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| Авторизация |
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| Поиск по указателям |
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| Bai Z. (ed.) — Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide |
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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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