flows",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "Algorithm; banded Gaussian elimination; inverse
                 iteration; nonsymmetric eigenvalue problem; Numerical
                 results; tubular chemical reactor",
  reviewer =     "A. Ruhe",
  ZMnumber =     "0623.65045",
}

@TechReport{Parlett:1987:MLA,
  author =       "Beresford N. Parlett",
  title =        "Misconvergence in the {Lanczos} algorithm",
  type =         "Technical Report",
  number =       "PAM-404",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        dec,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1987:PSD,
  author =       "Beresford N. Parlett and K. C. Ng",
  title =        "Programs to swap diagonal blocks",
  type =         "Technical Report",
  number =       "PAM-381",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Parlett:1987:SAE,
  author =       "Beresford N. Parlett",
  title =        "The state-of-the-art in extracting eigenvalues and
                 eigenvectors in structural mechanics",
  type =         "Technical Report",
  number =       "PAM-373",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        apr,
  year =         "1987",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@TechReport{Gao:1988:CCS,
  author =       "F. Gao and Beresford N. Parlett",
  title =        "Communication cost of sparse {Cholesky} factorization
                 on a hypercube",
  type =         "Technical Report",
  number =       "PAM-436",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        dec,
  year =         "1988",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Le:1988:FIT,
  author =       "J. Le and Beresford N. Parlett",
  title =        "On the forward instability of the {$QR$}
                 transformation",
  type =         "Technical Report",
  number =       "PAM-419",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jul,
  year =         "1988",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nour-Omid:1988:CLC,
  author =       "B. Nour-Omid and B. Parlett and A. Raefsky",
  title =        "Comparison of {Lanczos} with Conjugate Gradient Using
                 Element Preconditioning",
  crossref =     "Glowinski:1988:FIS",
  pages =        "250--260",
  year =         "1988",
  bibdate =      "Thu Nov 10 18:35:12 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/ovr.bib",
  acknowledgement = ack-nhfb,
  classmath =    "*65F10 Iterative methods for linear systems 65F35
                 Matrix norms, etc. (numerical linear algebra) 65N30
                 Finite numerical methods (BVP of PDE) 35J25 Second
                 order elliptic equations, boundary value problems",
  keywords =     "conjugate gradients; finite elements; Lanczos method;
                 preconditioning",
  reviewer =     "H. R. Schwarz",
  ZMnumber =     "0658.65034",
}

@TechReport{Parlett:1988:HMS,
  author =       "Beresford N. Parlett and B. Nour-Omid and Zhishun A.
                 Liu",
  title =        "How to maintain semi-orthogonality among {Lanczos}
                 vectors",
  type =         "Technical Report",
  number =       "PAM-420",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jul,
  year =         "1988",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1988:UII,
  author =       "Beresford N. Parlett and H. C. Chen",
  title =        "Use of an indefinite inner product for computing
                 damped natural modes",
  type =         "Technical Report",
  number =       "PAM-435",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        nov,
  year =         "1988",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@Article{Schreiber:1988:BRT,
  author =       "Robert S. Schreiber and Beresford N. Parlett",
  title =        "Block Reflectors: {Theory} and Computation",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "25",
  number =       "1",
  pages =        "189--205",
  month =        feb,
  year =         "1988",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  MRclass =      "65F05 (65F20)",
  MRnumber =     "MR923934 (89c:65040)",
  MRreviewer =   "David R. Hill",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 JSTOR database; Theory/Matrix.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/ovr.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  abstract =     "Block reflectors are the generalization of the
                 Householder transformation to block elimination
                 (instead of single element). A complete theory is
                 presented. Some stable algorithms are introduced. Block
                 reflectors are advantageous on parallel computers.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F05 Direct methods for linear systems 65F20
                 Overdetermined systems (numerical linear algebra) 65Y05
                 Parallel computation (numerical methods)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  keywords =     "block elimination; Block reflectors; Householder
                 transformation; parallel computers; QR-factorization;
                 stable algorithms",
  kwds =         "math, la, nla, Householder transformation, qrd, prll",
  reviewer =     "W. Sch{\"o}nauer",
  ZMnumber =     "0637.65017",
}

@TechReport{Parlett:1989:SBI,
  author =       "Beresford N. Parlett",
  title =        "Some basic information on information-based complexity
                 theory",
  type =         "Technical Report",
  number =       "PAM-460",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jul,
  year =         "1989",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1989:TBB,
  author =       "Beresford N. Parlett and Bahram Nour-Omid",
  title =        "Towards a black box {Lanczos} program",
  journal =      j-COMP-PHYS-COMM,
  volume =       "53",
  number =       "1-3",
  pages =        "169--179",
  year =         "1989",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  abstract =     "The Lanczos algorithm may be used to find a few
                 eigenvalues and eigenvectors of a large matrix. We
                 describe some of the difficulties encountered in trying
                 to make a black box program requiring no judgements
                 from the user.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  keywords =     "black box program; eigenvalues; eigenvectors; Lanczos
                 algorithm; large matrix",
  ZMnumber =     "0798.65054",
}

@Article{Gao:1990:NCA,
  author =       "Feng Gao and Beresford N. Parlett",
  title =        "A note on communication analysis of parallel sparse
                 {Cholesky} factorization on a hypercube",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "16",
  number =       "1",
  pages =        "59--60",
  month =        nov,
  year =         "1990",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191",
  MRclass =      "65Y05",
  MRnumber =     "MR1089846 (92a:65361)",
  bibdate =      "Mon Apr 14 12:07:40 MDT 1997",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290H (Linear algebra); C4140 (Linear algebra);
                 C4240 (Programming and algorithm theory)",
  corpsource =   "Dept. of Comput. Sci. British Columbia Univ.,
                 Vancouver, BC, Canada",
  fjournal =     "Parallel Computing. Theory and Applications",
  keywords =     "communication analysis; factorization; hypercube;
                 linear algebra; nested-dissection method; parallel
                 algorithms; parallel sparse Cholesky",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@InProceedings{Parlett:1990:CJH,
  author =       "Beresford N. Parlett",
  title =        "The Contribution of {J. H. Wilkinson} to Numerical
                 Analysis",
  crossref =     "Nash:1990:HSC",
  pages =        "17--30",
  year =         "1990",
  MRclass =      "01A70 (65-03)",
  MRnumber =     "MR1203099",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
  mycrossref =   "Nash:1990:HSC",
}

@InProceedings{Parlett:1990:LAI,
  author =       "B. N. Parlett and H. C. Chen",
  title =        "The {Lanczos} algorithm with indefinite inner
                 product",
  crossref =     "Kaashoek:1990:PIS",
  volume =       "5",
  pages =        "393--400",
  year =         "1990",
  MRclass =      "65F15 (15A18 70J10 73K12)",
  MRnumber =     "MR1115469 (92g:65043)",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  series =       "Progr. Systems Control Theory",
  abstract =     "A quadratic eigenvalue problem with symmetric positive
                 definite coefficient matrices may be reduced to linear
                 form while retaining symmetry in the new coefficients
                 but neither of them will be positive definite. Formally
                 the symmetric Lanczos algorithm and subspace iteration
                 may be used to compute some eigenpairs of the linear
                 problem. The trouble is that the basis vectors are
                 orthogonal with respect to an indefinite inner product
                 so there is no assurance that they will be linearly
                 independent. Nevertheless this is an attractive way to
                 solve the original problem and we discuss how to
                 implement it and how it relates to the unsymmetric
                 Lanczos procedures. We discuss complex origin shifts,
                 the Look-Ahead version, reorthogonalization, and error
                 bounds.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra)",
  keywords =     "complex origin shifts; eigenpairs; error bounds;
                 indefinite inner product; Look-Ahead version; quadratic
                 eigenvalue problem; reorthogonalization; subspace
                 iteration; symmetric Lanczos algorithm",
  ZMnumber =     "0719.65026",
}

@InProceedings{Parlett:1990:MLA,
  author =       "Beresford N. Parlett",
  title =        "Misconvergence in the {Lanczos} Algorithm",
  crossref =     "Cox:1990:RNC",
  pages =        "7--24",
  year =         "1990",
  MRclass =      "65F15",
  MRnumber =     "MR1098315 (91m:65110)",
  bibdate =      "Tue Nov 2 19:30:33 1999",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/tex/bib/numana1990.bib",
  abstract =     "Theoretical and computational tools are developed in
                 this paper that help to understand and predict the
                 apparent misconvergence in Lanczos' method for matrices
                 with clustered eigenvalues. A computable ``point of
                 discovery'' is given that aids with discovering
                 eigenvalues hidden by the misconvergence of the Ritz
                 values in Lanczos' algorithm. The solution hinges on
                 ``Ritz intervals'' and their ``effective spread'',
                 rather than the Ritz values themselves.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65F35
                 Matrix norms, etc. (numerical linear algebra) 15A42
                 Inequalities involving eigenvalues and eigenvectors",
  keywords =     "convergence; Lanczos' method; matrices with clustered
                 eigenvalues; misconvergence; point of discovery; Ritz
                 intervals; Ritz values",
  reviewer =     "F. Uhlig (Auburn)",
  ZMnumber =     "0726.65032",
}

@TechReport{Parlett:1990:RTF,
  author =       "Beresford N. Parlett",
  title =        "Reduction to tridiagonal form and minimal
                 realizations",
  type =         "Technical Report",
  number =       "PAM-486",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jan,
  year =         "1990",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@Article{Parlett:1990:UIP,
  author =       "B. N. Parlett and H. C. Chen",
  title =        "Use of indefinite pencils for computing damped natural
                 modes",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "140",
  number =       "??",
  pages =        "53--88",
  year =         "1990",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR1075543 (92b:65030)",
  MRreviewer =   "M. Tismenetsky",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/tex/bib/linala1990.bib",
  abstract =     "A quadratic eigenvalue problem $(\lambda\sp 2\sb
                 i\cdot M+\lambda\sb iC+K)\omega\sb i=0,$ $i=1,...,2n$
                 is solved where $M$, $C$, $K$ are real symmetric and
                 positive definite $n\times n$ matrices. This problem
                 may be reduced to linear symmetric but not positive
                 definite form. The new problem is $(A-1/\lambda B)z=0,$
                 where $A$, $B$ are symmetric but indefinite
                 matrices.\par

                 The problems are solved by means of the Lanczos
                 algorithm. When $K$ is singular, then the shifted
                 problem is solved. Real or complex origin shifts,
                 reorthogonalization, and error bounds are discussed.
                 Several methods for solving the reduced problem are
                 mentioned. Some dangers are described, and examples are
                 given comparing the Lanczos algorithm with subspace
                 iteration.",
  acknowledgement = ack-nhfb,
  classmath =    "*65H17 Eigenvalue and bifurcation problems of
                 nonlinear algebraic equations 65F15 Eigenvalues
                 (numerical linear algebra)",
  fjournal =     "Linear Algebra and its Applications",
  keywords =     "comparison of methods; error bounds; indefinite
                 pencils; Lanczos algorithm; quadratic eigenvalue
                 problem; reorthogonalization; subspace iteration;
                 symmetric positive definite matrices",
  reviewer =     "L. Boubel{\'\i}kov{\'a} (Praha)",
  ZMnumber =     "0725.65055",
}

@TechReport{Hill:1991:RIP,
  author =       "R. O. Hill and Beresford N. Parlett",
  title =        "Refined interlacing properties",
  type =         "Technical Report",
  number =       "PAM-517",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jan,
  year =         "1991",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@TechReport{Parlett:1991:IMR,
  author =       "Beresford N. Parlett and Wee-Liang Heng",
  title =        "Implementation of minimal representation in {$2$D}
                 {Ising} model calculations",
  type =         "Technical Report",
  number =       "PAM-550",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        may,
  year =         "1991",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  note =         "Longer version (60 pages)(to be published) of \#549",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author list??",
}

@InProceedings{Parlett:1991:QFI,
  author =       "Beresford N. Parlett and Jian Le",
  title =        "{QR}; its forward instability and failure to
                 converge",
  crossref =     "Albrecht:1991:NTE",
  pages =        "177--189",
  year =         "1991",
  MRclass =      "65F10 (65F35)",
  MRnumber =     "MR1109104",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  series =       "Internat. Ser. Numer. Math.",
  abstract =     "The QR factorization of a rectangular matrix $B$ is
                 known to be backward stable; however, forward
                 instability may occur, i.e., the computed orthogonal
                 transformations are far from the exact ones. On the
                 other hand, if the rank of $B$ happens to be smaller
                 than the number of columns, then the QR factorization
                 is not unique. The paper shows precisely that forward
                 instability occurs if and only if $B$ is close to a
                 matrix whose QR factorization is not unique. The
                 analysis is focussed on tridiagonal matrices and upper
                 Hessenberg ones; the implementation of the QR algorithm
                 is the usual one consisting in a shift followed by
                 premultiplication by plane rotation matrices. Several
                 illustrative examples are also discussed.",
  acknowledgement = ack-nhfb,
  classmath =    "*65F15 Eigenvalues (numerical linear algebra) 65F25
                 Orthogonalization (numerical linear algebra)",
  keywords =     "convergence; forward instability; Hessenberg matrices;
                 QR algorithm; QR factorization; rectangular matrix;
                 tridiagonal matrices",
  reviewer =     "J. P. Milaszewicz (Buenos Aires)",
  ZMnumber =     "0724.65036",
}

@Article{Parlett:1991:SMP,
  author =       "Beresford N. Parlett",
  title =        "Symmetric matrix pencils",
  journal =      j-J-COMP-APPL-MATH,
  volume =       "38",
  number =       "1-3",
  pages =        "373--385",
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427",
  MRclass =      "15A22 (65F15)",
  MRnumber =     "MR1146990 (92m:15011)",
  MRreviewer =   "F. Szidarovszky",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "Proceedings of the International Symposium on
                 Computational Mathematics (Matsuyama, 1990).",
  abstract =     "Typical matrix eigenvalue problems, quadratic or
                 linear, are best formulated as pencils $(A,M)$ in which
                 both $A$ and $M$ are real and symmetric. This fact is
                 emphasized in the paper through a set of physical
                 examples. Then, the canonical forms are used to explain
                 the role of the sign characteristic attached to real
                 eigenvalues.\par

                 The Rayleigh quotient is analyzed to describe real
                 eigenvalues and it seems plausible that the class of
                 definite Hermitian pencils is the broadest extension of
                 the class of Hermitian matrices that retains the
                 classical properties. This sheds new light on the class
                 of definite pencils and the stability of their
                 eigenvalues under perturbations. The reduction of
                 indefinite pencils to useful sparse forms is also
                 mentioned.",
  acknowledgement = ack-nhfb,
  classmath =    "*15A22 Matrix pencils 15A18 Eigenvalues of matrices,
                 etc",
  fjournal =     "Journal of Computational and Applied Mathematics",
  keywords =     "canonical forms; congruence; definite pencils;
                 equivalence; Hermitian pencils; indefinite pencils;
                 matrix eigenvalue problems; matrix pencils; Rayleigh
                 quotient; rotation transformation; stability; symmetric
                 matrix pencils",
  reviewer =     "M. de la Sen (Bilbao)",
  ZMnumber =     "0772.15005",
}

@TechReport{Fernando:1992:ASVa,
  author =       "K. Vince Fernando and Beresford N. Parlett",
  title =        "Accurate Singular Values and Differential $qd$
                 Algorithms",
  type =         "Technical Report",
  number =       "TR2/92",
  institution =  "NAG Ltd.",
  address =      "Oxford, UK",
  pages =        "????",
  month =        jul,
  year =         "1992",
  bibdate =      "Thu Nov 10 18:37:11 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  note =         "To appear in Numer. Math.",
  URL =          "ftp://ftp.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Fernando:1992:ASVb,
  author =       "K. Vince Fernando and Beresford N. Parlett",
  title =        "Accurate singular values and differential $qd$
                 algorithms",
  type =         "Technical Report",
  number =       "PAM-554",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jul,
  year =         "1992",
  bibdate =      "Fri Nov 11 09:09:56 2005",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1992:RIP,
  author =       "R. O. {Hill, Jr.} and B. N. Parlett",
  title =        "Refined Interlacing Properties",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "13",
  number =       "1",
  pages =        "239--247",
  month =        jan,
  year =