% Version dated June 30, 2003
REFERENCES FOR LEAST SQUARES METHODS
{\AA}ke Bj{\"o}rck
This is an updated vesrion of a BibTeX reference base which I have used for
the book Numerical Methods for Least Squares, SIAM, 1996 (reference {bjor:96}).
It has been modeled after the BibTeX reference base of Pete Stewart, and
the same comments applies to its use. Below I repeat some of the introductory
comments of his base:
CITATION KEYS
A citation key is divided into two fields, :, separated
by a colon. The author field is constructed as follows. If there is
only one author, the first four letters of his or her last name are
used to form the field (but only one letter each from prefixes, e.g.
van de Geign becomes vdge). If there are two authors the first two
letters in their last names are used. If there are three authors the
first two letters of the first are used with one letter from each of
the second and third. If their are four, one letter from each is used.
Warning: there may be a few exceptions to these conventions.
NAMES
Names appear in the order in which they appear in the reference, and entries
are alphabetized by the first name to appear. To keep BibTeX from
becoming confused, only initials of given names are used.
Between some entries you will find clusters of two letters--e.g. -ac- -ad-.
These can be used to position yourself within the reference base.
KEYWORDS
Each entry has a keyword field, labeled kwds. The program bibsrch (see below)
will search the file for matches in a user-specified
combination of conjunctions, disjunctions, and negations. The user
can also specify the author. The program getkey dumps the keywords
on the standard output. To get an alphabetized list of all key words
from the file ref.bib try
getkey ref | sort -uf > keywords
The choice of key words is a highly personal matter. I have used a number
of abbreviations to keep the kwds field to a manageable size. Here they are.
approximate methods (appr)
augmented system (augms)
backward perturbation (pert),
banded least squares (band),
blas (blas),
block angular system (basys),
block methods (block),
Chebyshev approximation (cheb),
Cholesky (chol),
condition (cond),
conjugate gradients (cg),
constrained least squares (constr),
control theory (contr),
covariance matrix (covar),
CS decomposition (csd),
downdating (downd),
eigenvalue problem (eigv)
equilibration (scale),
error estimate (err),
fast Fourier transform (fft),
fill-in (fill),
generalized eigenvalue problems (geig),
generalized inverse (ginv),
generalized linear model (glsq),
generalized QR decomposition (gqrd),
geodesy (geod),
geometric elements, fitting (geom),
generalized singular value decomposition (gsvd),
Givens rotation (rot),
graph theory (graph),
Gram-Schmidt (grsch),
history of least squares (hist),
Householder (house),
hyperbolic rotation/Householder (hyp),
ill-posed (illp),
interior point methods (intpoint),
interval analysis (err),
iterative method (iter),
iterative refinement (ir),
Kronecker product (kron),
Lanczos (lanczos),
linear algebra general (la),
LU decomposition (lud),
matrix approximation (max),
nested dissection (nestdis),
nonlinear least squares (nlsq),
normal equations (ne),
null basis (nullsp)
optimization (opt),
ordering for sparsity (perm),
orthogonalization (orth),
orthogonal regression (orthreg),
precision (err),
preconditioning (precond),
pseudo-inverse (ginv),
parallel computation (prll),
perturbation theory (pert),
polynomial approximation (poly),
projection (orth),
QR decomposition (qrd),
quadratic programming (quadpr),
random matrix (rand),
rank degenerate problems (rank),
rank revealing QR factorization (rrqr),
recursive least squares (rls),
regularization (regul),
regression (regr),
robust estimation (rob),
scaling (scale),
signal processing (signal),
singular value decomposition (svd),
software (soft),
sparse (sparse),
spline approximation (spline),
statistics (stat),
structured least squares (struc)
survey paper/book (survey),
systolic (syst),
test matrix (test),
Toeplitz (toep),
total least squares (tls),
underdetermined systems (uds),
updating, downdating (upd, downd),
Vandermonde systems (vand),
variable projection (varpro),
vector processing (prll),
weighted least squares (wlsq)"
The program getkey also prints out these correspondences in the
appropriate places. (They are actually key words in the last article
of the base; take a look.)
DISCLAIMERS
Do not use the references in a paper, unless you have checked them out
for yourself. Naturally, I am interested in hearing about any errors
you may find. This reference base downdated regularly, and items can
disappear. For example, I will generally remove techreports as I find them
published in journals. If you use this base in a \bibliograpy command,
save your bbl files!
BIBSRCH
The programs bibsrch and getkey, written by G.W. Stewart, may be generated from
the file bibsearch.tar, available by anonymous ftp at
thales.cs.umd.edu
in the directory
pub/references.
Simply place bibsearch.tar in the directory where you want the directory
containing the programs. Then
tar xf bibsearch.tar
cd bibsearch
more README
and you will be told what to do next.
@article{abde:71,
author = "N. N. Abdelmalek",
year = "1971",
title = "Roundoff Error Analysis for {Gram-Schmidt} Method and
Solution of Linear Least Squares Problems",
journal = "BIT",
volume = "11",
pages = "345--368",
kwds = "err,grsch,qrd"
}
@article{adco:1878,
author = "R. J. Adcock",
year = "1878",
title = "A Problem in Least Squares",
journal = "The Analyst",
volume = "5",
pages = "53--54",
kwds = "regr,stat,tls"
}
@phdthesis{adle:98,
author = "M. Adlers",
year = "1998",
title = "Sparse Least Squares Problems with Box Constraints",
school = "Department of Mathematics, Link{\"o}ping University",
address = "Sweden",
type = "{Lic.} thesis",
kwds = "sparse, constr,"
}
@phdthesis{adle:00,
author = "M. Adlers",
year = "2000",
title = "Topics in Sparse Least Squares Problems",
school = "Link{\"o}ping Studies in Science and Technology",
address = "Link{\"o}ping University, Sweden",
type = "{PhD thesis}",
number = "634",
kwds = "cg, iter"
}
@article{adbj:00,
author = "M.~Adlers. and {\AA}.~Bj{\"o}rck",
year = "2000",
title = "Matrix Stretching for Sparse Least Squares Problems",
journal = "Numer. Linear Algebra Appl.",
volume = "7",
pages = "51--65",
kwds = "sparse"
}
@book{ahhu:83,
author = "A. V. Aho and J. E. Hopcroft and J. D. Ullman",
year = "1983",
title = "Data Structures and Algorithms",
publisher = "Addison-Wesley",
address = "Reading, MA",
kwds = ""
}
@article{aike:34,
author = "A. C. Aiken",
year = "1934",
title = "On Least Squares and Linear Combinations of Observations",
journal = "Proceedings of the Royal Society of Edinburgh, Sec. A",
volume = "55",
pages = "42--47",
kwds = "regr,stat"
}
@article{ajje:84,
author = "M. A. Ajiz and A. Jennings",
year = "1984",
title = "A Robust Incomplete {Choleski}-Conjugate Gradient Algorithm",
journal = "Internat. J. Numer. Methods. Engrg.",
volume = "20",
pages = "949--966",
kwds = "cg, precond"
}
al-
@article{alfl:85,
author = "M. Al-Baali and R. Fletcher",
year = "1985",
title = "Variational Methods for Non-linear Least Squares",
journal = "J. Oper. Res. Soc.",
volume = "36",
pages = "405--421",
kwds = "nlsq"
}
@article{alfl:86,
author = "M. Al-Baali and R. Fletcher",
year = "1986",
title = "An Efficient Line Search for Nonlinear Least-squares",
journal = "J. Optim. Theory Appl.",
volume = "48",
pages = "359--377",
kwds = "nlsq"
}
@phdthesis{alba:84,
author = "M. Al-Baali",
year = "1984",
title = "Methods for Nonlinear Least Squares",
school = "Department of Mathematical Sciences, University of Dundee",
address = "Scotland",
type = "{Ph.D.} thesis",
kwds = "nlsq"
}
al- an-
@article{alpp:88,
author = "S. T. Alexander and C.-T. Pan and R. J. Plemmons",
year = "1988",
title = "Analysis of a Recursive Least Squares Hyperbolic
Rotation Algorithm for Signal Processing",
journal = "Linear Algebra Appl.",
volume = "98",
pages = "3-40",
kwds = "downd, hyp, signal, rls"
}
@article{alva:90,
author = "F. L. Alvarado",
year = "1990",
title = "Manipulating and Visualization of Sparse Matrices",
journal = "ORSA J. Comput.",
volume = "2",
pages = "186--207",
kwds = "sparse, soft"
}
@phdthesis{ames:91,
author = "P. R. Amestoy",
year = "1991",
title = "Factorization of Large Sparse Matrices Based on a
Multifrontal Approach in a Multiprocessor Environment",
school = "CERFACS",
address = " Toulouse, France",
type = "{Ph.D.} thesis",
number = "TH/PA/91/2",
kwds = "sparse, prll, thesis"
}
@article{amdd:96,
author = "P. R. Amestoy and T. Davis and I. S. Duff",
year = "1996",
title = "An Approximate Minimum Degree Ordering Algorithm",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "17",
pages = "886--905",
kwds = "sparse"
}
@article{amdu:89,
author = "P. R. Amestoy and I. S. Duff",
year = "1989",
title = "Vectorization of a Multiprocessor Multifrontal Code",
journal = "Internat. J. Supercomp. Appl.",
volume = "3",
pages = "41--59",
kwds = "sparse, prll"
}
@article{amdu:93,
author = "P. R. Amestoy and I. S. Duff",
year = "1993",
title = "Memory Allocation Issues in Sparse Multiprocessor
Multifrontal Methods",
journal = "Internat. J. Supercomput. Appl.",
volume = "7",
pages = "64--82",
kwds = "sparse, prll"
}
@article{amdp:96,
author = "P. R. Amestoy and I. S. Duff and C. Puglisi",
year = "1996",
title = "Multifrontal {QR} Factorization in a Multiprocessor Environment",
journal = "Numerical Linear Algebra with Applications",
volume = "3",
pages = "275--300",
kwds = "sparse, prll"
}
@article{anpa:94,
author = "A. A. Anda and H. Park",
year = "1994",
title = "Fast Plane Rotations with Dynamic Scaling",
journal = " SIAM J. Matrix Anal. Appl.",
volume = "15",
pages = "162--174",
kwds = "rot"
}
@article{anpa:96,
author = "A. A. Anda and H. Park",
year = "1996",
title = "Self-Scaling Fast Rotations for Stiff Least Squares Problems",
journal = "Linear Algebra Appl.",
volume = "234",
pages = "137--162",
kwds = "rot, qrd,wlsq,constr"
}
@book{anbb:95,
editor = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and
J. Dongarra and J. {Du Croz} and A. Greenbaum and
S. Hammarling and A. McKenney and S. Ostrouchov and
D. Sorensen ",
year = "1995",
title = "{LAPACK} Users' Guide. Second Edition",
publisher = "SIAM",
address = "Philadelphia",
kwds = "prll,soft"
}
@article{anbd:92,
author = "E. Anderssen and Z. Bai and J. Dongarra",
title = "Generalized {QR} Factorization and its Applications",
year = "1992",
journal = "Linear Algebra Appl.",
volume = "162--164",
pages = "243--271",
kwds = "gqr"
}
@article{anka:75,
author = "N. Anderson and I. Karasalo",
year = "1975",
title = "On Computing Bounds for the Least Singular Value of a Triangular
Matrix",
journal = "BIT",
volume = "15",
pages = "1--4",
kwds = "err, rank, svd"
}
@techreport{ango:72,
author = "R. S. Anderssen and G. Golub",
title = "Richardson's Non-Stationary Matrix Iterative Procedure",
institution = "Computer Science Department",
year = "1972",
type = "{Tech. Report}",
number = "STAN-CS-72-304",
address = "Stanford University, CA",
kwds = "iter"
}
ar- as-
@article{ario:00,
author = "M. Arioli",
year = "2000",
title = "The Use of {QR} Factorization in Sparse Quadratic Programming
and Backward Error Issues",
journal = " SIAM J. Matrix Anal. Appl.",
volume = "21",
pages = "825--839",
kwds = "sparse, qrd"
}
@article{ardd:89,
author = "M. Arioli and J. Demmel and I. S. Duff",
year = "1989",
title = "Solving Sparse Linear Systems with Sparse Backward Error",
journal = " SIAM J. Matrix Anal. Appl.",
volume = "10",
pages = "165--190",
kwds = "sparse, pert"
}
@article{ardr:89,
author = "M. Arioli and I. S. Duff and P. P. M. de Rijk",
year = "1989",
title = "On the augmented system approach to sparse least-squares problems",
journal = "Numer. Math.",
volume = "55",
pages = "667--684",
kwds = "sparse, augms"
}
@article{ardr:92,
author = "M. Arioli and I. S. Duff and D. Ruiz",
year = "1992",
title = "Stopping Criteria for Iterative Solvers",
journal = " SIAM J. Matrix Anal. Appl.",
volume = "13",
pages = "138--144",
kwds = "iter, pert"
}
@article{adrs:95,
author = "M. Arioli and I. S. Duff and D. Ruiz and M. Sadkane",
year = "1995",
title = "Block {Lanczos} Techniques for Accelerating the Block
{Cimmino} Method",
journal = " SIAM J. Sci. Comput.",
volume = "16",
pages = "1478--1511",
kwds = "iter, sparse, prll"
}
@article{ardn:92,
author = "M. Arioli and I. S. Duff and J. Noailles and D. Ruiz",
year = "1990",
title = "A Block Projection Method for Sparse Matrices",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "13",
pages = "47--70",
kwds = "sparse, iter"
}
@article{arla:86,
author = "M. Arioli and A. Laratta",
year = "1986",
title = "Error analysis of an algorithm for solving an underdetermined
linear system",
journal = "Numer. Math.",
volume = 46,
pages = "255--268",
kwds = "err, uds"
}
@article{arla:86a,
author = "M. Arioli and A. Laratta",
year = "1986",
title = "Error analysis of algorithms for computing the projection of a
Point onto a linear manifold",
journal = "Linear Algebra Appl.",
volume = 82,
pages = "1--26",
kwds = "uds, orth"
}
@article{asgr:89,
author = "C. Ashcraft and R. G. Grimes",
year = "1989",
title = "The Influence of Relaxed Supernode Partitions on the
Multifrontal Method",
journal = "ACM Trans. Math. Software",
volume = "15",
pages = "291--309",
kwds = "sparse, prll"
}
@techreport{ashc:87,
author = "C. Ashcraft",
year = "1987",
title = "A Vector Implementation of the Multifrontal
Method for Large Sparse Positive Definite Systems",
institution = "Engineering Technology Division,
Boeing Computer Services",
address= "Seattle, WA",
type = "{Tech. Report}",
number = "ETA-TR-51",
kwds = "sparse, prll"
}
@incollection{ashk:71,
author = "V. Ashkenazi",
year = "1971",
title = " Geodetic Normal Equations",
booktitle = "Large Sets of Linear Equations",
editor = "J. K. Reid",
pages = "57--74",
publisher = "Academic Press, New York",
kwds = "geod, ne"
}
av-
@inproceedings{avto:79,
author = "J. K. Avila and J. A. Tomlin",
year = "1979",
title = "Solution of Very Large Least Squares Problems by Nested Dissection
on a Parallel Processor",
booktitle = "Proceedings of the Computer Science and Statistics
12th Annual Symposium on the Interface",
editor = "J. F. Gentleman",
publisher = "University of Waterloo, Canada",
kwds = "sparse, perm, prll"
}
ba-
@techreport{bai:92,
author = "Z. Bai",
year = "1992",
title = "The {CSD}, {GSVD}, Their Applications and Computations",
institution = "Institute for Mathematics and Its Applications,
University of Minnesota",
address = "Minneapolis, MN",
type = "{Tech. Report}",
number = "IMA Preprint Series 958",
kwds = "csd, gsvd"
}
@article{bade:93,
author = "Z. Bai and J. W. Demmel",
year = "1993",
title = "Computing the Generalized Singular Value Decomposition",
journal = "SIAM J. Sci. Comput.",
volume = "14",
pages = "1464--1486",
kwds = "gsvd"
}
@article{bazh:93,
author = "Z. Bai and H. Zha",
year = "1993",
title = "A New Preprocessing Algorithm for the Computation of the
Generalized Singular Value Decomposition",
journal = "SIAM J. Sci. Comput.",
volume = "14",
pages = "1007--1012",
kwds = "gqrd, gsvd"
}
@article{bana:38,
author = "T. Banachiewicz",
year = "1938",
title = "Principes d'une nouvelle technique de la m\'ethode des
moindres carr\'es",
journal = "Bull. Internat. Acad. Polon. Sci. A",
pages = "134--135",
kwds = "chol"
}
@book{bard:74,
author = "Y. Bard",
year = "1974",
title = "Nonlinear Parameter Estimation",
publisher = "Academic Press",
address = "New York",
kwds = "stat, nlsq"
}
@techreport{bare:82,
author = "E. H. Bareiss",
year = "1982",
title = "Numerical Solution of the Weighted Linear Least Squares Problems
by {G}-transformations",
institution = "Department of Electrical Engineering and Computer Science",
address = "Northwestern University, Evanston, IL",
type = "{Tech. Report}",
number = "82-03-NAM-03",
kwds = "wlsq"
}
@article{barl:85,
author = "J. L. Barlow",
year = "1985",
title = "Stability Analysis of the {G}-algorithm and a Note on its Application
to Sparse Least Squares Problems",
journal = "BIT",
volume = "25",
pages = "507--520",
kwds = "wlsq"
}
@article{barl:88,
author = "J. L. Barlow",
year = "1988",
title = "Error Analysis and Implementation Aspects of Deferred Correction
for Equality Constrained Least Squares Problems",
journal = "SIAM J. Numer. Anal.",
volume = "25",
pages = "1340--1358",
kwds = "constr, err"
}
@techreport{barl:89,
author = "J. L. Barlow",
year = "1989",
title = "The Accurate Solution of Sparse Weighted and Equality
Constrained Least Squares Problems Using a Static Data Structure",
institution = "Dept. of Computer Science, The Pennsylvania State University",
address = "State College, PA",
type = "{Tech. Report}",
number = "CS-89-03",
kwds = "wlsq, constr,sparse"
}
@article{barl:90,
author = "J. L. Barlow",
year = "1990",
title = "On the Use of Structural Zeros in Orthogonal Factorization",
journal = "SIAM J. Sci. Stat. Comput.",
volume = "11",
pages = "600--601",
kwds = "constr, err"
}
@article{baha:88,
author = "J. L. Barlow and S. L. Handy",
year = "1988",
title = "The Direct Solution of Weighted and Equality Constrained
Least Squares Problems",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "9",
pages = "704--716",
kwds = "wlsq, constr"
}
@article{baip:87,
author = "J. L. Barlow and I. C. F. Ipsen",
year = "1987",
title = "Scaled {Givens} Rotations for the Solution of Linear
Least Squares Problems on Systolic Arrays",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "8",
pages = "716-734",
kwds = "prll, rot"
}
@article{banp:88,
author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
year = "1988",
title = " Iterative Methods for Equality-constrained Least Squares
Problems.",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "9",
pages = "892--906",
kwds = "iter, constr"
}
@article{bave:92a,
author = "J. L. Barlow and U. B. Vemulapati",
year = "1992",
title = "A Note on Deferred Correction for Equality Constrained
Least Squares Problems",
journal = "SIAM J. Numer. Anal.",
volume = "29",
pages = "249--256",
kwds = "constr"
}
@article{bave:92,
author = "J. L. Barlow and U. B. Vemulapati",
year = "1992",
title = "Rank Detection Methods for Sparse Matrices",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "13",
pages = "1279--1297",
kwds = "rank, rrqr, sparse"
}
@article{bayz:96,
author = "J. L. Barlow and P. A. Yoon and H. Zha",
year = "1996",
title = "An Algorithm and a Stability Theory for Downdating the {ULV} Decomposition",
journal = "BIT",
volume = "36",
pages = "14--40",
kwds = "upd, rrqr, svd"
}
@techreport{bazy:93,
author = "J. L. Barlow and H. Zha and P. A. Yoon",
year = "1993",
title = "Stable Chasing Algorithms for Modifying Complete and
Partial Singular Value Decompositions",
institution = "Department of Computer Science",
address = "The Pennsylvania State University, State College, PA",
type = "{Tech. Report}",
number = "CSE-93-19",
kwds = "upd, svd"
}
@inproceedings{bayo:97,
author = "J. L. Barlow and H. Zha and P. A. Yoon",
year = "1997",
title = "Solving Recursive TLS Problems Using Rank-Revealing
{ULV} Decompositions",
pages = "117--126",
booktitle = "Recent Advances in Total Least Squares Techniques and
Errors-in-Variable Modeling",
editor = "Sabine Van Huffel",
publisher = "SIAM, Philadelphia, PA",
kwds = "tls, rls, rrqr"
}
@book{babc:93,
editor = "R. Barret and M. W. Berry and T. Chan and J. Demmel and J.
Donato and J. Dongarra and V. Eijkhout and R. Pozo
and C. Romine and H. van der Vorst",
year = "1993",
title = "Templates for the Solution of Linear Systems: Building
Blocks for Iterative Methods ",
publisher = "SIAM",
address = "Philadelphia",
kwds = "iter, survey"
}
@article{barr:94,
author = "A. Barrlund",
year = "1994",
title = "Perturbation Bounds for the Generalized {QR} Factorization",
journal = "Linear Algebra Appl.",
volume = "207",
pages = "251--272",
kwds = "pert, qrd"
}
@article{barr:98,
author = "A. Barrlund",
year = "1998",
title = "Efficient Solution of Constrained Least Squares Problems
with {K}ronecker Product Structure",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "19",
pages = "154--160",
kwds = "kron,constr"
}
@article{baro:73,
author = "I. Barrodale and F. D. K. Roberts",
year = "1973",
title = "An Improved Algorithm for Discrete $\ell_1$ Linear Approximation",
journal = "SIAM J. Numer. Anal.",
volume = "10",
pages = "839--848",
kwds = "rob"
}
@article{baph:75,
author = "I. Barrodale and C. Phillips",
year = "1975",
title = "Algorithm {\rm 495}: Solution of an Overdetermined System of
Linear Equations in the {Chebyshev} Norm ",
journal = "ACM Trans. Math. Software",
volume = "1",
pages = "264--270",
kwds = "cheb"
}
@article{baro:78,
author = "I. Barrodale and F. D. K. Roberts",
year = "1978",
title = "An Efficient Algorithm for Discrete $\ell_1$ Linear Approximation
with Linear Constraints",
journal = "SIAM J. Numer. Anal.",
volume = "15",
pages = "603--611",
kwds = "rob"
}
@incollection{bags:70,
author = "R. H. Bartels and G. H. Golub and M. A. Saunders",
year = "1970",
title = "Numerical Techniques in Mathematical Programming",
pages = "123--176",
booktitle = "Nonlinear Programming",
editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter",
publisher = "Academic Press, New York",
kwds = "qrd, rank"
}
@article{baco:80,
author = "R. H. Bartels and A. R. Conn",
year = "1980",
title = "Linearly Constrained Discrete $\ell_1$ Problems",
journal = "ACM Trans. Math. Software",
volume = "6",
pages = "594--608",
kwds = "rob, constr"
}
@article{bacc:80,
author = "R. H. Bartels and A. R. Conn and C. Charalambous",
year = "1980",
title = "On {Cline's} Direct Method for Solving Overdetermined Linear Systems
in the {$\ell_\infty$} Sense",
journal = " SIAM J. Numer. Anal.",
volume = "15",
pages = "255--270",
kwds = "cheb"
}
@article{bacs:78,
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%fa-
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%fl-
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ge-
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author = "W. M. Gentleman",
year = "1975",
title = "Error Analysis of {QR} Decompositions by {Givens} Transformations",
journal = "Linear Algebra Appl.",
volume = "10",
pages = "189--197",
kwds = "err, rot"
}
@inproceedings{gent:76,
author = "W. M. Gentleman",
year = "1976",
title = "Row Elimination for Solving Sparse Linear Systems and
Least Squares Problems",
booktitle = "Proceedings of the Dundee Conference on Numerical
Analysis 1975",
editor = "G. A. Watson",
publisher = "Springer-Verlag, Berlin",
series = " Lecture Notes in Mathematics",
volume = "506",
pages = "122--133",
kwds = "sparse, perm"
}
@phdthesis{geor:71,
author = "J. A. George",
year = "1971",
title = "Computer Implementation of the Finite-Element Method",
school = "Stanford University, CA",
type = "{Ph.D.} thesis",
kwds = "sparse"
}
@article{gehe:80,
author = "J. A. George and M. T. Heath",
year = "1980",
title = "Solution of Sparse Linear Least Squares Problems
Using {Givens} Rotations",
journal = "Linear Algebra Appl.",
volume = "34",
pages = "69--83",
kwds = "sparse, qrd, rot"
}
@article{gehp:81,
author = "J. A. George and M. T. Heath and R. J. Plemmons",
year = "1981",
title = "Solution of Large-Scale Sparse Least Squares Problems
Using Auxiliary Storage",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "2",
pages = "416--429",
kwds = "sparse, qrd"
}
@article{gehn:83,
author = "J. A. George and M. T. Heath and E. G. Ng",
year = "1983",
title = "A Comparison of Some Methods for Solving Sparse Linear Least
Squares Problems",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "4",
pages = "177--187",
kwds = "sparse, test"
}
@book{geli:81,
author = "J. A. George and J. W.-H. Liu",
year = "1981",
title = "Computer Solution of Large Sparse Positive Definite Systems",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, NJ",
kwds = "sparse, survey"
}
@article{geli:87,
author = "J. A. George and J. W.-H. Liu",
year = "1987",
title = "{Householder} Reflections versus {Givens} Rotations in Sparse
Orthogonal Decomposition",
journal = "Linear Algebra Appl.",
volume = "88/89",
pages = "223--238",
kwds = "sparse, rot, qrd"
}
@article{geli:89,
author = "J. A. George and J. W.-H. Liu",
year = "1989",
title = "The Evolution of the Minimum Degree Ordering Algorithm",
journal = "SIAM Review",
volume = "31",
pages = "1--19",
kwds = "sparse, perm, hist"
}
@article{geln:84,
author = "J. A. George and J. W.-H. Liu and E. G. Ng",
year = "1984",
title = "Row Ordering Schemes for Sparse {Givens} Transformations,
{I.} {Bipartite} Graph Model",
journal = "Linear Algebra Appl.",
volume = "61",
pages = "55--81",
kwds = "sparse, perm, rot"
}
@article{geln:86,
author = "J. A. George and J. W.-H. Liu and E. G. Ng",
year = "1986",
title = "Row Ordering Schemes for Sparse {Givens} Transformations,
{II.} {Implicit} Graph Model",
journal = "Linear Algebra Appl.",
volume = "75",
pages = "203--223",
kwds = "sparse, perm, rot"
}
@article{geln:86a,
author = "J. A. George and J. W.-H. Liu and E. G. Ng",
year = "1984",
title = "Row Ordering Schemes for Sparse {Givens} Transformations,
{III.} {Analysis} for a Model Problem",
journal = "Linear Algebra Appl.",
volume = "75",
pages = "225--240",
kwds = "sparse, perm, rot"
}
@article{geng:83,
author = "J. A. George and E. G. Ng",
year = "1983",
title = "On Row and Column Orderings for Sparse Least Squares Problems",
journal = "SIAM J. Numer. Anal.",
volume = "20",
pages = "326--344",
kwds = "sparse, perm, rot"
}
@techreport{geng:84,
author = "J. A. George and E. G. Ng",
year = "1984",
title = "{SPARSPAK}: Waterloo Sparse Matrix Package User's Guide for
{SPARSPAK-B}",
institution = "Department of Computer Science, University of Waterloo",
address = "Canada",
type = "Res. Report",
number = "CS-84-37",
note = "",
kwds = "sparse, soft"
}
@article{geng:85,
author = "J. A. George and E. G. Ng",
year = "1985",
title = "An Implementation of {Gaussian} Elimination with
Partial Pivoting for Sparse Systems",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "6",
pages = "390--409",
kwds = "sparse, lud"
}
@article{geng:86,
author = "J. A. George and E. G. Ng",
year = "1986",
title = "Orthogonal Reduction of Sparse Matrices to Upper Triangular
Form Using {H}ouseholder Transformations",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "7",
pages = "460--472",
kwds = "sparse, qrd"
}
@article{geng:87,
author = "J. A. George and E. G. Ng",
year = "1987",
title = "Symbolic Factorization for Sparse {Gaussian} Elimination with
Partial Pivoting",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "8",
pages = "877--898",
kwds = "sparse, lud"
}
@article{geng:88,
author = "J. A. George and E. G. Ng",
year = "1988",
title = "On the Complexity of Sparse {QR and LU} Factorization
of Finite-Element Matrices",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "9",
pages = "849--861",
kwds = "sparse, qrd, lud"
}
@article{geln:88,
author = "J. A. George and J. W.-H. Liu and E. G. Ng",
year = "1988",
title = "A Data Structure for Sparse {QR and LU} Factorization",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "9",
pages = "100--121",
kwds = "sparse, qrd, lud"
}
@article{gepv:78,
author = "J. A. George and W. G. Poole and R. G. Voigt",
year = "1978",
title = "Incomplete Nested Dissection for Solving $n$ by $n$ Grid Problems",
journal = "SIAM J. Numer. Anal.",
volume = "15",
pages = "90--112",
kwds = "sparse, perm, nestdis"
}
gi-
@phdthesis{gilb:80,
author = "J. R. Gilbert",
year = "1980",
title = "Graph Separator Theorems and Sparse {Gaussian} Elimination",
school = "Stanford University, CA",
type = "{Ph.D.} thesis",
kwds = "sparse, graph"
}
@article{gilb:94,
author = "J. R. Gilbert",
year = "1994",
title = "Predicting Structure in Sparse Matrix Computation",
journal = "SIAM J. Matrix. Anal. Appl.",
volume = "15",
pages ="62--79",
kwds = "sparse, soft"
}
@article{gims:92,
author = "J. R. Gilbert and C. Moler and R. Schreiber",
year = "1992",
title = "Sparse Matrices in {MATLAB}: Design and Implementation",
journal = "SIAM J. Matrix. Anal. Appl.",
volume = "13",
pages ="333--356",
kwds = "sparse, soft"
}
@article{ginp:97,
author = "J. R. Gilbert and E. G. Ng and B. W. Peyton",
year = "1997",
title = "Separators and Structure Prediction in Sparse Orthogonal
Factorization",
journal = "Linear Algebra Appl.",
volume = "262",
pages = "83--97",
kwds = "sparse, qrd"
}
@article{gipe:88,
author = "J. R. Gilbert and T. Peierls",
year = "1988",
title = "Sparse Partial Pivoting in Time Proportional to Arithmetic Operations",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "9",
pages ="862--874",
kwds = "sparse"
}
@article{ggms:74,
author = "P. E. Gill and G. H. Golub and W. Murray and M.A. Saunders",
year = "1974",
title = "Methods for Modifying Matrix Factorizations",
journal = "Math. Comp",
volume = "28",
pages = "505--535",
kwds = "upd, downd, chol, qrd"
}
@techreport{gihm:86,
author = "P. E. Gill and S. J. Hammarling and W. Murray and M. A. Saunders
and M. H. Wright",
year = "1986",
title = "User's Guide for {LSSOL} (version {\rm 1.0}): a {Fortran} Package for
Constrained Linear Least-squares and Convex Quadratic Programming",
institution = "Department of Operations Research, Stanford University",
type = "{Report SOL}",
address = "CA",
kwds = "constr, quadpr, soft"
}
@inproceedings{gimu:76,
author = "P. E. Gill and W. Murray",
year = "1976",
title = "Nonlinear Least Squares and Nonlinearly Constrained Optimization",
booktitle = "Proceedings Dundee Conference on Numerical Analysis 1975",
editor = "G. A. Watson",
publisher = "Springer-Verlag, Berlin",
series = " Lecture Notes in Mathematics",
volume = "506",
pages = "135--147",
kwds = "nlsq, quadpr"
}
@inproceedings{gimu:76a,
author = "P. E. Gill and W. Murray",
year = "1976",
title = "The Orthogonal Factorization of a Large Sparse Matrix",
pages = "201--212",
booktitle = "Sparse Matrix Computations",
editor = "J. R. Bunch and D. J. Rose",
publisher = "Academic Press, New York",
kwds = "sparse, qrd"
}
@article{gimu:78,
author = "P. E. Gill and W. Murray",
year = "1978",
title = "Algorithms for the Solution of the Nonlinear Least Squares Problem",
journal = "SIAM J. Numer. Anal.",
volume = "15",
pages = "977--992",
kwds = "nlsq"
}
@book{gimw:81,
author = "P. E. Gill and W. Murray and M. H. Wright",
year = "1981",
title = "Practical Optimization",
publisher = "Academic Press",
address = "London and New York",
kwds = "nlsq, opt, survey"
}
@inproceedings{gmsw:90,
author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright",
year = "1990",
title = "A {Schur}-complement Method for Sparse Quadratic Programming",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. Hammarling",
pages = "113--138",
publisher = "Clarendon Press, Oxford, UK",
kwds = "sparse, quadpr, augms"
}
@article{give:58,
author = "W. Givens",
year = "1958",
title = "Computation of Plane Unitary Rotations Transforming a General
Matrix to Triangular Form",
journal = " SIAM J. Appl. Math.",
volume = "6",
pages = "26--50",
kwds = "qrd, rot"
}
@article{glsm:90,
author = "J. Gluchowska and A. Smoktunowicz",
year = "1990",
title = "Solving the Linear Least Squares Problem with Very High
Relative Accuracy",
journal = "Computing",
volume = "45",
pages = "345--354",
kwds = "err, ir"
}
@book{gold:77,
author = "H.~H. Goldstine",
year = "1977",
title = "A History of Numerical Analysis from the {\rm 16}th through the
{\rm 19}th Century",
publisher = "Springer-Verlag",
address = "New York",
kwds = "hist"
}
@article{golu:65,
author = "G. H. Golub",
year = "1965",
title = "Numerical Methods for Solving Least Squares Problems",
journal = "Numer. Math.",
volume = "7",
pages = "206-216",
kwds = "qrd, upd"
}
@article{golu:68,
author = "G. H. Golub",
year = "1968",
title = "Least Squares, Singular Values and Matrix Approximations",
journal = "Aplikace Matematiky",
volume = "13",
pages = "44--51",
kwds = "svd, max"
}
@inproceedings{golu:69,
author = "G. H. Golub",
year = "1969",
title = "Matrix Decompositions and Statistical Computation",
pages = "365--397",
booktitle = "Statistical Computation",
editor = "R.C. Milton and J. A. Nelder",
publisher = "Academic Press, New York",
kwds = "qrd, grsch, stat"
}
@article{golu:73,
author = "G. H. Golub",
year = "1973",
title = "Some Modified Matrix Eigenvalue Problems",
journal = "SIAM Review",
volume = "15",
pages = "318--344",
kwds = "upd"
}
@article{gohw:79,
author = "G. H. Golub and M. T. Heath and G. Wahba",
year = "1979",
title = "Generalized Cross-Validation as a Method for Choosing a Good
Ridge Parameter",
journal = "Technometrics",
volume = "21",
pages = "215--223",
kwds = "regul"
}
@article{gohs:87,
author = "G. H. Golub and A. Hoffman and G. W. Stewart",
year = "1987",
title = "A Generalization of the {Eckhard-Young-Mirsky} Matrix
Approximation Theorem",
journal = "Linear Algebra Appl.",
volume = "88/89",
pages = "317--327",
kwds = "max"
}
@article{goka:65,
author = "G. H. Golub and W. Kahan",
year = "1965",
title = "Calculating the Singular Values and Pseudo-inverse of a Matrix",
journal = "SIAM J. Numer. Anal. Ser. B",
volume = "2",
pages = "205--224",
kwds = "svd, lanczos"
}
@techreport{goks:76,
author = "G. H. Golub and V. Klema and G. W. Stewart",
year = "1976",
title = "Rank Degeneracy and Least Squares Problems",
institution = "Computer Science Department, Stanford University",
address = "CA",
type = " {Tech. Report}",
number = "STAN-CS-76-559, August 1976",
kwds = "rank, rrqr"
}
@inproceedings{golv:79,
author = "G. H. Golub and R. J. LeVeque",
year = "1979",
title = "Extensions and Uses of the Variable Projection Algorithm for
Solving Nonlinear Least Squares Problems",
pages = "1--12",
booktitle = "Proceedings of the 1979 Army Numerical Analysis and
Computers Conf. ",
publisher = "White Sands Missile Range, White Sands, NM, ARO Report 79-3",
kwds = "nlsq, varpro"
}
@inproceedings{golu:77,
author = "G. H. Golub and F. T. Luk",
year = "1977",
title = "Singular Value Decomposition: Applications and Computations",
booktitle = "Trans. 22nd Conference of Army Mathematicians, ARO Report 77-1",
pages = "577--605",
kwds = "svd"
}
@article{golo:81,
author = "G. H. Golub and F. T. Luk and M. L. Overton",
year = "1981",
title = "A Block {Lanczos} Method for Computing the Singular Values and
Corresponding Singular Vectors of a Matrix",
journal = "ACM Trans. Math. Software",
volume = "7",
pages = "149--169",
kwds = "svd, lanczos"
}
@inproceedings{golp:79,
author = "G. H. Golub and F. T. Luk and M. Pagano",
year = "1979",
title = "A Sparse Least Squares Problem in Photogrammetry",
booktitle = "Proceedings of the Computer Science and Statistics
12th Annual Symposium on the Interface",
editor = "J. F. Gentleman",
publisher = "University of Waterloo, Canada",
pages = "26--30",
kwds = "sparse, nestdis"
}
@article{gomt:86,
author = "G. H. Golub and P. Manneback and P. Toint",
year = "1986",
title = "A Comparison Between some Direct and Iterative Methods for
Large Scale Geodetic Least Squares Problems",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "7",
pages = "799--816",
kwds = "sparse, nestdis, iter, cg, precond"
}
@inproceedings{gosv:95,
author = "G. H. Golub and K. Solna and P. {Van Dooren}",
year = "1995",
title = "A {QR}-Like {SVD} Algorithm for a Product/Quotient of
Several Matrices",
booktitle = "{SVD} and Signal Processing, III: Algorithms,
Architectures and Applications",
editor = "M. Moonen and B. {De Moor}",
pages = "139--147",
publisher = "Elsevier Science B.V., Amsterdam",
kwds = "gqrd, gsvd"
}
@article{goma:91,
author = "G. H. Golub and U. von Matt",
year = "1991",
title = "Quadratically Constrained Least Squares and Quadratic Problems",
journal = "Numer. Math.",
volume = "59",
pages = "561--580",
kwds = "regul, constr",
}
@inproceedings{goma:97,
author = "G. H. Golub and U. von Matt",
year = "1997",
title = "Tikhonov Regularization for Large Scale Problems",
pages = "",
booktitle = "Workshop on Scientific Computing",
editor = "G. H. Golub and S. H. Lui and F. Luk and R. Plemmons",
publisher = "Springer-verlag, New York",
kwds = "tls, lanczos"
}
@article{goma:97b,
author = "G. H. Golub and U. von Matt",
year = "1997",
title = "Generalized Cross-Validation for Large Scale Problems",
journal = "J. Comput. Graph. Stat..",
volume = "6",
pages = "1--34",
kwds = "tls, regul, lanczos"
}
@article{gona:82,
author = "G. H. Golub and S. G. Nash",
year = "1982",
title = " Nonorthogonal Analysis of Variance using a Generalized
Conjugate-Gradient Algorithm",
journal = "J. Amer. Statist. Assoc.",
volume = "77",
pages = "109--116",
kwds = "cg, stat",
}
@article{gope:73,
author = "G. H. Golub and V. Pereyra",
year = "1973",
title = "The Differentiation of Pseudoinverses and Nonlinear
Least Squares Problems Whose Variables Separate",
journal = "SIAM J. Numer. Anal.",
volume = "10",
pages = "413--432",
kwds = "pert, ginv, varpro,"
}
@inproceedings{gope:76,
author = "G. H. Golub and V. Pereyra",
year = "1976",
title = "Differentiation of Pseudoinverses, Separable
Nonlinear Least Squares Problems and Other Tales",
booktitle = "Generalized Inverses and Applications",
editor = "M. Z. Nashed",
pages = "303--324",
publisher = "Academic Press, New York",
kwds = "pert, ginv, varpro,"
}
@article{gopl:80,
author = "G. H. Golub and R. J. Plemmons",
year = "1980",
title = "Large-Scale Geodetic Least-Squares Adjustment by Dissection
and Orthogonal Decomposition",
journal = "Linear Algebra Appl.",
volume = "34",
pages = "3--28",
kwds = "sparse, qrd, geod, nestdis"
}
@inproceedings{gops:88,
author = "G. H. Golub and R. J. Plemmons and A. Sameh",
year = "1988",
title = "Parallel Block Schemes for Large-Scale Least-Squares Computations",
pages = "171-179",
booktitle = "High-Speed Computing, Scientific Applications and Algorithm
Design",
publisher = "University of Illinois Press",
address = "",
kwds = "iter, prll"
}
@article{gore:70,
author = "G. H. Golub and C. Reinsch",
year = "1970",
title = "Singular Value Decomposition and Least Squares Solution",
journal = "Numer. Math.",
volume = "14",
pages = "403--420",
kwds = "svd, rank, reg"
}
@inproceedings{gosa:70,
author = "G. H. Golub and M. A. Saunders",
year = "1970",
title = "Linear Least Squares and Quadratic Programming",
pages = "229--256",
booktitle = "Integer and Nonlinear Programming",
editor = "J. Abadie",
publisher = "North-Holland, Amsterdam",
kwds = "qrd, opt, quadpr"
}
@article{gost:73,
author = "G. H. Golub and G. P. Styan",
year = "1973",
title = "Numerical Computations for Univariate Linear Models",
journal = "J. Statist. Comput. Simul.",
volume = "2",
pages = "253-274",
kwds = "stat, regr, qrd"
}
@techreport{goun:69,
author = "G. H. Golub and R. Underwood",
year = "1969",
title = "Stationary Values of the Ratio of Quadratic Forms Subject to
Linear Constraints",
institution = "Computer Science Department, Stanford University, CA",
type = "{Tech. Report}",
number = "CS-142",
note = "",
kwds = "geig, regul"
}
@inproceedings{govl:79,
author = "G. H. Golub and C. F. {Van Loan}",
year = "1979",
title = "Total least squares",
pages = "69--76",
booktitle = "Smoothing Techniques for Curve Estimation",
editor = "T. Gasser and M. Rosenblatt",
publisher = "Springer-Verlag, New York",
kwds = "svd, tls"
}
@article{govl:80,
author = "G. H. Golub and C. F. {Van Loan}",
year = "1980",
title = "An Analysis of the Total Least Squares Problem",
journal = "SIAM J. Numer. Anal.",
volume = "17",
pages = "883-893",
kwds = "svd, tls"
}
@book{govl:96,
author = "G. H. Golub and C. F. {Van Loan}",
year = "1996",
title = "Matrix Computations, {\rm 3rd ed.}",
publisher = "Johns Hopkins University Press",
address = "Baltimore",
kwds = "la, survey"
}
@article{gova:61,
author = "G. H. Golub and R. S. Varga",
year = "1961",
title = "{Chebyshev} semi-iterative methods, successive Overrelaxation
Iterative Methods and Second Order {Richardson} Iterative
Methods, {Parts I and II}",
journal = "Numer. Math.",
volume = "3",
pages = "147--168",
kwds = "iter"
}
@inproceedings{gowi:65,
author = "G. H. Golub and J. H. Wilkinson",
year = "1965",
title = "Iterative Refinement of Least Squares Solutions",
booktitle = "Proceedings of the IFIP Congress 65, New York, 1965",
editor = "W. A. Kalenich",
pages = "606--607",
publisher = "Spartan Books, Washington",
kwds = "ir, qrd, err"
}
@article{gowi:66,
author = "G. H. Golub and J. H. Wilkinson",
year = "1966",
title = "Note on the Iterative Refinement of Least Squares Solution",
journal = "Numer. Math.",
volume = "9",
pages = "139-148",
kwds = "ir, qrd, err"
}
@article{gozh:94,
author = "G. H. Golub and H. Zha",
year = "1994",
title = "Perturbation Analysis of the Canonical Correlation of Matrix Pairs",
journal = "Linear Algebra Appl.",
volume = "210",
pages = "3--28",
kwds = "pert, err"
}
@incollection{gozh:95,
author = "G. H. Golub and H. Zha",
year = "1995",
title = "The Canonical Correlations of Matrix Pairs and Their
Numerical Computation",
booktitle = "Linear Algebra for Signal Processing",
publisher = "IMA",
editor = "A. Bojanczyk and G. Cybenko",
volume = "69",
pages = "27--49",
series = "Volumes in Mathematics and Its Applications",
kwds = "pert, err"
}
gr-
@article{grha:84,
author = "W. H. Gragg and W. J. Harrod",
year = "1984",
title = "The Numerically Stable Reconstruction of {Jacobi} Matrices
from Spectral Data",
journal = "Numer. Math.",
volume = "44",
pages = "317--335",
kwds = "eigv"
}
@article{gram:1883,
author = "J. P. Gram",
year = "1883",
title = "{\"U}ber die {E}ntwickelung reeller {F}unktionen in {R}eihen
mittelst der {M}ethode der kleinsten {Q}uadrate",
journal = "J. Reine Angew. Math.",
volume = "94",
pages = "41--73",
kwds = "grsch"
}
@article{gree:89,
author = "A. Greenbaum",
year = "1989",
title = "Behavior of Slightly Perturbed {Lanczos} and
Conjugate-gradient Recurrences",
journal = "Linear Algebra Appl.",
volume = "113",
pages = "7--63",
kwds = "cg, lanczos"
}
@article{grst:92,
author = "A. Greenbaum and Z. Strako{\v{s}}",
year = "1992",
title = "Predicting the Behavior of Finite Precision {Lanczos} and
Conjugate Gradient Computations",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "13",
pages = "121-137",
kwds = "cg, lanczos"
}
@article{grev:66,
author = "T. E. Greville",
year = "1966",
title = "Note on the Generalized Inverse of a Matrix Product",
journal = "SIAM Review",
volume = "8",
pages = "518--521",
kwds = "ginv"
}
@book{grhi:85,
author = "P. Griffiths and I. D. Hill",
year = "1985",
title = "Applied Statistical Algorithms",
publisher = "Ellis Horwood Ltd.",
address = "Chichester, UK",
kwds = "stat"
}
@article{grle:81,
author = "R. G. Grimes and J. G. Lewis",
year = "1981",
title = "Condition Number Estimation for Sparse Matrices",
journal = "SIAM J. Sci. Statist. Comput.",
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pl-
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po-
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pu-
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qu-
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ra- re-
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%re-
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%ri-
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%ru-
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rut-
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sa-
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title = "Numerical Methods for Large Eigenvalue Problems",
publisher = "Manchester University Press",
address = "Manchester, UK",
kwds = "iter"
}
@article{sala:87,
author = "D. E. Salane",
year = "1987",
title = "A Continuation Approach for Solving Large Residual Least
Squares Problems",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "8",
pages = "655--671",
kwds = "nlsq"
}
@techreport{saun:72,
author = "M. A. Saunders",
year = "1972",
title = "Large-Scale Linear Programming Using The {Cholesky} Factorization",
institution = "Computer Science Department, Stanford University",
address = "CA",
type = "{Tech. Report}",
number = "CS252",
kwds = "chol, upd, downd"
}
@inproceedings{saun:79,
author = "M. A. Saunders",
year = "1979",
title = "Sparse Least Squares by Conjugate Gradients: {A} Comparison
of Preconditioning Methods",
booktitle = "Proceedings of Computer Science and Statistics:
Twelfth Annual Conference on the Interface",
editor = "",
pages = "",
publisher = "",
address = "Waterloo, Canada",
kwds = "iter, precond, cg"
}
@article{saun:95,
author = "M. A. Saunders",
year = "1995",
title = "Solution of Sparse Rectangular Systems Using {LSQR} and {CRAIG}",
journal = "BIT",
volume = "35",
pages = "588--604",
kwds = "iter, cg, lanczos"
}
@article{saut:78,
author = "W. Sautter",
year = "1978",
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volume = "30",
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kwds = "rank, ginv"
}
sc-
@article{scha:85,
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author = "K. Schittkowski",
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journal = "IMA J. Numer. Anal.",
volume = "3",
pages = "11--36",
kwds = "constr"
}
@incollection{schi:85,
author = "K. Schittkowski",
year = "1985",
title = "Solving Constrained Nonlinear Least Squares Problems by a
General Purpose {SOP}-method",
booktitle = "Trends in Mathematical Optimization",
editor = "K.-H. Hoffmann and J. -B. Hiriart-Urruty and
C. Lemar\'echal and J. Zowe",
series = "International Series of Numerical Mathematics",
volume = "84",
publisher = "Birkh{\"a}user-Verlag, Basel, Switzerland",
pages = "49--83",
kwds = "nlsq"
}
@article{scst:79,
author = "K. Schittkowski and J. Stoer",
year = "1979",
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Linear Least Squares Problems Allowing Subsequent
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journal = "Numer. Math.",
volume = "31",
pages = "431--463",
kwds = "qrd, constr, upd, grsch"
}
@techreport{sczi:85,
author = "K. Schittkowski and P. Zimmermann",
year = "1985",
title = "A Factorization Method for Constrained Least Squares Problems with
Data Changes. {Part} {\rm 2}: Numerical Tests, Comparisons, and {ALGOL} Codes",
institution = "Institut f{\"u}r Angewandte Mathematik und Statistik,
Universit{\"a}t W{\"u}rzburg",
address = "Germany",
type = "{Tech. Report}",
number = "Preprint No. 30",
kwds = "qrd, constr, upd, soft, grsch"
}
@article{schm:07,
author = "E. Schmidt",
year = "1907",
title = "{Zur Theorie der linearen und nichtlinearen Integralgleichungen.
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kwds = "grsch"
}
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author = "E. Schmidt",
year = "1908",
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kwds = "grsch"
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@article{scta:86,
author = "R. Schreiber and W.-P. Tang",
year = "1986",
title = "On Systolic Arrays for Updating the {Cholesky} Factorization",
journal = "BIT",
volume = "26",
pages = "451--466",
kwds = "chol,syst,upd,downd"
}
@article{scvl:89,
author = "R. Schreiber and C. F. {Van Loan}",
year = "1989",
title = "A Storage Efficient {WY} Representation for Products of
{Householder} Transformations",
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volume = "10",
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kwds = "block, prll, house"
}
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author = "H. Schwetlick",
year = "1992",
title = "Nonlinear Parameter Estimating: Models, Criteria and Algorithms",
pages = "164--193",
booktitle = "Numerical Analysis 1991: Proceedings of the 14th
Dundee Conference, June 1991",
editor = "D. F. Griffiths and G. A. Watson",
publisher = "Longman Scientific and Technical, Harlow, UK",
series = "Pitman Research Notes in Mathematics 260",
kwds = "nlsq, robust, orthreg"
}
@article{scti:85,
author = "H. Schwetlick and V. Tiller",
year = "1985",
title = "Numerical Methods for Estimating Parameters in Nonlinear Models
with Errors in the Variables",
journal = "Technometrics",
volume = "27",
pages = "17--24",
kwds = "nlsq, tls, orthreg"
}
@article{scti:89,
author = "H. Schwetlick and V. Tiller",
year = "1989",
title = "Nonstandard Scaling Matrices for Trust Region
{G}auss-{N}ewton Methods",
journal = "SIAM J. Sci Statist. Comput.",
volume = "10",
pages = "654--670",
kwds = "nlsq, tls, orthreg"
}
@inproceedings{scol:72,
author = "H. D. Scolnik",
year = "1972",
title = "On the Solution of Non-linear Least Squares Problems",
booktitle = "Proceedings of the {IFIP} Congress 71",
editor = "H. Freeman",
pages = "1258--1265",
publisher = "North-Holland, Amsterdam",
kwds = "varpro, nlsq"
}
@book{sebe:77,
author = "G. A. F. Seber",
year = "1977",
title = "Linear Regression Analysis",
publisher = "John Wiley",
address = "New York",
kwds = "regr, stat, survey"
}
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author = "P. L. Seidel",
year = "1874",
title = "{\"U}ber ein {V}erfahren, die {G}leichungen, auf welche
die {M}ethode der kleinsten {Q}uadrate f{\"u}hrt, sowie lineare
{G}leichungen {\"u}berhaupt, durch successive {A}nn{\"a}herung aufzul{\"o}sen",
journal = "Abh. Bayer Akad. Wiss.",
volume = "11:81",
pages = "",
kwds = "iter"
}
@article{sham:75,
author = "L. F. Shampine",
year = "1975",
title = "Discrete Least Squares Polynomial Fits",
journal = "Comm. ACM",
volume = "18",
pages = "179--180",
kwds = "scale, lud"
}
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author = "A. H. Sherman",
year = "1978",
title = "Algorithm {\rm 533}, {NSPIV}, a {FORTRAN} Subroutine for Sparse
{Gaussian} Elimination with Partial Pivoting",
journal = "ACM Trans. Math. Software",
volume = "4",
pages = "391--398",
kwds = "sparse, lud"
}
@article{sieg:65,
author = "I. H. Siegel",
year = "1965",
title = "Deferment of Computation in the Method of Least Squares",
journal = "Math. Comp.",
volume = "19",
pages = "329--331",
kwds = "augms"
}
sk-
@article{skee:79,
author = "R. D. Skeel",
year = "1979",
title = "Scaling for Numerical Stability in {Gaussian} Elimination",
journal = "J. Assoc. Comput. Mach.",
volume = "26",
pages = "494--526",
kwds = "scale, lud"
}
@article{skee:80,
author = "R. D. Skeel",
year = "1980",
title = "Iterative Refinement Implies Numerical Stability for {Gaussian}
Elimination",
journal = "Math. Comp.",
volume = "35",
pages = "817--832",
kwds = "ir, lud"
}
sl-
@article{slui:69,
author = "A. van der Sluis",
year = "1969",
title = "Condition Numbers and Equilibration of Matrices",
journal = "Numer. Math.",
volume = "14",
pages = "14--23",
kwds = "pert, cond, scale"
}
@article{slui:75,
author = "A. van der Sluis",
year = "1975",
title = "Stability of the Solutions of Linear Least Squares
Problems",
journal = "Numer. Math.",
volume = "23",
pages = "241--254",
kwds = "err, pert"
}
@article{slve:79,
author = "A. van der Sluis and G. Veltkamp",
year = "1979",
title = "Restoring Rank and Consistency by Orthogonal Projection",
journal = "Linear Algebra Appl.",
volume = "28",
pages = "257--278",
kwds = "rank, orth"
}
@incollection{slvo:87,
author = "A. van der Sluis and H. van der Vorst",
year = "1987",
title = "Numerical Solution of Large Sparse Linear Equations and
Least Squares Problems",
booktitle = "Seismic Tomography",
editor = "G. Nolet",
publisher = "Reidel, Dordrecht, the Netherlands",
pages = "49--83",
kwds = "rank, orth"
}
@article{slvo:90,
author = "A. van der Sluis and H. van der Vorst",
year = "1990",
title = "{SIRT-} and {CG-}Type Methods for Iterative Solution of
Sparse Linear Least-Squares Problems",
journal = "Linear Algebra Appl.",
volume = "130",
pages = "257--302",
kwds = "iter, cg"
}
@article{sost:74,
author = "T. S{\"o}derstr{\"o}m and G. W. Stewart",
year = "1974",
title = "On the Numerical Properties of an Iterative Method for
Computing the Moore--Penrose Generalized Inverse",
journal = "SIAM J. Numer. Anal.",
volume = "11",
pages = "61--74",
kwds = "iter, ginv"
}
@phdthesis{sode:93,
author = "I. S{\"o}derquist",
year = "1993",
title = "Computing Parameters in Nonlinear Least Squares Models",
school = "University of Ume{\aa}",
institution = "Department of Computer Science",
address = "Sweden",
type = "{Ph.D.} thesis",
kwds = "nlsq, constr"
}
%st-
@article{spat:82,
author = "H. Sp{\"a}th",
year = "1982",
title = "On Discrete Linear Orthogonal $L_p$ Approximation",
journal = "Z. Angew. Math. Mech.",
volume = "62",
pages = "354--355",
kwds = "nlsq, geom"
}
@article{spat:86,
author = "H. Sp{\"a}th",
year = "1986",
title = "Orthogonal Least Squares Fitting with Linear Manifolds",
journal = "Numer. Math.",
volume = "48",
pages = "441--445",
kwds = "nlsq, geom"
}
@article{spat:90,
author = "H. Sp{\"a}th",
year = "1990",
title = "Modified {Gram-Schmid}t for Solving Linear Least Squares Problems
is Equivalent to {Gaussian} Elimination for the Normal Equations",
journal = "Appl. Math.",
volume = "20",
pages = "587--589",
kwds = "ne, grsch"
}
@book{spat:92,
author = "H. Sp{\"a}th",
year = "1992",
title = "Mathematical Algorithms for Linear Regression",
publisher = "Academic Press",
address = "New York",
kwds = "regr, stat, survey"
}
@article{stew:69,
author = "G. W. Stewart",
year = "1969",
title = "On the Continuity of the Generalized Inverse",
journal = "SIAM J. Appl. Math.",
volume = "17",
pages = "33--45",
kwds = " pert, ginv"
}
@book{stew:73,
author = "G. W. Stewart",
year = "1973",
title = "Introduction to Matrix Computations",
publisher = "Academic Press",
address = "New York",
kwds = " survey"
}
@article{stew:76,
author = "G. W. Stewart",
year = "1976",
title = "The Economical Storage of Plane Rotations",
journal = "Numer. Math.",
volume = "25",
pages = "137--138.",
kwds = "qrd, rot"
}
@article{stew:77,
author = "G. W. Stewart",
year = "1977",
title = "Perturbation Bounds for the {QR} Factorization of a Matrix",
journal = "SIAM J. Numer. Anal.",
volume = "14",
pages = "509--518",
kwds = "err, qrd"
}
@inproceedings{stew:77a,
author = "G. W. Stewart",
year = "1977",
title = "Research Development and {LINPACK}",
booktitle = "Mathematical Software III",
editor = "J. R. Rice",
publisher = "Academic Press, New York",
pages = "1-14",
kwds = "soft, pert, survey"
}
@article{stew:77b,
author = "G. W. Stewart",
year = "1977",
title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear
Least Squares Problems",
journal = "SIAM Review",
volume = "19",
pages = "634-662",
kwds = " pert, ginv, orth"
}
@article{stew:79,
author = "G. W. Stewart",
year = "1979",
title = "The Effects of Rounding Error on an Algorithm for Downdating a
{Cholesky} Factorization",
journal = "J. Inst. Maths. Applic.",
volume = "23",
pages = "203-213",
kwds = " err, downd, chol"
}
@article{stew:79a,
author = "G. W. Stewart",
year = "1979",
title = "A Note on the Perturbation of Singular Values",
journal = "Linear Algebra Appl.",
volume = "28",
pages = "213--216",
kwds = "svd, pert"
}
@article{stew:80,
author = "G. W. Stewart",
year = "1980",
title = "The Efficient Generation of Random Orthogonal Matrices
with an Application to Condition Estimators",
journal = "SIAM J. Numer. Anal.",
volume = "17",
pages = "403--404",
kwds = " rand, qrd, cond, orth"
}
@article{stew:81,
author = "G. W. Stewart",
year = "1981",
title = "On the Implicit Deflation of Nearly Singular Systems of Linear
Equations",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "2",
pages = "136--140",
kwds = "rank,ginv"
}
@article{stew:82,
author = "G. W. Stewart",
year = "1982",
title = "Computing the {CS} Decomposition of a
Partitioned Orthogonal Matrix",
journal = "Numer. Math.",
volume = "40",
pages = "297-306",
kwds = "svd, csd, orth"
}
@inproceedings{stew:83,
author = "G. W. Stewart",
year = "1983",
title = "A Method for Computing the Generalized Singular Value
Decomposition",
pages = "207--220",
booktitle = "Matrix Pencils. Proceedings, Pite Havsbad, 1982",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
publisher = "Springer-Verlag, Berlin",
series = "Lecture Notes in Mathematics",
volume = "973",
kwds = "gsvd"
}
@techreport{stew:83a,
author = "G. W. Stewart",
year = "1983",
title = "A Generalization of the {Eckart-Young} Approximation Theorem",
institution = "Department of Computer Science,
University of Maryland",
address = "College Park, MD",
number = "TR-1325",
kwds = "pert, max, tls"
}
@techreport{stew:83b,
author = "G. W. Stewart",
year = "1983",
title = "A Nonlinear Version of {Gauss's} Minimum Variance Theorem
with Applications to an Errors-in-the-Variables Model",
institution = "Department of Computer Science, University of Maryland",
address = "College Park, MD",
type = "{Tech. Report}",
number = "TR-1263",
kwds = "tls, regr, nlsq, pert"
}
@article{stew:84,
author = "G. W. Stewart",
year = "1984",
title = "Rank Degeneracy",
journal = "SIAM J. Sci. Statist. Comput.",
volume = "5",
pages = "403--413",
kwds = "rank, rrqr"
}
@article{stew:84a,
author = "G. W. Stewart",
year = "1984",
title = "On the Invariance of Perturbed Null Vectors under Column Scaling",
journal = "Numer. Math.",
volume = "44",
pages = "61--65",
kwds = "scale, pert"
}
@article{stew:84b,
author = "G. W. Stewart",
year = "1984",
title = "On the Asymptotic Behavior of Scaled Singular and {QR} Decompositions",
journal = "Math. Comp.",
volume = "43(168)",
pages = "168--489",
kwds = "rank, rrqr"
}
@article{stew:87,
author = "G. W. Stewart",
year = "1987",
title = "Collinearity and Least Squares Regression",
journal = "Statistical Science",
volume = "2",
pages = "68-100",
kwds = "stat, regr, tls, rank"
}
@article{stew:90,
author = "G. W. Stewart",
year = "1990",
title = "On Scaled Projections and Pseudoinverses",
journal = "Linear Algebra Appl.",
volume = "132",
pages = "115--117",
kwds = "wlsq"
}
@inproceedings{stew:90a,
author = "G. W. Stewart",
year = "1990",
title = "Perturbation Theory and Least Squares with Errors in
the Variables",
booktitle = "Contemporary Mathematics 112: Statistical
Analysis of Measurement Error Models and
Applications",
editor = "P. J. Brown and W. A. Fuller",
pages = "171--181",
publisher = "American Mathematical Society, Providence, RI",
kwds = "stat, pert, regr"
}
@techreport{stew:91,
author = "G. W. Stewart",
year = "1991",
title = "On an Algorithm for Refining a Rank-Revealing {URV}
Factorization and a Perturbation Theorem for Singular Values",
institution = "Department of Computer Science, University of Maryland",
address = "College Park, MD",
type = "{Tech. Report}",
number = "UMIACS-TR-91-38, CS-TR-2626",
kwds = "rrqr, pert, svd"
}
@article{stew:92,
author = "G. W. Stewart",
year = "1992",
title = "An Updating Algorithm for Subspace Tracking",
journal = "IEEE Trans. Signal Process.",
volume = "40",
pages = "1535--1541",
kwds = "upd, rrqr"
}
@article{stew:93a,
author = "G. W. Stewart",
year = "1993",
title = "Updating a Rank-Revealing {ULV} Decomposition",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "14",
pages = "494--499",
kwds = "upd, rrqr"
}
@article{stew:93b,
author = "G. W. Stewart",
year = "1993",
title = "On the Perturbation of {LU}, {Cholesky}, and {QR} Factorizations",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "14",
pages = "1141--1145",
kwds = "pert, qrd, chol"
}
@article{stew:93c,
author = "G. W. Stewart",
year = "1993",
title = "On the Early History of the Singular Value Decomposition",
journal = "SIAM Review",
volume = "35",
pages = "551--566",
kwds = "svd, hist"
}
@article{stew:95,
author = "G. W. Stewart",
year = "1995",
title = "On the Stability of Sequential Updates and Downdates",
journal = "IEEE Trans. Signal Process.",
volume = "43",
pages = "1643--1648",
kwds = "downd, stab"
}
@article{stew:97,
author = "G. W. Stewart",
year = "1997",
title = "On the Weighting Method for Least squares Problems with Linear
Equality Constraints",
journal = "BIT.",
volume = "37:4",
pages = "961--967",
kwds = "wlsq, constr"
}
@book{stsu:90,
author = "G. W. Stewart and J.{-G}. Sun",
year = "1990",
title = "Matrix Perturbation Theory",
publisher = "Academic Press",
address = "Boston",
kwds = "pert, survey"
}
@article{stst:98,
author = "M. Stewart and G. W. Stewart",
year = "1998",
title = "On Hyperbolic Triangularization: Stability and Pivoting",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "19:4",
pages = "8471--860",
kwds = "hyp, downd"
}
@article{stie:52,
author = "E. Stiefel",
year = "1952/53",
title = "{Ausgleichung ohne Aufstellung der Gausschen Normalgleichungen}",
journal = "Wiss. Z. Tech. Hochsch. Dresden",
volume = "2",
pages = "441--442",
kwds = "cg, iter"
}
@article{stie:77,
author = "S. M. Stigler",
year = "1977",
title = "An Attack on {Gauss}, Published by {Legendre} in {\rm 1820}",
journal = "Hist. Math.",
volume = "4",
pages = "31--35",
kwds = "hist"
}
@article{stie:81,
author = "S. M. Stigler",
year = "1981",
title = "{Gauss} and the Invention of Least Squares",
journal = "Ann. Statist.",
volume = "9",
pages = "465--474",
kwds = "hist"
}
@article{stie:1887,
author = "T. J. Stieltjes",
year = "1887",
title = "Sur les racines de l'{\'e}quation $x_n=0$",
journal = "Acta. Math.",
volume = "9",
pages = "385--400",
kwds = "iter"
}
@article{stoe:71,
author = "J. Stoer",
year = "1971",
title = "On the Numerical Solution of Constrained Least Squares Problems",
journal = "SIAM J. Numer. Anal.",
volume = "8",
pages = "382--411",
kwds = "constr, upd"
}
@article{stra:91,
author = "Z. Strako{\v{s}}",
year = "1991",
title = "On the Real Convergence of the Conjugate Gradient Method",
journal = "Linear Algebra Appl.",
volume = "154/156",
pages = "535--549",
kwds = "cg, lanczos, iter"
}
@article{stra:74,
author = "C. N. Strand",
year = "1974",
title = "Theory and Methods Related to the Singular Function
Expansion and {Landweber's} Iteration for Integral
Equations of the First Kind",
journal = "SIAM J. Numer. Anal.",
volume = "11",
pages = "798--825",
kwds = "iter, regul"
}
%su-
@techreport{sunc:95,
author = "C. Sun",
year = "1995",
title = "Dealing with Dense Rows in the Solution of Sparse Linear Least
Squares Problems",
institution = "Cornell Theory Center, Cornell University",
address = "Ithaca, NY",
type = "{Tech. Report}",
number = "",
kwds = "sparse, qrd"
}
@article{sunc:96,
author = "C. Sun",
year = "1996",
title = "Parallel Sparse Orthogonal Factorization on
Distributed-Memory Multiprocessors",
journal = "SIAM J. Sci. Comput.",
volume = "17",
pages = "666--685",
kwds = "sparse, qrd, prll"
}
@article{sun:91,
author = "J.-G. Sun",
year = "1991",
title = "Perturbation Bounds for the {Cholesky} and {QR} Factorizations",
journal = "BIT",
volume = "31",
pages = "341--352",
kwds = "pert, chol, qrd"
}
@article{sun:95,
author = "J.-G. Sun",
year = "1995",
title = "On Perturbation Bounds for the {QR} Factorization",
journal = "Linear Algebra Appl.",
volume = "215",
pages = "95--111",
kwds = "pert, qrd"
}
@article{sun:95a,
author = "J.-G. Sun",
year = "1995",
title = "Perturbation Analysis of the {Cholesky} Downdating and
{QR} Updating Problems",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "16",
pages = "760--775",
kwds = "err, pert, upd",
}
@article{sun:96,
author = "J.-G. Sun",
year = "1996",
title = "Optimal Backward Perturbation Bounds for the Linear Least-Squares
Problem With Multiple Right-Hand Sides",
journal = "IMA J. Numer. Anal.",
volume = "16",
pages = "1--11",
kwds = "err, pert",
}
@article{susu:97,
author = "J.-G. Sun and Zheng Sun",
year = "1997",
title = "Optimal Backward Perturbation Bounds for Underdetermined Systems",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "18",
pages = "393--402",
kwds = "err, pert",
}
%sw-
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title = "Analysis of the Total Least Squares Problem
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school = "Katholieke Universiteit Leuven, Belgium",
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author = "X. Wang",
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institution = "Department of Computer Sciences, Lund University",
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author = "P.-{\AA}. Wedin",
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author = "P. A. Yoon",
year = "1996",
title = "Modifying Two-sided Orthogonal Decompositions: Algorithms, Implementations,
and Applications",
school = "The Pennsylvania State University",
address = "Univesrity Park, PA",
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kwds = "rrqr"
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author = "J.-Y. Yuan",
year = "1993",
title = "Iterative Methods for the Generalized Least-Squares Problem",
school = "Instituto de Matem\'atica Pura e Aplicada",
address = " Rio de Janeiro, Brazil",
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kwds = "iter, thesis"
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author = "J.-Y. Yuan",
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title = "The Convergence of the {\rm 2}-block {SAOR} Method for the
Least-Squares Problem ",
journal = "Appl. Numer. Math.",
volume = "11",
pages = "429--441",
kwds = "iter"
}
%za-
@article{zha:91,
author = "H. Zha",
year = "1991",
title = "Implicit {QR} Factorization of a Product of Three Matrices",
journal = "BIT",
volume = "31",
pages = "375--379",
kwds = "qrd, ginv, test"
}
@article{zha:91a,
author = "H. Zha",
year = "1991",
title = "Restricted Singular Value Decomposition of Matrix Triples",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "12",
pages = "172--194",
kwds = "qrd, ginv, test"
}
@article{zha:92,
author = "H. Zha",
year = "1992",
title = "A Two-way Chasing Scheme for Reducing a Symmetric
Arrowhead Matrix to Tridiagonal Form",
journal = "J. Numerical Linear Algebra Appl.",
volume = "1",
pages = "49--57",
kwds = "svd, upd"
}
@article{zha:93,
author = "H. Zha",
year = "1993",
title = "A Componentwise Perturbation Analysis of the {$QR$} Decomposition",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "14",
pages = "1124--1131",
kwds = "qrd, pert"
}
@article{zhzh:98,
author = "H. Zha and Z. Zhang",
year = "1998",
title = "Modifying the Generalized Singular Value Decomposition with Applications
in Direction-of-Arrival Finding",
journal = "BIT",
volume = "38",
pages = "200--216",
kwds = "upd, gsvd"
}
@incollection{zele:62,
author = "M. Zelen",
year = "1962",
title = "Linear Estimation and Related Topics",
booktitle = "Survey of Numerical Analysis",
editor = "J. Todd",
publisher = "McGraw-Hill, New York",
pages = "558--584",
kwds = "stat, hist"
}
@article{ziel:86,
author = "G. Zielke",
year = "1986",
title = "Report on Test Matrices for Generalized Inverses",
journal = "Computing",
volume = "36",
pages = "105--162",
kwds = "ginv, test"
}
@phdthesis{zimm:77,
author = "P. Zimmermann",
year = "1977",
title = "{Ein Algorithmus zur L{\"o}sung linearer Least Squares Probleme
mit unteren und oberen Schranken als Nebenbedingungen}",
school = "Universit{\"a}t W{\"u}rzburg",
address = "Germany",
institution = "Institut f{\"u}r Angewandte Mathematik und Statistik",
type = "{D}iplomarbeit",
kwds = "constr"
}
@article{zlat:82,
author = "Z. Zlatev",
year = "1982",
title = "Comparison of Two Pivotal Strategies in Sparse Plane Rotations",
journal = " Comput. Math. Appl.",
volume = "8",
pages = "119--135",
kwds = "sparse, perm, rot"
}
@book{zlat:92,
author = "Z. Zlatev",
year = "1992",
title = "Computational Methods for General Sparse Matrices",
publisher = "Kluwer Academic Publishers",
address = "Norwell, MA",
kwds = "sparse, perm, rot"
}
@techreport{zlni:79,
author = "Z. Zlatev and H. Nielsen",
year = "1979",
title = "{LLSS{\rm 01}} - A {Fortran} Subroutine for Solving Least Squares
Problems ({User's} Guide)",
institution = "Institute of Numerical Analysis, Technical University of
Denmark",
address = "Lyngby, Denmark",
type = "{Tech. Report}",
number = "79-07",
kwds = "soft, sparse"
}
@article{zlni:88,
author = "Z. Zlatev and H. Nielsen",
year = "1988",
title = "Solving Large and Sparse Linear Least-Squares Problems by
Conjugate Gradient Algorithms",
journal = "Comput. Math. Appl.",
volume = "15",
pages = "185--202",
note = "",
kwds = "cg, precond, sparse, iter"
}
@unpublished{altkeys,
author = "Zzzzz, Rip van",
year = "1991",
title = "Alternate Key Words",
kwds = " approximate methods (appr)
augmented system (augms)
backward perturbation (pert),
banded least squares (band),
blas (blas),
block angular system (basys),
block methods (block),
Chebyshev approximation (cheb),
Cholesky (chol),
condition (cond),
conjugate gradients (cg),
constrained least squares (constr),
control theory (contr),
covariance matrix (covar),
CS decomposition (csd),
downdating (downd),
eigenvalue problem (eigv)
equilibration (scale),
error estimate (err),
fast Fourier transform (fft),
fill-in (fill),
generalized eigenvalue problems (geig),
generalized inverse (ginv),
generalized linear model (glsq),
generalized QR decomposition (gqrd),
geodesy (geod),
geometric elements, fitting (geom),
generalized singular value decomposition (gsvd),
Givens rotation (rot),
graph theory (graph),
Gram-Schmidt (grsch),
history of least squares (hist),
Householder (house),
hyperbolic rotation/Householder (hyp),
ill-posed (illp),
interior point methods (intpoint),
interval analysis (err),
iterative method (iter),
iterative refinement (ir),
Kronecker product (kron),
Lanczos (lanczos),
linear algebra general (la),
LU decomposition (lud),
matrix approximation (max),
nested dissection (nestdis),
nonlinear least squares (nlsq),
normal equations (ne),
null basis (nullsp)
optimization (opt),
ordering for sparsity (perm),
orthogonalization (orth),
orthogonal regression (orthreg),
precision (err),
preconditioning (precond),
pseudo-inverse (ginv),
parallel computation (prll),
perturbation theory (pert),
polynomial approximation (poly),
projection (orth),
QR decomposition (qrd),
quadratic programming (quadpr),
random matrix (rand),
rank degenerate problems (rank),
rank revealing QR factorization (rrqr),
recursive least squares (rls),
regularization (regul),
regression (regr),
robust estimation (rob),
scaling (scale),
signal processing (signal),
singular value decomposition (svd),
software (soft),
sparse (sparse),
spline approximation (spline),
statistics (stat),
structured least squares (struc)
survey paper/book (survey),
systolic (syst),
test matrix (test),
Toeplitz (toep),
total least squares (tls),
underdetermined systems (uds),
updating, downdating (upd, downd),
Vandermonde systems (vand),
variable projection (varpro),
vector processing (prll),
weighted least squares (wlsq)"
}