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| Bjoerck A., Dahlquist G. — Numerical mathematics and scientific computation |
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| Предметный указатель |
Iterative method, residual reducing 349
Iterative method, rounding errors in 313—316
Iterative method, stationary 308
Iterative method, symmetrizable 327
Iterative method, terminating 316—317
Iterative methods, preconditioned 362—367
Iterative refinement of solutions 79—82
Iterative refinement, error bound 82
Iteratively reweighted least squares 182—184
Jacobi transformation 230
Jacobi's iterative method 349
Jacobi's method 304
Jacobi's method, classical 231
Jacobi's method, cyclic 231
Jacobi's method, for SVD 232—235
Jacobi's method, nonlinear 384
Jacobi's method, sweep 231
Jacobi's method, threshold 231
Jacobian 443
Jacobian matrix 387
Jordan block 196
Jordan canonical form 202—204
Kalman gain vector 161
Kantorovich Inequality 337
Kogbetliantz's method 232 235
Kronecker product 52 197
Kronecker sum 197 307
Kronecker's canonical form 291
Krylov sequence 196
Krylov subspace 282 338 366
Krylov subspace, best approximation in 352—354
Krylov subspaces 282—284
Lagrange multipliers 96
Lanczos bi-orthogonalization 358—360
Lanczos bi-orthogonalization process 359
Lanczos bidiagonalization 288 see
Lanczos process 285—287 344—345
Landweber's method 348
Least squares fitting of circles 420—423
Least squares fitting of ellipses 420—424
Least squares method, nonlinear 408—420
Least squares method, separable problem 417—418
Least squares problem, damped 145
Least squares, banded problems 100—101 141—142
Least squares, characterization of solution 94—96
Least squares, general problem 113
Least squares, principle of 92
Least squares, problem 91
Least squares, solution 91
Least squares, total 178—180
Least squares, with linear equality constraints 170
Left-preconditioned system 362
Levenberg — Marquardt method 414
Line search 396
Linear inequality constraints by QR 177
Linear model, general univariate 94
Linear model, standard 93
Linear optimization 425—440
Linear optimization, dual problem 438
Linear optimization, duality 438—439
Linear optimization, duality gap 438
Linear optimization, interior point method 439—440
Linear optimization, primal problem 438
Linear optimization, standard form 429
Linear programming see "Linear optimization"
Linear regression 103
Linear system, augmented 96
Linear system, consistent 3
Linear system, homogeneous 3
Linear system, ill-scaling 79
Linear system, over determined 91
Linear system, scaling 76—79
Linear system, scaling rule 79
Linear system, under determined 97
LINPACK algorithm see "Saunders algorithm"
Lipschitz condition 443
Lipschitz constant 386 443
Local minimum, necessary conditions 403
LU factorization 11—15
LU factorization, incomplete 369
LU factorization, theorem 13
Lyapunov's equation 205
M-matrix 371
Matrix approximation 112—113
Matrix pencil 290
Matrix pencil, congruent 290
Matrix pencil, equivalent 290
Matrix pencil, regular 290
Matrix pencil, singular 290
Matrix splitting, Gauss — Seidel 309
Matrix splitting, Jacobi 309
Matrix, adjoint 190
Matrix, arrowhead 59
Matrix, banded 449
Matrix, bidiagonal 23
Matrix, block 42
Matrix, block-tridiagonal 36
Matrix, bordered 45 54
Matrix, circulant 198
Matrix, congruent 222
Matrix, consistently ordered 320
Matrix, defective 196
Matrix, derogatory 203
Matrix, diagonalizable 193
Matrix, diagonally dominant 10 26—28 312
Matrix, eigenvalue 191
Matrix, eigenvector 191
Matrix, elementary divisors 204
Matrix, elementary elimination 15
Matrix, exponential 206
Matrix, functions 206—212
Matrix, graded 251
Matrix, hermitian 190
Matrix, Hessenberg 23
Matrix, idempotent 97
Matrix, indefinite 29
Matrix, inverse 20—21
Matrix, irreducible 193 312
Matrix, non-negative irreducible 212
Matrix, normal 201
Matrix, orthogonal 129
Matrix, permutation 12
Matrix, positive definite 11 28—33
Matrix, property A 320
Matrix, quasi-triangular 200
Matrix, reducible 193
Matrix, scaled diagonally dominant 251
Matrix, semidefinite 29
Matrix, shift 198
Matrix, sparse 54
Matrix, splitting 308
Matrix, Stieltjes 371
Matrix, symmetric 28
Matrix, totally nonnegative 11
Matrix, trace 191
Matrix, trapezoidal form 6
Matrix, tridiagonal 23 449
Matrix, unitary 190
Matrix, unreduced 267
Matrix, variable-band 56
Matrix, well-conditioned 65
Mean 183
Median 183
Method of steepest descent 336—338
MGS see "Modified Gram — Schmidt"
Midrange 183
Minimal polynomial 204
Minimal polynomial of vector 196
Minimax characterization of eigenvalues 221
Minimax characterization of singular values 111
| Minimum distance between matrices 112
Minimum, global 402
Minimum, local 402
Minres 345—346
Moore — Penrose inverse 114
Multilinear 442
Multilinear, symmetric mapping 445
Neumann expansion 377
Newton step 404
Newton — Kantorovich theorem 390
Newton's interpolation formula for matrix functions 214
Newton's method 388—392
Newton's method for least squares 415—416
Newton's method for minimization 404
Newton's method, damped 396
Newton's method, discretized 392
Normal curvature matrix 412
Normal equation, generalized 96
Normal equations 95
Normal equations of second kind 350
Normal equations, accuracy of 102—106
Normal equations, first kind 347
Normal equations, iterative refinement 106
Normal equations, method of 99—102
Normal equations, scaling of 105
Normal equations, second kind 348
Normalized residual 102
Null space (of matrix) 3
Null space method 171
Nullspace, numerical 118
Nullspace, numerical from SVD 118
Numerical differentiation, errors 446
Numerical differentiation, optimal 446
Numerical rank 118
Numerical rank by SVD 117—119
Oettli — Prager error bounds 70
Ordering, Markowitz 60
Ordering, minimum-degree 61
Ordering, reverse Cuthill — McKee 60
Orthogonal distance 419
Orthogonal iteration 244 281
Orthogonal projections 114
Orthogonal projector 95
Orthogonal regression 180—182
Orthogonal, Matrix 129
Orthogonal, projector 97
Orthogonality, loss of 123—126
Partial derivative 443
Partitioning (of matrix) 42
Partitioning, conformal 42
Penrose conditions 114
Permutation matrix 12
Perron — Frobenius theorem 212
Personnel-assignment problem 431
Perturbation bound for linear system 66
Perturbation bound for linear system, component-wise 69
Perturbation of eigenvalue 217—226
Perturbation of eigenvector 217—226
Perturbation of least squares solution 115—117
Perturbation of linear systems 64—69
Perturbation, component-wise 117
Petrov — Galerkin conditions 332
Pivotal elements 4
Pivoting for sparsity 58—61
Pivoting, Bunch — Kaufman 39
Pivoting, complete 10
Pivoting, partial 9
Plane rotations 131
Poisson's equation 306
Polar decomposition 113
Polynomial acceleration 328
Positive semidefinite matrices 34—35
Powell's hybrid method 397
Power method 236—245
Preconditioners 367—376
Preconditioning, Schur complement 373
Principal radius of curvature 412
Principal vector 204
Projection methods 332—352
Projection methods, one-dimensional 334—336
Projection, oblique 98
Projector, oblique 98
Projector, orthogonal 97
Property A 320 373
Pseudoinverse 114
Pseudoinverse, solution 114 115
qmr see "Quasi-Minimal Residual method"
QR algorithm 257—276
QR algorithm for SVD 270—274
QR algorithm, explicit-shift 262
QR algorithm, Hessenberg matrix 262—267
QR algorithm, implicit shift 264
QR algorithm, perfect shifts 269
QR algorithm, rational 269
QR algorithm, Rayleigh quotient shift 263
QR algorithm, symmetric tridiagonal matrix 267—270
QR algorithm, Wilkinson shift 268
QR decomposition, appending a column 164—165
QR decomposition, appending a row 165—166
QR decomposition, deleting a column 163—164
QR decomposition, deleting a row 166—167
QR decomposition, modifying 167
QR decomposition, rank one change 162
QR factorization 122 134
QR factorization for rank deficient problems 144—158
QR factorization of banded matrix 143
QR factorization, backward stability 139
QR factorization, column pivoting 137
QR factorization, complete 152
QR factorization, partial 128
QR factorization, rank revealing 150
Quadratic model 404
Quasi-Minimal Residual method 361
Quasi-Newton, condition 405 415
Quasi-Newton, method 393 405
QZ algorithm 294
Radius of convergence 210
Range (of matrix) 3
Rayleigh quotient 223
Rayleigh quotient, iteration 242—243 293
Rayleigh quotient, matrix 279 286
Rayleigh — Ritz procedure 278—280
Recursive least squares 161—162
Reduction to bidiagonal form 153—155
Reduction to Hessenberg form 248—250
Reduction to standard form 291—293
Reduction to symmetric tridiagonal form 250—252
Regression, orthogonal distance 418—420
Regularization 145—146
Regularization, filter factor 146
Regularization, Tikhonov 173
Relaxation parameter 319 350
Residual vector 224
Residual, normalized 102
Richardson's method 306 348
Right-preconditioned system 362
Ritz values 279
Ritz vectors 279
Rooted trees 447 450
RQI see "Rayleigh quotient iteration"
Saddle point 403
Saunders algorithm 170
Scaled diagonally dominant 251
Schur — Banachiewicz formula 44
Schur, canonical form 199—202
Schur, canonical form, generalized 291
Schur, complement 38 44 373
Schur, vectors 200
Search direction 403
Search directions 335
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