|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Saad Y. — Numerical Methods for Large Eigenvalue Problems |
|
|
|
| Предметный указатель |
a-posteriori error bounds 76
Addition of matrices 3
Algebraic multiplicity 14
Angle between a vector and a subspace 62 130
Angle between vectors 62
Approximate problem 127 170
ARNINV 263
ARNIT 271
ARNLS 270
Arnoldi — Chebyshev iteration 226
Arnoldi’s method 172 263
Arnoldi’s method as a purification process 226
Arnoldi’s method with implicit deflation 179
Arnoldi’s method with modified Gram — Schmidt 176
Arnoldi’s method, breakdown of 174
Arnoldi’s method, convergence 204—213
Arnoldi’s method, iterative version 179
Arnoldi’s method, practical implementations 176
Banded matrices 6
Bandwidth of a matrix 6
Basis of a subspace 11
Bauer — Fike theorem 77
Best uniform approximation in C 205
Bidiagonal matrices 6
Bifurcation 315
Bifurcation analysis 315
Bifurcation, Hopf 316
Bifurcation, real bifurcation point 315
Bifurcation, turning point 315
Biorthogonal vectors 64 188
Block Arnoldi algorithm 196
Block Arnoldi algorithm, Ruhe’s variant 197
Block diagonal matrices 7
Block Gram — Schmidt 197
Block Krylov Methods 168 195
Block Lanczos 304
Block-tridiagonal matrices 7
Breakdown in the Lanczos algorithm 192—194
Breakdown in the Lanczos algorithm, incurable 193
Breakdown in the Lanczos algorithm, serious 193
Breakdown in the Lanczos algorithm, ‘lucky’ 192
Brusselator model 317
Cancellations 177
Canonical forms of matrices 14—25
Canonical forms of matrices, diagonal 15
Canonical forms of matrices, Jordan 15
Canonical forms of matrices, Schur 23
Canonical forms of matrices, triangular 16
Cauchy — Schwartz inequality 8
Characteristic polynomial 4 170
Characteristic polynomial in Krylov methods 170
Chebsyshev — Subspace iteration 237
Chebyshev bases 243
Chebyshev iteration 220
Chebyshev iteration with Arnodi’s method 226
Chebyshev iteration, algorithm 223
Chebyshev iteration, basic scheme 220
Chebyshev iteration, convergence 224
Chebyshev iteration, convergence ratio 224
Chebyshev iteration, damping coefficients 224
Chebyshev iteration, optimal ellipse in 228
Chebyshev polynomials 141—148
Chebyshev polynomials, asymptotic optimality 148
Chebyshev polynomials, complex 143—144
Chebyshev polynomials, optimality 146
Chebyshev polynomials, real 142—143
Chebyshev polynomials, relation with ellipses 144
Chemical reaction example 50 267
Chemical reactions 316
Condition number 93
Condition number of an eigenvalue 93
Condition number of an eigenvector 96
Condition number of an invariant subspace 100
Configuration interaction method 313
Conjugate gradient method 47
Consistent matrix norms 9
Coordinate storage scheme 40
Courant characterization 32 132
Cramer’s Rule 66
Critical points 206
CSC storage format 42
CSR storage format 42
Damping 305—307
Davidson’s method 272—276 313
Davidson’s method, convergence 275
Defective eigenvalue 15
Deflated Arnoldi — Chebyshev algorithm 236
Deflation techniques 117 235 292
Deflation techniques with several vectors 122
Derogatory 15
Determinant 3
Diagonal form of matrices 16
Diagonal matrices 6
Diagonal storage format 43
Diagonalizable matrices 16
Direct sum of subspaces 11 60
Distances between subspaces 63
Double orthogonalization 177
Double shift approach 261
Dunford integral 67
Dynamical systems 313
Dynamical systems, locally stable solutions 314
Eigenspace 12
Eigenvalue 3
Eigenvalue, averages, analyticity 73
Eigenvalue, branches 74
Eigenvalue, index 17
Eigenvalue, pair 284
Eigenvector 4
Eigenvector, left 5
Eigenvector, right 5
Electrical networks 311
Ellipses for Chebyshev iteration 222
Ellpack — Itpack storage format 43
Enhanced initial vector 227
Equivalent pencils 286
Error bounds 76
Essential convergence 153
Essential singularities 66
Exponential propagation operator 277
Field of values 28
First resolvent equality 67
Frobenius norm 9
Galerkin condition 127
Galerkin process 268
Gap between subspaces 63
Generalized Arnoldi’s method 276
Generalized eigenvalue 283—284
Generalized eigenvalue problem 258 282 300
Generalized eigenvector 17
Geometric multiplicity 15
Gerschgorin discs 103
Gerschgorin’s theorem 102
Grade of a vector 169 226
Gram matrices 244
Gram — Schmidt procedure 12
Haar conditions 205 207
HARWELL library 47
Harwell — Boeing collection 47 52
Hausdorff’s convex hull theorem 28
Hermitian definite matrix pairs 295
Hermitian matrices 5 29
Hessenberg matrices 6
Holder norms 8
Hopf bifurcation 316
Hotelling’s deflation 119
Householder orthogonalization 177
Idempotent 11
Implicit deflation 179
Indefinite inner product 193
| Index of an eigenvalue 17
Indirect addressing 40
Instability, in power systems 312
Invariant subspace 11 128
Inverse iteration 114
Inverse power method 114
Iterative Arnoldi method 179
Iterative Arnoldi method, example 271
Jacobian matrix 314
Jordan block 18
Jordan box 19
Jordan canonical form 17
Jordan curve 67
Jordan submatrix 19
Joukowski mapping 144
Kahan, Jiang, Parlett theorem 86—87
Kahan, Parlett, Jiang error bound 79
Kato — Temple’s theorem 81
Kernel 11
Kernel polynomials 248
Krylov Subspace Methods 168—217
Krylov Subspace Methods, characteristic property 171
Krylov subspaces 168
Lanczos algorithm 183—184 198 296
Lanczos algorithm and orthogonal polynomials 185
Lanczos algorithm for matrix pairs 297
Lanczos algorithm, breakdown 191
Lanczos algorithm, convergence 198—204.
Lanczos algorithm, Hermitian case 183
Lanczos algorithm, incurable breakdown 193
Lanczos algorithm, look-ahead version 192
Lanczos algorithm, loss of orthogonality 185
Lanczos algorithm, modified Gram — Schmidt version 184
Lanczos algorithm, non-Hermitian case 186
Lanczos algorithm, partial reorthogonalization 185
Lanczos algorithm, practical implementation 192
Lanczos algorithm, selective reorthogonalization 185
Lanczos algorithm, serious breakdown in 193
Least squares Arnoldi algorithm 239 251
Least squares polynomials 240
Least squares polynomials, Gram matrices 244
Least squares preconditioning 268
Left eigenvector 5 286
Left subspace 126 138
Leontiev’s model 318
Linear mappings 3
Linear perturbations of a matrix 71
Linear shifts for matrix pairs 162 293
Linear span 11
Linear stability 314
Localization of eigenvalues 101
Locking technique 160
Locking vectors 160
Look-ahead Lanczos algorithm 192—194
Lower triangular matrices 6
Lucky breakdown 192
MA28 package 47
Macro-economics 318
Markov chain models 319
Matrices 3
Matrix exponentials 277
Matrix pair 283
Matrix pencil 260 283
Matrix reduction 14
Mechanical vibrations 305
Min-max problem 221
Min-max theorem 30
Modified Gram — Schmidt 176
Moment matrix 243
Moment matrix in Lanczos procedure 193
Moment matrix in least squares approach 244
MSR storage format 42
Multiple eigenvalue 15
Multiplication of matrices 3
NASTRAN 304
Neuman series expansion 66
Newton’s law of motion 306
Nilpotent matrix 21—22
Nonnegative matrices 5 33
Normal matrices 5 26
Norms of matrices 9
Null space 11 60—61 292
Oblique projection method 138 186
Oblique projector 63 139
Optimal ellipse 228
Optimal polynomial 246
Orthogonal complement 14 60—61
Orthogonal matrix 6
Orthogonal projection methods 127
Orthogonal projector 14 60 129
Orthogonality 12
Orthogonality between vectors 12
Orthogonality of a vector to a subspace 14
Orthogonalization 12
Orthonormal 12
Oscillatory solutions 311
Outer product matrices 6
Partial reorthogonalization 195
Partial Schur decomposition 24 123
Permutation matrices 7
Perron — Frobenius theorem 319 321
Petrov — Galerkin condition 138
Petrov — Galerkin method 126
Polynomial acceleration 220
Polynomial iteration 220
Polynomial preconditioning 267
Positive definite matrix 32
Positive real matrices 47
Positive semi-definite 32
Power method 110 152 162 178
Power method, convergence 112
Power method, example 112
Power systems 312
Preconditioning 163 257 272
Principal vector 17
Projection method 126 170
Projection method for matrix pairs 294
Projection method, Hermitian case 131
Projection method, oblique 126
Projection method, orthogonal 126
Projection operators 129
Projector 11 60
QR decomposition 13
Quadratic eigenvalue problem 282 299
Quantum chemistry 312
Quasi-Schur form 24 124
Random walk example 48
RANGE 11
Rank 11
Rayleigh quotient 28 30
Rayleigh quotient iteration 116
Rayleigh — Ritz procedure 128
Real Chebyshev polynomials 142
Real Schur form 24
Reduced resolvent 95
Reducible 33
Reduction of matrices 14
Regular matrix pair 285
Residual norm 176
Resolvent 66
Resolvent equalities 67
Resolvent operator 66
Resonance phenomena 308
Right eigenvector 286
Right subspace 126 138
Ritz eigenvalues 175
Ritz values 175 187
RQI (Rayleigh Quotient Iteration) 116
Schrodinger’s equation 313
Schur form 23—25
|
|
|
| Реклама |
|
|
|
|
|
О проекте