|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Stewart G.W., Sun J. — Matrix perturbation theory |
|
|
|
| Предметный указатель |
Norm, vector 1—norm 51 55
Norm, vector norm 49 50
Normal matrix 3 5 171 191 194
Normal matrix, condition number 134
Normal matrix, departure from normality (q.v.) 171
Normal matrix, eigenvectors 19
Normal matrix, field of values 24
Normal matrix, Hoffman Wielandt theorem (q.v.) 189
Normal matrix, matrices similar to a normal matrix 216
Normal matrix, perturbation of eigenvalues 192 195
Normal matrix, residual bound 191
Normal matrix, Schur decomposition 18
Normalizable matrix (see diagonalizable matrix) 189
Null space 2
Oet tli, W. 133
Oettli Prager theorem 130 161
Orthogonal matrix 3 194
Orthogonal matrix, perturbation of eigenvalues 195
Orthonormal basis 8
Ostrowski Eisner theorem 170
Ostrowski, A. 88 177 187
O’Leary, D. P. 112
Paige, C. C. 45 40 99 111 324
Parlett, B. N. 4 178 180 209
Pavel — Parvu, M. 152
Peano, G. 71
Penrose, R 108 110 151
Penrose’s conditions 102 110
Pereyra, V. 152 155 163
Permutation matrix 3 83 85
Permutation vector 83 85
Perturbation of eigenvalues 192 215 217
Picard, E 35
Polar decomposition 36
Positive definite matrix 3 5 27 73 74
Positive definite matrix, condition number 122
Positive definite matrix, norm generated by 53
Positive semi-definite matrix 3 5
Positive semi-definite matrix, square root 20
Powers of a matrix 73
Prager, W. 133
Principal vector 21
Projection (oblique) 11 14 152
Projection (oblique) with respect, to an inner product 111
Projection (oblique), generalized inverse 110
Projection (oblique), spectral projection 114
Projection (orthogonal) 9
Projection (orthogonal) as Hermitian idempotent 10
Projection (orthogonal), acute perturbation 137 140 153
Projection (orthogonal), asymptotic forms and derivatives 154
Projection (orthogonal), canonical angles 43
Projection (orthogonal), complementary 10
Projection (orthogonal), condition number 154
Projection (orthogonal), continuity 153
Projection (orthogonal), generalized inverse 110
Projection (orthogonal), least squares 10
Projection (orthogonal), perturbation of products 141
Projection (orthogonal), perturbation theory 153 154
Projection (orthogonal), pseudo-inverse 100
Projection (orthogonal), reduced form 153
Projection (with respect to a norm) 91
Pseudo-inverse 101 102
Pseudo-inverse, acute perturbations 146 150
Pseudo-inverse, application to least squares 107
Pseudo-inverse, asymptotic forms and derivatives 150—152
Pseudo-inverse, Bjerhannner’s characterization 109
Pseudo-inverse, condition number 146 149 103
Pseudo-inverse, continuity 136 140 146 151
Pseudo-inverse, counterexamples 105
Pseudo-inverse, distance from matrix of lower rank 152
Pseudo-inverse, elementary properties 104
Pseudo-inverse, elliptic 109 111
| Pseudo-inverse, existence and uniqueness 104 110
Pseudo-inverse, expressions for perturbed pseudo-inverse 142
Pseudo-inverse, full rank case 108
Pseudo-inverse, Gauss, C. F. 108
Pseudo-inverse, general results 140 146
Pseudo-inverse, minimality 110
Pseudo-inverse, Moore’s characterization 109
Pseudo-inverse, nonacute perturbations 140
Pseudo-inverse, orthogonal projections 106
Pseudo-inverse, perturbation theory 140—151
Pseudo-inverse, Wedin’s bounds 142 146
Qi, L. 187
QR algorithm 11 18
QR decomposition 6 8 11 30
QR decomposition with pivoting 11
QR decomposition, existence 7
QR decomposition, pseudo-inverse 110
QR decomposition, Pythagorean equality 10
QR decomposition, reduced form 137
QR decomposition, scaled 111
QR decomposition, uniqueness 13
QR decomposition, weighted 111
QR factorization 8 13
QR factorization, generalized singular value decomposition 47
QR factorization, partitioned 13
Quasi — Newton method 134
Rail, L. B. 108
Random perturbation 131 134 163
Rayleigh quotient 185 241
Rayleigh — Ritz approximation 207 209
Rayleigh, Lord (J. W. Strutt) 210
Residual bounds (see Under linear system, eigenvalue, etc.) 128
Riesz, F. 60
Rigal — Caches theorem 128
Rigal, J. L. 134
Right inverse 110
Ritz vectors 210
Ritz, W. 210
Rodman, L. 227
Rohrback, H. 186
Rosenblum, M. 227 228
Rouclie’s theorem 167 176
Rounding error 274
Rounding-error analysis 132 133
Row sum norm (see Norm matrix
Rulie, A. 244
Saunders, M. A. 45 46
Schaffer, J. J. 99
Schmidt — Mirsky theorem 208 210
Schmidt, E. 11 35 209 210
Schnr decomposition 17—20 26 28 171 222
Schnr decomposition of a real matrix 26 29
Schnr decomposition of normal matrix 18
Schnr decomposition, existence 17
Schnr decomposition, uniqueness 26
Schur complement 13
Schur, I. 13 26 71
Schwarz 60
SEP 244
Sep, continuity 23 1 236
Sep, definition 231
Sep, Hermitian matrices 247 258
Sep, properties 245
Sep, relation to separation of eigenvalues 233 247 258
Set operations 2
Sherman Morrison Woodbury, formula 5
Similarity transformation 16
Similarity transformation, ill conditioned 1 7 21
Similarity transformation, unitary 17
Singular subspace 259
Singular subspace, residual bound 260 262 266 267
Singular subspace, Wedin’s  theorems 260 262 267
Singular value 31
|
|
|
| Реклама |
|
|
|
|
|
О проекте