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| Авторизация |
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| Demmel J. — Applied numerical linear algebra |
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| Предметный указатель |
LAPACK, sgebrd 167
LAPACK, sgeequ 61
LAPACK, sgees 185
LAPACK, sgees(x) 153
LAPACK, sgeesx 185
LAPACK, sgeev 185
LAPACK, sgeev(x) 153
LAPACK, sgeevx 185
LAPACK, sgehrd 165
LAPACK, sgelqf 132
LAPACK, sgels 121
LAPACK, sgelss 133
LAPACK, sgeqlf 132
LAPACK, sgeqpf 132 133
LAPACK, sgeqrf 137
LAPACK, sgerfs 61
LAPACK, sgerqf 132
LAPACK, sgesv 88
LAPACK, sgesvx 35 53 54 57 61 88
LAPACK, sgetf2 72 88
LAPACK, sgetrf 72 88
LAPACK, sgges 179 185
LAPACK, sggesx 185
LAPACK, sggev 185
LAPACK, sggevx 185
LAPACK, sgglse 138
LAPACK, slacon 53
LAPACK, slaed3 227
LAPACK, slaed4 222 224
LAPACK, slahqr 164
LAPACK, slamch 13
LAPACK, slatms 90
LAPACK, spotrf 76
LAPACK, sptsv 79
LAPACK, ssbsv 77
LAPACK, sspsv 77
LAPACK, sstebz 231 237
LAPACK, sstein 231
LAPACK, ssteqr 214
LAPACK, ssterf 214
LAPACK, sstev 211
LAPACK, sstevd 211 217
LAPACK, ssyev 211 214
LAPACK, ssyevd 217 236
LAPACK, ssyevx 212
LAPACK, ssygv 179 185
LAPACK, ssysv 76
LAPACK, ssytrd 166
LAPACK, strevc 148
LAPACK, strsen 153
LAPACK, strsna 153
LAPACK90 61
Laplace's equation 265
Least squares 101-138
Least squares, condition number 117-118 125 126 128 134
Least squares, in GMRES 321
Least squares, normal equations 105-107
Least squares, overdetermined 2 101
Least squares, performance 132-133
Least squares, perturbation theory 117-118
Least squares, pseudoinverse 127
Least squares, QR decomposition 105 107-109 114 121
Least squares, rank-deficient 125-132
Least squares, rank-deficient, failure to recognize 132
Least squares, rank-deficient, pseudoinverse 127
Least squares, roundoff error 123-124
Least squares, software 121
Least squares, SVD 105 109-117
Least squares, underdetermined 2 101 136
Least squares, weighted 135
Linear equations, Arnoldi's method 320
Linear equations, band matrices 73 76-79 81 82
Linear equations, block algorithm 61-73
Linear equations, block cyclic reduction 328-331
Linear equations, Cauchy matrices 85
Linear equations, Chebyshev acceleration 279 294-300
Linear equations, Cholesky 74-76 277
Linear equations, condition estimation 50
Linear equations, condition number 32-38
Linear equations, conjugate gradients 307-321
Linear equations, direct methods 31-92
Linear equations, distance to ill-posedness 33
Linear equations, domain decomposition 319 348-357
Linear equations, error bounds 44-58
Linear equations, fast Fourier transform 321-328
Linear equations, FFT see Fast Fourier transform
Linear equations, Gauss — Seidel 279 282-294
Linear equations, Gaussian elimination 38-44
Linear equations, Gaussian elimination, with complete pivoting (GECP) 41 50
Linear equations, Gaussian elimination, with partial pivoting (GEPP) 41 49 87
Linear equations, iterative methods 265-361
Linear equations, iterative refinement 58-61
Linear equations, Jacobi's method (for  ) 279 281-282 285-294
Linear equations, Krylov subspace methods 300-321
Linear equations, LAPACK 88
Linear equations, multigrid 331-348
Linear equations, perturbation theory 32-38
Linear equations, pivoting 44
Linear equations, relative condition number 35-38
Linear equations, relative perturbation theory 35-38
Linear equations, sparse Cholesky 79-83
Linear equations, sparse Gaussian elimination 79-83
Linear equations, sparse matrices 79-83
Linear equations, SSOR see Symmetric successive overrelaxation
Linear equations, successive overrelaxation 279 283-294
Linear equations, symmetric matrices 76
Linear equations, symmetric positive definite 74-76
Linear equations, symmetric successive overrelaxation 279 294-300
Linear equations, Toeplitz matrices 85
Linear equations, Vandermonde matrices 83
LINPACK 62 64
LINPACK, benchmark 73 86
LINPACK, spofa 62
LR iteration 243 263
Lyapunov equation 188
Machine epsilon, machine precision, macheps 11
Mass matrix 143 179 255
Mass-spring system 142 174 179 182 183 196 209 254
MATLAB 6 57
Matlab, bisect.m 30
Matlab, clown 114
Matlab, cond 53
MATLAB, eig 179 185 211
Matlab, eigscat.m 150 189
MATLAB, fft 328
Matlab, hess 165
Matlab, homework 28 30 91 134 138 189-191 358-360
Matlab, iterative methods for 266 301
Matlab, Jacobi's method for 282 358
Matlab, Lanczos method for  369 377 384
Matlab, least squares 121 129
Matlab, massspring.m 144 197
Matlab, multigrid 337 360
Matlab, notation 1 41 42 91 92 251 327
Matlab, pinv 117
Matlab, pivot.m 50 55 56 61
Matlab, Poisson's equation 275 358 359
Matlab, polyfit 102
Matlab, polyplot.m 29
Matlab, qrplt.m 161 190
Matlab, QRStability.m 134
Matlab, RankDeficient.m 129
Matlab, RayleighContour.m 201
MATLAB, rcond 53
MATLAB, roots 183
Matlab, schur 185
Matlab, sparse matrices 82
Matlab, speig 388
Matrix pencils 173
Matrix pencils, regular 173
| Matrix pencils, singular 173
Memory hierarchy 63
MGS see Gram-Schmidt orthogonalization process modified
Minimum residual algorithm 320
Minres see Minimum residual algorithm
Model problem 265-276 285-286 300 314 319 324 325 328 331 348 360 361
Model problem, diagonal dominance 288 290
Model problem, irreducibility 290
Model problem, red-black ordering 291
Model problem, strong connectivity 289
Model problem, summary of methods 277-279
Model problem, symmetric positive definite 291
Moore — Penrose pseudoinverse see Pseudoinverse
Multigrid 331-348 357 360
Multigrid, model problem 277
NETLIB 86
Newton's method 58 219 221 231 300
Nonsymmetric eigenproblem 139
Nonsymmetric eigenproblem, algorithms 153-173
Nonsymmetric eigenproblem, condition number 148
Nonsymmetric eigenproblem, eigenvalue 140
Nonsymmetric eigenproblem, eigenvector 140
Nonsymmetric eigenproblem, equivalence transformation 175
Nonsymmetric eigenproblem, generalized 173-184
Nonsymmetric eigenproblem, generalized, algorithms 184
Nonsymmetric eigenproblem, ill-posedness 148
Nonsymmetric eigenproblem, invariant subspace 145
Nonsymmetric eigenproblem, inverse iteration 155
Nonsymmetric eigenproblem, inverse power method see Inverse iteration
Nonsymmetric eigenproblem, matrix pencils 173
Nonsymmetric eigenproblem, nonlinear 182
Nonsymmetric eigenproblem, orthogonal iteration 156
Nonsymmetric eigenproblem, perturbation theory 148
Nonsymmetric eigenproblem, power method 154
Nonsymmetric eigenproblem, QR iteration 160
Nonsymmetric eigenproblem, regular pencil 173
Nonsymmetric eigenproblem, Schur canonical form 146
Nonsymmetric eigenproblem, similarity transformation 141
Nonsymmetric eigenproblem, simultaneous iteration see Orthogonal iteration
Nonsymmetric eigenproblem, singular pencil 173
Nonsymmetric eigenproblem, software 153
Nonsymmetric eigenproblem, subspace iteration see Orthogonal iteration
Nonsymmetric eigenproblem, Weierstrass canonical form 175
Normal equations 105 106 118 135 136 320
Normal equations, backward stability 118
Norms 19
Notation 1
Null space 111
ODEs see Ordinary differential equations
Ordinary differential equations 175 177 184 185
Ordinary differential equations, impulse response 178
Ordinary differential equations, overdetermined 181
Ordinary differential equations, underdetermined 181
Ordinary differential equations, with algebraic constraints 178
Orthogonal iteration 156
orthogonal matrices 22 74 118 126 131 160
Orthogonal matrices, backward stability 124
Orthogonal matrices, error analysis 123
Orthogonal matrices, Givens rotation 119
Orthogonal matrices, Householder reflection 119
Orthogonal matrices, implicit  theorem 168
Orthogonal matrices, in bidiagonal reduction 167
Orthogonal matrices, in definite pencils 179
Orthogonal matrices, in generalized real Schur form 179
Orthogonal matrices, in Hessenberg reduction 164
Orthogonal matrices, in orthogonal iteration 156
Orthogonal matrices, in Schur form 147
Orthogonal matrices, in symmetric QR iteration 213
Orthogonal matrices, in Toda flow 256
Orthogonal matrices, Jacobi rotations 232
PARPRE 319
PCS 10
Pencils see Matrix pencils
Perfect shuffle 240 263
Perturbation theory 2 4 7 17
Perturbation theory, generalized nonsymmetric eigenproblem 180
Perturbation theory, least squares 101 117 125
Perturbation theory, linear equations 31 32 44 49
Perturbation theory, nonsymmetric eigenproblem 79 139 141 148 180 187 189
Perturbation theory, polynomial roots 28
Perturbation theory, rank-deficient least squares 125
Perturbation theory, relative, for 32 35-38 60
Perturbation theory, relative, for 195 198 207-210 212 242 245-247 249 260 263
Perturbation theory, relative, for SVD 207-210 246-251
Perturbation theory, singular pencils 180
Perturbation theory, symmetric eigenproblem 195 197 207 261 263 367
Pivoting 41
Pivoting, average pivot growth 86
Pivoting, band matrices 77
Pivoting, by column in QR decomposition 130
Pivoting, Cholesky 76
Pivoting, Gaussian elimination with complete pivoting (GECP) 49
Pivoting, Gaussian elimination with partial pivoting (GEPP) 49 132
Pivoting, growth factor 49 59
Poisson's equation 266-279
Poisson's equation, in one dimension 265 267-270
Poisson's equation, in two dimensions 270-279
Polynomial, characteristic see Characteristic polynomial
Polynomial, convolution 326
Polynomial, evaluation 34 83
Polynomial, evaluation, at roots of unity 326
Polynomial, evaluation, backward stability 16
Polynomial, evaluation, condition number 15 16 24
Polynomial, evaluation, roundoff error 15 46
Polynomial, evaluation, with Horner's rule 7 15
Polynomial, fitting 101 138
Polynomial, interpolation 83
Polynomial, interpolation, at roots of unity 326
Polynomial, multiplication 326
Polynomial, zero finding, bisection 7
Polynomial, zero finding, computational geometry 191
Polynomial, zero finding, condition number 28
Power method 154
Preconditioning 317 352-356 388
Projection 189
Pseudoinverse 117 127 136
Pseudospectrum 190
Qds algorithm 243
qmr see Quasi-minimum residuals
QR algorithm see QR iteration
QR decomposition 105 107 131 147
QR decomposition, backward stability 118 119
QR decomposition, block algorithm 137
QR decomposition, column pivoting 130
QR decomposition, in orthogonal iteration 157
QR decomposition, in QR flow 258
QR decomposition, in QR iteration 163 170
QR decomposition, rank-revealing 132 134
QR decomposition, underdetermined least squares 136
QR iteration 160 190 210
QR iteration, backward stability 119
QR iteration, bidiagonal 242
QR iteration, convergence failure 173
QR iteration, Hessenberg 163 165 184 213
QR iteration, implicit shifts 167-173
QR iteration, tridiagonal 211 212 236
QR iteration, tridiagonal, convergence 214
QRD see QR decomposition
Quasi-minimum residuals 321
Quasi-triangular matrix 147
Range space 111
Rayleigh quotient 198 205
Rayleigh quotient, iteration 211 215 262 364
Rayleigh — Ritz method 205 261 364
Red-black ordering 283 291
Relative perturbation theory for 35-38
Relative perturbation theory for 207-210
Relative perturbation theory for SVD 207-210 246-249
Roundoff error 2 4 5 10 11 301
Roundoff error, bisection 30 230
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