Foreword |
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xi | |
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xiii | |
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1 Biography of G. W. Stewart |
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3 | (8) |
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2 Publications, Honors, and Students |
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11 | (14) |
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3 Introduction to the Commentaries |
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25 | (2) |
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4 Matrix Decompositions: Linpack and Beyond |
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27 | (18) |
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5 Updating and Downdating Matrix Decompositions |
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45 | (14) |
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6 Least Squares, Projections, and Pseudoinverses |
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59 | (12) |
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7 The Eigenproblem and Invariant Subspaces: Perturbation Theory |
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71 | (24) |
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8 The SVD, Eigenproblem, and Invariant Subspaces: Algorithms |
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95 | (10) |
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9 The Generalized Eigenproblem |
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105 | (6) |
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10 Krylov Subspace Methods for the Eigenproblem |
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111 | (10) |
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121 | (16) |
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125 | (8) |
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133 | (4) |
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12 Papers on Matrix Decompositions |
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137 | (126) |
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12.1 GWS-B2 Introduction from Linpack Users Guide |
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139 | (14) |
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12.2 GWS-J17 "Algorithm 432: Solution of the Matrix Equation AX + XB = C" |
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153 | (8) |
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12.3 GWS-J32 "The Economical Storage of Plane Rotations" |
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161 | (3) |
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12.4 GWS-J34 "Perturbation Bounds for the QR Factorization of a Matrix" |
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164 | (1) |
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12.5 GWS-J42 "An Estimate for the Condition Number of a Matrix" |
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164 | (20) |
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12.6 GWS-J49 "Rank Degeneracy" |
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184 | (12) |
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12.7 GWS-J78 "On the Perturbation of LU, Cholesky, and QR Factorizations" |
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196 | (6) |
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12.8 GWS-J89 "On Graded QR Decompositions of Products of Matrices" |
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202 | (12) |
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12.9 GWS-J92 "On the Peturbation of LU and Cholesky Factors" |
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214 | (7) |
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12.10 GWS-J94 "The Triangular Matrices of Gaussain Elimination and Related Decompositions" |
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221 | (11) |
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12.11 GWS-J103 "Four Algorithms for the the (sic) Efficient Computation of Truncated Pivoted QR Approximations to a Sparse Matrix" |
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232 | (12) |
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12.12 GWS-J118 "Algorithm 844: Computing Sparse Reduced-Rank Approximations to Sparse Matrices" |
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244 | (19) |
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13 Papers on Updating and Downdating Matrix Decompositions |
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263 | (77) |
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13.1 GWS-J29 "A Stable Variant of the Secant Method for Solving Nonlinear Equations" |
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264 | (16) |
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13.2 GWS-J31 "Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization" |
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280 | (25) |
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13.3 GWS-J40 "The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization" |
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305 | (12) |
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13.4 GWS-J73 "An Updating Algorithm for Subspace Tracking" |
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317 | (8) |
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13.5 GWS-J77 "Updating a Rank-Revealing ULV Decomposition" |
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325 | (7) |
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13.6 GWS-J87 "On the Stability of Sequential Updates and Downdates" |
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332 | (8) |
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14 Papers on Least Squares, Projections, and Generalized Inverses |
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340 | (51) |
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14.1 GWS-J4 "On the Continuity of the Generalized Inverse" |
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341 | (14) |
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14.2 GWS-J35 "On the Perturbation of Pseudo-inverses, Projections and Linear Least Squares Problems" |
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355 | (30) |
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14.3 GWS-J65 "On Scaled Projections and Pseudoinverses" |
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385 | (6) |
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15 Papers on the Eigenproblem and Invariant Subspaces: Perturbation Theory |
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391 | (130) |
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15.1 GWS-J15 "Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators" |
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392 | (14) |
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15.2 GWS-J19 "Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems" |
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406 | (39) |
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15.3 GWS-J48 "Computable Error Bounds for Aggregated Markov Chains" |
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445 | (16) |
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15.4 GWS-J70 "Two Simple Residual Bounds for the Eigenvalues of a Hermitian Matrix" |
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461 | (5) |
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15.5 GWS-J71 "Eigenvalues of Graded Matrices and the Condition Numbers of a Multiple Eigenvalue" |
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466 | (11) |
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15.6 GWS-J108 "A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations" |
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477 | (6) |
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15.7 GWS-J109 "On the Eigensystems of Graded Matrices" |
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483 | (23) |
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15.8 GWS-J114 "On the Powers of a Matrix with Perturbations" |
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506 | (15) |
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16 Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms |
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521 | (111) |
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16.1 GWS-J5 "Accelerating the Orthogonal Iteration for the Eigenvectors of a Hermitian Matrix" |
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522 | (16) |
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16.2 GWS-J30 "Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices" |
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538 | (15) |
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16.3 GWS-J33 "Algorithm 506: HQR3 and EXCHNG: FORTRAN Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix" |
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553 | (7) |
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16.4 GWS-J37 "An Algorithm for Computing Reducing Subspaces by Block Diagonalization" |
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560 | (35) |
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16.5 GWS-J75 "A Block QR Algorithm and the Singular Value Decomposition" |
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595 | (11) |
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16.6 GWS-J102 "The QLP Approximation to the Singular Value Decomposition" |
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606 | (14) |
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16.7 GWS-J107 "An Analysis of the Rayleigh-Ritz Method for Approximating Eigenspaces" |
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620 | (12) |
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17 Papers on the Generalized Eigenproblem |
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632 | (63) |
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17.1 GWS-J16 "On the Sensitivity of the Eigenvalue Problem Ax = λBx" |
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633 | (19) |
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17.2 GWS-J18 "An Algorithm for Generalized Matrix Eigenvalue Problems" |
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652 | (17) |
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17.3 GWS-J27 "Gershgorin Theory for the Generalized Eigenvalue Problem Ax = lambda;Bx" |
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669 | (8) |
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17.4 GWS-J38 "Perturbation Bounds for the Definite Generalized Eigenvalue Problem" |
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677 | (18) |
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18 Papers on Krylov Subspace Methods for the Eigenproblem |
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695 | |
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18.1 GWS-J111 "A Krylov-Schur Algorithm for Large Eigenproblems" |
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696 | (15) |
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18.2 GWS-J113 "Addendum to `A Krylov-Schur Algorithm for Large Eigenproblems'" |
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711 | (4) |
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18.3 GWS-J110 "Backward Error Bounds for Approximate Krylov Subspaces" |
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715 | (7) |
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18.4 GWS-J112 "Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods" |
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722 | |