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G.W. Stewart: Selected Works with Commentaries [Hardback]

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  • Formāts: Hardback, 729 pages, height x width: 254x178 mm, weight: 3300 g, XIII, 729 p., 1 Hardback
  • Sērija : Contemporary Mathematicians
  • Izdošanas datums: 02-Aug-2010
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817649670
  • ISBN-13: 9780817649678
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  • Formāts: Hardback, 729 pages, height x width: 254x178 mm, weight: 3300 g, XIII, 729 p., 1 Hardback
  • Sērija : Contemporary Mathematicians
  • Izdošanas datums: 02-Aug-2010
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817649670
  • ISBN-13: 9780817649678
Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. It is widely accepted that Stewart is the successor to James Wilkinson, the first giant in the field, taking up the perturbation theory research that Wilkinson so ably began and using it as a foundation for algorithmic insights. Stewarts results in many areas of computational linear algebra broke new ground and are still widely used in an increasing number of applications. Stewarts papers, widely cited, are characterized by elegance in theorems and algorithms and clear, concise, and beautiful exposition. His six popular textbooks are excellent sources of knowledge and history. Stewart is a member of the National Academy of Engineering and has received numerous additional honors, including the Bauer Prize. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. G.W. Stewart: Selected Works with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics.
Foreword xi
List of Contributors
xiii
Part I G. W. Stewart
1 Biography of G. W. Stewart
3(8)
Iain S. Duff
2 Publications, Honors, and Students
11(14)
Part II Commentaries
3 Introduction to the Commentaries
25(2)
Misha E. Kilmer
Dianne P. O'Leary
4 Matrix Decompositions: Linpack and Beyond
27(18)
Charles F. Van Loan
Misha E. Kilmer
Dianne P. O'Leary
5 Updating and Downdating Matrix Decompositions
45(14)
Lars Elden
Misha E. Kilmer
Dianne P. O'Leary
6 Least Squares, Projections, and Pseudoinverses
59(12)
Misha E. Kilmer
Dianne P. O'Leary
7 The Eigenproblem and Invariant Subspaces: Perturbation Theory
71(24)
Ilse C. F. Ipsen
8 The SVD, Eigenproblem, and Invariant Subspaces: Algorithms
95(10)
James W. Demmel
9 The Generalized Eigenproblem
105(6)
Zhaojun Bai
10 Krylov Subspace Methods for the Eigenproblem
111(10)
Howard C. Elman
Dianne P. O'Leary
11 Other Contributions
121(16)
Misha E. Kilmer
Dianne P. O'Leary
References
125(8)
Index
133(4)
Part III Reprints
12 Papers on Matrix Decompositions
137(126)
12.1 GWS-B2 Introduction from Linpack Users Guide
139(14)
J. J. Dongarra
J. R. Bunch
C. B. Moler
12.2 GWS-J17 "Algorithm 432: Solution of the Matrix Equation AX + XB = C"
153(8)
R. H. Bartels
12.3 GWS-J32 "The Economical Storage of Plane Rotations"
161(3)
12.4 GWS-J34 "Perturbation Bounds for the QR Factorization of a Matrix"
164(1)
12.5 GWS-J42 "An Estimate for the Condition Number of a Matrix"
164(20)
A. K. Cline
C. B. Moler
J. H. Wilkinson
12.6 GWS-J49 "Rank Degeneracy"
184(12)
12.7 GWS-J78 "On the Perturbation of LU, Cholesky, and QR Factorizations"
196(6)
12.8 GWS-J89 "On Graded QR Decompositions of Products of Matrices"
202(12)
12.9 GWS-J92 "On the Peturbation of LU and Cholesky Factors"
214(7)
12.10 GWS-J94 "The Triangular Matrices of Gaussain Elimination and Related Decompositions"
221(11)
12.11 GWS-J103 "Four Algorithms for the the (sic) Efficient Computation of Truncated Pivoted QR Approximations to a Sparse Matrix"
232(12)
12.12 GWS-J118 "Algorithm 844: Computing Sparse Reduced-Rank Approximations to Sparse Matrices"
244(19)
M. W. Berry
S. A. Pulatova
13 Papers on Updating and Downdating Matrix Decompositions
263(77)
13.1 GWS-J29 "A Stable Variant of the Secant Method for Solving Nonlinear Equations"
264(16)
W. B. Gragg
13.2 GWS-J31 "Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization"
280(25)
J. W. Daniel
W. B. Gragg
L. Kaufman
13.3 GWS-J40 "The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization"
305(12)
13.4 GWS-J73 "An Updating Algorithm for Subspace Tracking"
317(8)
13.5 GWS-J77 "Updating a Rank-Revealing ULV Decomposition"
325(7)
13.6 GWS-J87 "On the Stability of Sequential Updates and Downdates"
332(8)
14 Papers on Least Squares, Projections, and Generalized Inverses
340(51)
14.1 GWS-J4 "On the Continuity of the Generalized Inverse"
341(14)
14.2 GWS-J35 "On the Perturbation of Pseudo-inverses, Projections and Linear Least Squares Problems"
355(30)
14.3 GWS-J65 "On Scaled Projections and Pseudoinverses"
385(6)
15 Papers on the Eigenproblem and Invariant Subspaces: Perturbation Theory
391(130)
15.1 GWS-J15 "Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators"
392(14)
15.2 GWS-J19 "Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems"
406(39)
15.3 GWS-J48 "Computable Error Bounds for Aggregated Markov Chains"
445(16)
15.4 GWS-J70 "Two Simple Residual Bounds for the Eigenvalues of a Hermitian Matrix"
461(5)
15.5 GWS-J71 "Eigenvalues of Graded Matrices and the Condition Numbers of a Multiple Eigenvalue"
466(11)
G. Zhang
15.6 GWS-J108 "A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations"
477(6)
15.7 GWS-J109 "On the Eigensystems of Graded Matrices"
483(23)
15.8 GWS-J114 "On the Powers of a Matrix with Perturbations"
506(15)
16 Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms
521(111)
16.1 GWS-J5 "Accelerating the Orthogonal Iteration for the Eigenvectors of a Hermitian Matrix"
522(16)
16.2 GWS-J30 "Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices"
538(15)
16.3 GWS-J33 "Algorithm 506: HQR3 and EXCHNG: FORTRAN Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix"
553(7)
16.4 GWS-J37 "An Algorithm for Computing Reducing Subspaces by Block Diagonalization"
560(35)
C. A. Bavely
16.5 GWS-J75 "A Block QR Algorithm and the Singular Value Decomposition"
595(11)
R. Mathias
16.6 GWS-J102 "The QLP Approximation to the Singular Value Decomposition"
606(14)
16.7 GWS-J107 "An Analysis of the Rayleigh-Ritz Method for Approximating Eigenspaces"
620(12)
Z. Jia
17 Papers on the Generalized Eigenproblem
632(63)
17.1 GWS-J16 "On the Sensitivity of the Eigenvalue Problem Ax = λBx"
633(19)
17.2 GWS-J18 "An Algorithm for Generalized Matrix Eigenvalue Problems"
652(17)
C. B. Moler
17.3 GWS-J27 "Gershgorin Theory for the Generalized Eigenvalue Problem Ax = lambda;Bx"
669(8)
17.4 GWS-J38 "Perturbation Bounds for the Definite Generalized Eigenvalue Problem"
677(18)
18 Papers on Krylov Subspace Methods for the Eigenproblem
695
18.1 GWS-J111 "A Krylov-Schur Algorithm for Large Eigenproblems"
696(15)
18.2 GWS-J113 "Addendum to `A Krylov-Schur Algorithm for Large Eigenproblems'"
711(4)
18.3 GWS-J110 "Backward Error Bounds for Approximate Krylov Subspaces"
715(7)
18.4 GWS-J112 "Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods"
722