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Bai Z. (ed.) — Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide
Bai Z. (ed.) — Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide



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Название: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide

Автор: Bai Z. (ed.)

Аннотация:

This provides a unified overview of theory, algorithms, and practical software for eigenvalue problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: New Edition

Год издания: 2000

Количество страниц: 410

Добавлена в каталог: 24.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
ABLE      199
Accuracy assessment of GHEP      127
Accuracy assessment of GNHEP      277
Accuracy assessment of HEP      105
Accuracy assessment of NHEP      228
Accuracy assessment of SVD      137
Adaptive blocking      202
Arnoldi factorization      167
Arnoldi method with inexact Cayley transform      343
Arnoldi method, basic      161
Arnoldi method, block      185
Arnoldi method, implicitly restarted      166
Arnoldi procedure      161 167
Arnoldi vector      161 167
ARPACK for GHEP      122
ARPACK for HEP      80
ARPACK for NHEP      184
ARPACK for SVD      145
Backward error analysis      10
Backward error analysis of GHEP      129 132
Backward error analysis of GNHEP      278
Backward error analysis of HEP      105
Backward error analysis of NHEP      229
Balancing, accuracy of eigenvalues      155
Balancing, dense matrix      153
Balancing, direct, dense matrix      153
Balancing, direct, sparse matrix      153
Balancing, iterative      154
Bidiagonalization for dense matrices      138
Bidiagonalization for sparse matrices      142
Biorthogonality, full      199
Biorthogonality, loss of      193
Biorthogonality, semi-      199
Bisection method for GHEP      113
Bisection method for HEP      50
Bisection method for SVD      139
BLAS      320
BLAS for structured matrices      323
BLAS, sparse      321
Breakdown of band Lanczos method      207
Breakdown of block Lanczos method      199
Breakdown of complex symmetric Lanczos method      218
Breakdown of Lanczos method      192
Breakdown of symmetric indefinite Lanczos method      255
Cayley transform      340
Cayley transform for QEP      286
Characteristic polynomial      11 15 23
Chordal metric      31 131 278
Companion matrix      27
Companion matrix, block      27 289
Complex symmetric eigenproblem      216
Condition number      8 10
Condition number of eigenvalue, GNHEP      279
Condition number of eigenvalue, NHEP      230
Conditioning of GHEP      16
Conditioning of GNHEP      31 35
Conditioning of HEP      12 26
Conditioning of SVD      20
Congruence transformation      15
Conjugate gradient method, covariant      307
Conjugate gradient method, preconditioned for GHEP      362
Convergence properties of inexact Cayley for GNHEP      343
Convergence properties of inverse iteration for HEP      53
Convergence properties of inverse iteration for NHEP      159
Convergence properties of IRAM      172
Convergence properties of IRLM      71
Convergence properties of Lanczos method for GHEP      121
Convergence properties of Lanczos method for HEP      59
Convergence properties of Lanczos method for NHEP      193
Convergence properties of power method for HEP      52
Convergence properties of power method for NHEP      159
Convergence properties of preconditioned power method      356
Convergence properties of preconditioned subspace iteration      363
Convergence properties of subspace iteration for HEP      54
Convergence properties, Davidson method      343
Covariant conjugate gradient method      307
Covariant differentiation      312
Covariant Newton's method      307
Covariant Stiefel — Grassmann gradient      310
Crawford number      131
CS (cosine/sine) decomposition      22
Davidson method      89
Definite (matrix) pencil      14
Deflating subspace      29
Deflation, band Lanczos method for HEP      81
Deflation, band Lanczos method for NHEP      206
Deflation, block Arnoldi method      188
Deflation, IRAM      175
Deflation, IRLM      73
Deflation, Jacobi — Davidson method for GNHEP      240
Deflation, Jacobi — Davidson method for HEP      95
Deflation, Jacobi — Davidson method for NHEP      224
Deflation, subspace iteration for HEP      55
Deflation, subspace iteration for NHEP      159
Diagonal form of GNHEP      30
Diagonal form of NHEP      24
Differentiation, covariant      312
Direct methods for GHEP      113
Direct methods for GNHEP      234
Direct methods for HEP      49
Direct methods for NHEP      157
Direct methods for SVD      138
Divide-and-conquer method for GHEP      114
Divide-and-conquer method for HEP      50
Divide-and-conquer method for SVD      139
Domain decomposition methods      371
Dqds algorithm      139
Eigendecompositions of GHEP      15
Eigendecompositions of GNHEP      29 35
Eigendecompositions of HEP      12
Eigendecompositions of NHEP      24
Eigenproblems of parameterized matrices      369
Eigenproblems of structured matrices, Hamiltonian      369
Eigenproblems of structured matrices, quaternion      369
Eigenproblems of structured matrices, symplectic      369
Eigenproblems of unitary matrices      369
Eigenproblems, inverse      370
Eigenproblems, modified      370
Eigenproblems, updating      370
Eigenspace      8
Eigenvalue optimization      370
Equivalence transformations      19 29 34
Error bound of eigenvalue, GHEP      129 132
Error bound of eigenvalue, GNHEP      279
Error bound of eigenvalue, HEP      106
Error bound of eigenvalue, NHEP      230
Error bound of eigenvalues, singular pencil      272
Error bound of eigenvector, GHEP      130 132
Error bound of eigenvector, GNHEP      279
Error bound of eigenvector, HEP      106
Error bound of eigenvector, NHEP      230
Galerkin condition      39
Gap      13 106 129 137 271
Generalized      344
Generalized Hermitian eigenproblem (GHEP)      14 109
Generalized non-Hermitian eigenproblem (GNHEP)      28 233
Generalized Schur decomposition      31
Generalized Schur-staircase form      35 266
Golub — Kahan — Lanczos method      142
Gradient, Stiefel — Grassmann      310
Gram — Schmidt process, classical      168
Gram — Schmidt process, modified      92
Gram — Schmidt process, modified with refinement      93
Gram — Schmidt process, two-sided      193 213
GUPTRI      261
Harmonic Ritz value      41 100
Hermitian definite pencil      109 131
Hermitian eigenproblem (HEP)      11 45
Hessenberg matrix      162
Hessenberg reduction      158
High relative accuracy eigensolvers      370
Homotopy continuation      370
Ill-conditioning      9
Ill-conditioning of singular pencil      264
Implicitly restarted Arnoldi method (IRAM)      170
Implicitly restarted Lanczos method (IRLM)      68
Inexact method, Arnoldi method      343
Inexact method, Lanczos method      346
Inexact method, rational Krylov method      348
Invariant subspace      12
Inverse eigenproblems      370
Inverse iteration for GHEP      114
Inverse iteration for HEP      50 52
Inverse iteration for NHEP      159
Inverse iteration for SVD      139
Jacobi method for HEP      51
Jacobi method for SVD      140
Jacobi — Davidson method for GHEP      123
Jacobi — Davidson method for GNHEP      238
Jacobi — Davidson method for HEP      88
Jacobi — Davidson method for NHEP      221
Jacobi — Davidson method for QEP      287
Jacobi — Davidson method, Cayley transform      346
Jordan (canonical) form      25
Jordan structure, nearest      295
Jordan structure, nearest, sg_min example      299
Jordan — Schur form      26
Kronecker (canonical) form      35 262
Krylov subspace      39
Lanczos factorization for HEP      67
Lanczos factorization for NHEP      190
Lanczos method for complex symmetric eigenproblem      216
Lanczos method for GHEP      116
Lanczos method for SVD      142
Lanczos method in GEMV form      70
Lanczos method, band for HEP      80
Lanczos method, band for NHEP      205
Lanczos method, basic for HEP      56
Lanczos method, basic for NHEP      189
Lanczos method, block for NHEP      196
Lanczos method, implicitly restarted      67
Lanczos method, preconditioned      346
Lanczos method, preconditioned for GHEP      359
Lanczos method, symmetric indefinite for GNHEP      249
Lanczos vector      67 190
LAPACK for GHEP      113
LAPACK for GNHEP      234
LAPACK for HEP      49
LAPACK for NHEP      157
LAPACK for SVD      138
Linear least squares problem      147
Linear solver, direct      326
Linear solver, direct for band matrices      328
Linear solver, direct for dense matrices      328
Linear solver, direct for sparse matrices      329
Linear solver, direct for structured matrices      331
Linear solver, iterative      332
Linearization of PEP      289
Linearization of QEP      283
Locking, IRAM      176
Locking, IRLM      74
Locking, subspace iteration      54
Look-ahead technique      192 195 220
Manifolds      309
MATLAB for GHEP      113
MATLAB for GNHEP      234
MATLAB for HEP      49
MATLAB for NHEP      157
MATLAB for SVD      138
Matrix sign function      371
Multigrid methods      371
Multilevel methods      371
Nearest Jordan structure      295
Nearest Jordan structure, by sg_min      295
Nearest Jordan structure, sg_min example      299
Newton's method, covariant      307
Non-Hermitian eigenproblem (NHEP)      23 149
Nonlinear eigenproblem (NLEP)      36 281
Numerical rank      271
Numerical stability      10
Numerical stability assessment of GHEP      127
Numerical stability assessment of GNHEP      277
Numerical stability assessment of HEP      105
Numerical stability assessment of NHEP      228
Numerical stability of IRAM for NHEP      173
Numerical stability of Lanczos method for NHEP      189
Numerical stability of QR algorithm      158
Oblique projection      40
Optimization, sg_min      291
Orthogonal projection      39
Orthogonality constraints      290
Orthogonality of Arnoldi vectors      163 168
Orthogonality, full      58
Orthogonality, local      58
Orthogonality, loss of      58
Orthogonality, selective      58
Parallelism      334-336
Parallelism, inner products      334
Parallelism, matrix-vector products      335
Parallelism, solver      336
Parallelism, vector updates      335
Petrov — Galerkin condition      38 40
Polynomial acceleration      55
Polynomial eigenproblem (PEP)      289
Power method for GHEP      114
Power method for HEP      51
Power method for NHEP      159
Preconditioned      356
Preconditioned eigensolvers      337
Preconditioned Lanczos method      359
Preconditioned power method      356
Preconditioned RQI      361
Preconditioned steepest ascent method      358
Preconditioned subspace iteration      363
Preconditioning, left-      93
Preconditioning, right-      93
Procrustes problem      294
Procrustes problem, by sg_min      294
Procrustes problem, sg_min example      298
Projection method      38
Projection method, approximate problem      39
Projection method, oblique      39
Projection method, orthogonal      39
Projection method, refined      43
Projection process      37
Pseudospectra      369
Purging in IRAM      176
Purging in IRLM      74
QR algorithm for GHEP      113
QR algorithm for HEP      50
QR algorithm for NHEP      157
QR algorithm for SVD      139
Quadratic eigenproblem (QEP)      281
Quadratic Rayleigh quotient      282
Quotient SVD (QSVD)      21 146
QZ algorithm      234
Rational Krylov method      246
Rational Krylov method, inexact      348
Rayleigh quotient      53
Rayleigh quotient iteration (RQI)      53
Rayleigh quotient iteration (RQI) for GHEP      115
Rayleigh quotient iteration (RQI), preconditioned      361
Rayleigh quotient, by sg_min      295
Rayleigh quotient, sg_min example      300
Rayleigh quotient, Stiefel — Grassmann optimization      295
Rayleigh — Ritz procedure      39
Reduced-order modeling      214
Reducing subspace      34
Refined projection method      43
Regular matrix pencil      261
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