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| Авторизация |
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| Demmel J. — Applied numerical linear algebra |
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| Предметный указатель |
Roundoff error, block cyclic reduction 330
Roundoff error, conjugate gradients (CG) 317
Roundoff error, Cray 13 26
Roundoff error, dot product 25
Roundoff error, Gaussian elimination 25 44 57
Roundoff error, geometric modeling 193
Roundoff error, in logarithm 25
Roundoff error, inverse iteration 231
Roundoff error, iterative refinement 58
Roundoff error, Jacobi's method for  253
Roundoff error, Jacobi's method for the SVD 251
Roundoff error, Jordan canonical form 146
Roundoff error, Lanczos algorithm 305 364 369 377 378 381
Roundoff error, matrix multiplication 25
Roundoff error, orthogonal iteration 157
Roundoff error, orthogonal transformations 101 123
Roundoff error, polynomial evaluation 15
Roundoff error, polynomial root finding 30
Roundoff error, QR iteration 164
Roundoff error, rank-deficient least squares 125 127 128
Roundoff error, rank-revealing QR decomposition 131
Roundoff error, simulating quadruple precision 27
Roundoff error, substitution, forward or back 26
Roundoff error, SVD 241 247
Roundoff error, symmetric eigenproblem 191
Scalapack 61 72
ScaLAPACK, ARPACK 385
ScaLAPACK, PARPRE 319
Schur canonical form 3 140 146-148 152 158 160 163 175 178 180 184 185
Schur canonical form, block diagonalization 188
Schur canonical form, computing eigenvectors 148
Schur canonical form, computing matrix functions 187
Schur canonical form, for real matrices 147 163 184 213
Schur canonical form, generalized for real regular pencils 179 185
Schur canonical form, generalized for regular pencils 178 180 185
Schur canonical form, generalized for singular pencils 180 185
Schur canonical form, solving Sylvester or Lyapunov equations 188
Schur complement 91 351
Secular equation 219
SGI symmetric multiprocessor 62 82 84
Shifting 155
Shifting, convergence failure 173
Shifting, exceptional shift 173
Shifting, Francis shift 172
Shifting, in double shift Hessenberg QR iteration 163 170 172
Shifting, in QR iteration 161 172
Shifting, in single shift Hessenberg QR shifting, iteration 168
Shifting, in tridiagonal QR iteration 213
Shifting, Rayleigh quotient shift 215
Shifting, Wilkinson shift 213
Shifting, zero shift 242
Similarity transformation 141
Similarity transformation, best conditioned 153 187
Simultaneous iteration see Orthogonal iteration
Singular value 109
Singular value decomposition see SVD
Singular value, algorithms 237-254
Singular vector 109
Singular vector, algorithms 237-254
SOR see successive overrelaxation sparse matrices direct
Sparse matrices, iterative methods for  265-361
| Sparse matrices, iterative methods for 363-389
Spectral projection 189
Splitting 279
SSOR see Symmetric successive overrelaxation
Stiffness matrix 143 179 255
Strassen's method 68
Strong connectivity 289
Subspace iteration see Orthogonal iteration
Substitution (forward or backward) 3 38 44 48 86 177 188
Substitution (forward or backward), error analysis 26
Successive overrelaxation 279 283-294 357
Successive overrelaxation, model problem 277
SUN, symmetric multiprocessor 62 82
SUN, workstations 10 14
SVD 105 109-117 134 136 174 195
SVD, algorithms 237-254 260
SVD, backward stability 118 119 128
SVD, reduction to bidiagonal form 166 240
SVD, relative perturbation theory 207-210
SVD, underdetermined least squares 136
Sylvester equation  188 358
Sylvester's inertia theorem 202
Symmetric eigenproblem 195
Symmetric eigenproblem, algorithms 210
Symmetric eigenproblem, bisection 211 260
Symmetric eigenproblem, condition numbers 197 207
Symmetric eigenproblem, Courant — Fischer minimax theorem 199 261
Symmetric eigenproblem, definite pencil 179
Symmetric eigenproblem, divide-and-conquer 13 211 217 260
Symmetric eigenproblem, inverse iteration 211
Symmetric eigenproblem, Jacobi's method 212 232 260
Symmetric eigenproblem, model problem 277
Symmetric eigenproblem, perturbation theory 197
Symmetric eigenproblem, Rayleigh quotient 198
Symmetric eigenproblem, Rayleigh quotient iteration 211 215
Symmetric eigenproblem, relative perturbation theory 207
Symmetric eigenproblem, Sylvester's inertia theorem 202
Symmetric eigenproblem, symmetric successive overrelaxation 279 294-300
Symmetric eigenproblem, tridiagonal QR iteration 211 212
SYMMLQ 320
Templates for 266 279 301
Toda flow 256 260
Toda lattice 255
Toeplitz matrices 85
TRANSPOSE 1
Tridiagonal form 119 166 179 232 236 237 244 247 256 308 330
Tridiagonal form, bisection 228-232
Tridiagonal form, block 293 359
Tridiagonal form, divide-and-conquer 217
Tridiagonal form, in block cyclic reduction 330 331
Tridiagonal form, in boundary value problems 78
Tridiagonal form, inverse iteration 228-232
Tridiagonal form, nonsymmetric 321
Tridiagonal form, QR iteration 211 212
Tridiagonal form, reduction 163 166 197 213 236 253
Tridiagonal form, reduction, using Lanczos 303 304 320 321 366 389
Tridiagonal form, relation to bidiagonal form 240
Unitary matrices 22
Vandermonde matrices 83
Vec( ) 274
Weierstrass canonical form 173 175 176 178 180 181 185 187
Weierstrass canonical form, solving differential equations 176
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