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| Demmel J. — Applied numerical linear algebra |
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| Предметный указатель |
Arnoldi's algorithm 119 303 305 320 360 388 389
ARPACK 385
Backward error see Backward stability
Backward stability 4
Backward stability, bisection 230 247
Backward stability, Cholesky 76 80 253 263
Backward stability, convergence criterion 164
Backward stability, direct versus iterative methods for  31
Backward stability, eigenvalue problem 123
Backward stability, Gaussian elimination 41
Backward stability, GEPP 41 46 49
Backward stability, Gram — Schmidt 108 134
Backward stability, instability of Cramer's rule 87
Backward stability, Jacobi's method for  242
Backward stability, Jacobi's method for the SVD 263
Backward stability, Jordan canonical form 146
Backward stability, Lanczos algorithm 306 321
Backward stability, linear equations 44 49
Backward stability, normal equations 118
Backward stability, orthogonal transformations 124
Backward stability, polynomial evaluation 16
Backward stability, QR decomposition 118 119 123
Backward stability, secular equation 224
Backward stability, single precision iterative refinement 60
Backward stability, Strassen's method 69 86
Backward stability, substitution 26
Backward stability, SVD 118 119 123 128
Band matrices, linear equations 73 76-79 81 82
Band matrices, symmetric eigenproblem 185
Bauer — Fike theorem 150
Biconjugate gradients 321
Bidiagonal form 131 240 308 357
Bidiagonal form, condition number 87
Bidiagonal form, dqds algorithm 242
Bidiagonal form, LR iteration 242
Bidiagonal form, perturbation theory 207 242 245 246 263
Bidiagonal form, qds algorithm 242
Bidiagonal form, QR iteration 242
Bidiagonal form, reduction 166 240 253
Bidiagonal form, SVD 246 260
Bisection, finding zeros of polynomials 7 30
Bisection, SVD 241 242 247 249
Bisection, symmetric eigenproblem 119 201 210 211 228 236 241 260
BLAS (Basic Linear Algebra Subroutines) 28 64-72 83 86
BLAS (Basic Linear Algebra Subroutines), in Cholesky 76 91
BLAS (Basic Linear Algebra Subroutines), in Hessenberg reduction 165
BLAS (Basic Linear Algebra Subroutines), in Householder transformations 137
BLAS (Basic Linear Algebra Subroutines), in nonsymmetric eigenproblem 184 185
BLAS (Basic Linear Algebra Subroutines), in QR decomposition 121
BLAS (Basic Linear Algebra Subroutines), in sparse Gaussian elimination 84
Block algorithms, Cholesky 64 76 91
Block algorithms, Gaussian elimination 70-72
Block algorithms, Hessenberg reduction 165
Block algorithms, Householder reflection 137
Block algorithms, matrix multiplication 66
Block algorithms, nonsymmetric eigenproblem 184 185
Block algorithms, QR decomposition 121 137
Block algorithms, sparse Gaussian elimination 83 411
Block cyclic reduction 266 328-331 333 357
Block cyclic reduction, model problem 277
Boundary value problem, Dirichlet 267
Boundary value problem, eigenproblem 270
Boundary value problem, L-shaped region 349
Boundary value problem, one-dimensional heat equation 77
Boundary value problem, Poisson's equation 267 325 349
Boundary value problem, Toda lattice 255
Bulge chasing 169 171 213
Canonical form 139 140 145
Canonical form, generalized Schur for real regular pencils 179 185
Canonical form, generalized Schur for regular pencils 178 180 185
Canonical form, generalized Schur for singular pencils 180 185
Canonical form, Jordan 3 19 140 141 144-146 150 175 176 178 180 184 185 188 280
Canonical form, Kronecker iv 179-182 185 187
Canonical form, polynomial 19
Canonical form, real Schur 147 163 184 213
Canonical form, Schur 3 140 146-148 152 158 160 163 175 178 180 184 185 187 188
Canonical form, Weierstrass iv 173 175 176 178 180 181 185 187
CAPSS 84
Cauchy interlace theorem 261 369
Cauchy matrices 85
Cayley transform 264
Cayley — Hamilton theorem 296
CG 306; see Conjugate gradients
cgs see Gram-Schmidt orthogonalization process (classical); Conjugate gradients squared
Characteristic polynomial 140 149 296
Characteristic polynomial, companion matrix 302
Characteristic polynomial, of  173
Characteristic polynomial, of  290
Characteristic polynomial, of a matrix polynomial 182
Characteristic polynomial, secular equation 218 225 231
Chebyshev acceleration 279 294-300 331
Chebyshev acceleration, model problem 277
Chebyshev polynomial 296 314 330 357 358
cholesky 2 74-76 253
Cholesky band 2 77 78 277
Cholesky block algorithm 64 91
Cholesky condition number 88
Cholesky conjugate gradients 308
Cholesky definite pencils 179
Cholesky incomplete (as preconditioner) 319
Cholesky LINPACK 62
Cholesky LR iteration 243 263
Cholesky mass spring system 179
Cholesky model problem 277
Cholesky normal equations 107
Cholesky of  270 357
Cholesky on a Cray YMP 62
Cholesky sparse 80 81 277
Cholesky symmetric eigenproblem 253 263
Cholesky tridiagonal 78 331
CLAPACK 61 86 88
Companion matrix 183 302
Companion matrix, block 183
Computational geometry 139 175 184 187 191
Condition number 2 4 5
Condition number, convergence of iterative methods 285 312 314 317 320 351
Condition number, distance toill-posedness 17 19 23 33 86 152
Condition number, equilibration 61
Condition number, estimation 50
Condition number, infinite 17 148
Condition number, iterative refinement of linear systems 58
Condition number, least squares 101 102 106 108 117 125 126 128 129 134
Condition number, linear equations 32-38 46 50 87 89 105 124 132 146
Condition number, nonsymmetric eigenproblem 32 148-153 189
Condition number, Poisson's equation 269
Condition number, polynomial evaluation 15-17 24
Condition number, polynomial roots 28 29
Condition number, preconditioning 317
Condition number, rank-deficient least squares 101 125 126 128 129
Condition number, relative, for 35 54 60
Condition number, symmetric eigenproblem 197
Conjugate gradients 266 278 301 306-319 351
Conjugate gradients squared 321
Conjugate gradients stabilized 321
Conjugate gradients, convergence 306 312 352
Conjugate gradients, model problem 277
Conjugate gradients, preconditioning 317 351 354
Conjugate transpose 1
Conservation law 255 256
Consistent ordering 293
Controllable subspace 182 187
Convolution 324 326
Courant — Fischer minimax theorem 198 199 201 261
Cray 13 14 2 226
Cray, C90/J90 13 62 82 226
Cray, extended precision 27
Cray, roundoff error 12 25 26 224 226
Cray, square root 26
Cray, T3 series 12 62 82
Cray, YMP 62 64
| DAEs see Differential algebraic equations
DEC, symmetric multiprocessor 62 82
DEC, workstations 10 12 14
Deflation 221
Deflation, during QR iteration 214
Deflation, in secular equation 221 237 262
Diagonal dominance 91 388
Diagonal dominance, convergence of Jacobi and Gauss — Seidel 286-294
Diagonal dominance, weak 289
Differential algebraic equations 175 178 185
Divide-and-conquer 13 195 211 212 217-228 231 236
Divide-and-conquer, SVD 133 241 242
Domain decomposition 266 285 317 319 348-357 361
Dqds algorithm 195 243
Eigenvalue 140
Eigenvalue, generalized nonsymmetric eigenproblem 173
Eigenvalue, generalized nonsymmetric eigenproblem, algorithms 173-184
Eigenvalue, nonsymmetric eigenproblem algorithms 153-173 184
Eigenvalue, nonsymmetric eigenproblem perturbation theory 148-153
Eigenvalue, symmetric eigenproblem algorithms 210-237
Eigenvalue, symmetric eigenproblem perturbation theory 197-210
Eigenvector 140
Eigenvector, generalized nonsymmetric eigenproblem 174
Eigenvector, generalized nonsymmetric eigenproblem, algorithms 173-184
Eigenvector, nonsymmetric eigenproblem algorithms 153-173 184
Eigenvector, of Schur form 148
Eigenvector, symmetric eigenproblem algorithms 210-237
Eigenvector, symmetric eigenproblem perturbation theory 197-210
EISPACK 62
Equilibration 37 61
Equivalence transformation 175
Fast Fourier Transform 266 278 319 321-328 333 348 351 352 357 359-361
Fast Fourier transform, model problem 277
FFT see Fast Fourier transform
Floating point arithmetic 2 5 9 23
Floating point arithmetic,  12 28 231
Floating point arithmetic, complex numbers 11 26
Floating point arithmetic, cost of comparison 50
Floating point arithmetic, cost of division, square root 245
Floating point arithmetic, cost versus memory operations 63
Floating point arithmetic, Cray 13 26 27 226
Floating point arithmetic, exception handling 12 28 231
Floating point arithmetic, extended precision 14 27 45 60 224
Floating point arithmetic, IEEE standard 10 241
Floating point arithmetic, interval arithmetic 14 45
Floating point arithmetic, Lanczos algorithm 377
Floating point arithmetic, machine epsilon, machine precision, macheps 11
Floating point arithmetic, NaN (Not a Number) 12
Floating point arithmetic, normalized numbers 9
Floating point arithmetic, overflow 11
Floating point arithmetic, roundoff error 11
Floating point arithmetic, subnormal numbers 11
Floating point arithmetic, underflow 11
flops 5
Gauss — Seidel 266 278 279 282-283 285-294 357
Gauss — Seidel, in domain decomposition 355
Gauss — Seidel, model problem 277
Gaussian elimination 31 38-44
Gaussian elimination, band matrices 76-79
Gaussian elimination, block algorithm 31 61-73
Gaussian elimination, error bounds 31 44-58
Gaussian elimination, GECP 46 49 55 56 88
Gaussian elimination, GEPP 46 49 55 56 87 88 132
Gaussian elimination, iterative refinement 31 58-61
Gaussian elimination, pivoting 45
Gaussian elimination, sparse matrices 79-83
Gaussian elimination, symmetric matrices 76
Gaussian elimination, symmetric positive definite matrices 74-76
Gershgorin's theorem 79 91 150
Givens rotation 119 121-123
Givens rotation, error analysis 123
Givens rotation, in GMRES 321
Givens rotation, in Jacobi's method 233 251
Givens rotation, in QR decomposition 121 135
Givens rotation, in QR iteration 167 168
gmres 306 320
GMRES, restarted 321
Gram — Schmidt orthogonalization process 107 377
Gram — Schmidt orthogonalization process, Arnoldi's algorithm 304 320
Gram — Schmidt orthogonalization process, classical 107 119 134
Gram — Schmidt orthogonalization process, modified 107 119 134 231
Gram — Schmidt orthogonalization process, QR decomposition 107 119
Gram — Schmidt orthogonalization process, stability 108 118 134
Graph, bipartite 286 291
Graph, directed 288
Graph, strongly connected 289
Guptri (generalized upper triangular form) 186
Hessenberg form 163 184 213 302 360
Hessenberg form, double shift QR iteration 170 172
Hessenberg form, implicit  theorem 167
Hessenberg form, in Arnoldi's algorithm 303 304 388 389
Hessenberg form, in GMRES 320
Hessenberg form, QR iteration 165 167-173 183
Hessenberg form, reduction 164-166 212 303 389
Hessenberg form, single shift QR iteration 168
Hessenberg form, unreduced 166
Hilbert matrix 85
Householder reflection 119-123 135
Householder reflection, block algorithm 133 137 165
Householder reflection, error analysis 123
Householder reflection, in bidiagonal reduction 166 252
Householder reflection, in double shift QR iteration 170
Householder reflection, in Hessenberg reduction 212
Householder reflection, in QR decomposition 119 134 135 157
Householder reflection, in QR decomposition with pivoting 132
Householder reflection, in tridiagonal reduction 213
HP workstations 10
IBM 370 9
IBM RS6000 5 14 27 68 95 133 184 236
IBM SP-2 62 82
IBM workstations 10
Ill-posedness 17 23 33 34 86 148
Implicit theorem 167
Impulse response 178
Incomplete Cholesky 319
Incomplete LU decomposition 319
Inertia 202 208 228 247
Intel 8086/8087 14
Intel paragon 62 73 82
Intel Pentium 14 60
Invariant subspace 145 147 153 154 156-158 189 207
Inverse iteration 155 162
Inverse iteration, SVD 242
Inverse iteration, symmetric eigenproblem 119 211 215 228-232 236 237 241 260 363
Inverse power method see Inverse iteration
Irreducibility 286 288-290
Iterative methods for 265-361
Iterative methods for , convergence rate 281
Iterative methods for , splitting 279
Iterative methods for 363-389
Jacobi's method (for ) 278 279 281-282 285-294 357
Jacobi's method (for ), in domain decomposition 355
Jacobi's method (for ), model problem 277
Jacobi's method (for ) 195 210 212 232-237 260 263
Jacobi's method (for the SVD) 242 249-254 263
Jordan canonical form 3 19 140 141 144-146 150 175 176 178 180 184 185 188 280
Jordan canonical form, instability 146 178
Jordan canonical form, solving differential equations 176
Korteweg-de Vries equation 260
Kronecker canonical form iv 182
Kronecker canonical form, solving differential equations 181
Kronecker product 274 358
Krylov subspace 266 278 300-321 351 354 360 363-389
Lanczos algorithm 119 304-306 308 310 320 360 364-389
Lanczos algorithm, nonsymmetric 321 388
LAPACK 6 61 62 86 87 153
LAPACK++ 61
LAPACK, dlamch 13
LAPACK, sbdsdc 242
LAPACK, sbdsqr 242 243
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