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| Авторизация |
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| Saad Y. — Iterative methods for sparse linear systems |
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| Предметный указатель |
Fischer, B. 203 216
Fix, G.J. 72
Flaherty, J.E. 101
Fletcher, R. 222 243
Flexible GMRES see “FGMRES”
Flexible iteration 273
Flux vector 68
FMG 424 429
FOM 159
FOM, algorithm 159
FOM, with restarting 160
Foster, I.T. 375
Fps see “Fast Poisson solvers”
Freund, R.W. 176 203 216 234 243 244
Frobenius norm 8
Frontal methods 65 400
Full matrix methods 481^83
Full multigrid 424 429
Full Orthogonalization Method see “FOM”
Full weighting see “FW”
FW 421 422
Galerkin conditions 131
Galerkin projection 423
Galerkin projection, in multigrid 423
Gallopoulos, E. 216 243
Gastinel's method 146
Gastinel, N. 149 216
Gather operation 362
Gauss — Seidel iteration 103
Gauss — Seidel iteration, backward 105
Gauss — Seidel iteration, for normal equations 247
Gauss — Seidel iteration, for normal equations, in parallel 402
Gauss — Seidel iteration, symmetric 105
Gaussian elimination 65 188 288—292 297 303 305—307 392 393 452
Gaussian elimination, block 453
Gaussian elimination, frontal methods 400
Gaussian elimination, IKJ variant 290
Gaussian elimination, in IOM and DIOM 164
Gaussian elimination, in Lanczos process 189
Gaussian elimination, in skyline format 314
Gaussian elimination, parallel 479
Gaussian elimination, parallelism in 76
Gaussian elimination, reordering in 80
Gaussian elimination, sparse 75
Gautschi, W. 187
GCR 194—196
Generalized Conjugate Residual see “GCR”
Geometric multiplicity 15
George, A. 84 94 101 299 487
Gershgorin discs 117
Gershgorin's theorem 117
Gilbert — Peierls algorithm 317
Gilbert, J.R. 317
Global iteration 321—323 328
Global reduction operations 361
gmres 164—177 196 197 205—207
GMRES, algorithm 165
GMRES, block algorithm 211
GMRES, breakdown 171
GMRES, complex version 184
GMRES, convergence 205
GMRES, flexible variant 268 273—275
GMRES, Householder version 165
GMRES, lucky breakdown 171
GMRES, practical implementation 167
GMRES, relation with FOM 177 181
GMRES, stagnation 172
GMRES, truncated 172
GMRES, via residual smoothing 183
GMRES, with polynomial preconditioning 387
GMRES, with restarting 171
Godunov, S.K. 216
Golub, G.H. 43 278 281 350 351
Goovaerts, D. 467 493
Grade of a vector 152
Gram — Schmidt algorithm 10—11 342
Gram — Schmidt algorithm, block 208
Gram — Schmidt algorithm, cancellations in 156
Gram — Schmidt algorithm, modified 11
Gram — Schmidt algorithm, standard 10
Graph 75
Graph separator 82
Graph, bipartite 87 335
Graph, coloring 87 474
Graph, diameter 299
Graph, directed 75
Graph, edges 75
Graph, Laplacian of a 486
Graph, partitioning 451 483
Graph, partitioning, geometric 484
Graph, partitioning, graph theory techniques 487
Graph, partitioning, spectral techniques 486
Graph, partitioning, type 453
Graph, separator 82
Graph, undirected 75
Graph, vertices 75
Greenbaum, A. 179 375
Grid transfer 414
Griewank, A. 350
Gropp, W.D 359 493
Grote, M. 350
Group independent sets 443
Gutknecht, M.H. 243
Hackbusch, W. 449 493
Halmos, P.R. 16
Hankel matrix 221
Harmonic functions 47
Harwell — Boeing collection 94 96
Hausdorff's convex hull theorem 22
Haws, J.C. 337
Heap-sort, in ILUT 311
heaps 317
Hendrickson, B. 493
Hermitian inner product 5
Hermitian matrices 4 23
Hermitian positive definite 30
Hessenberg matrices 5
Hesteness, M.R. 215
High frequency 413
High frequency modes 407
High modes 413
Hindmarsh, A.C. 216
Hirsch, C. 72
Hockney, R.W. 72
Holder norms 7
Horn, R.A. 23
Householder algorithm 11
Householder orthogonalization in Amoldi's method 156
Householder reflectors 11
Householder, A.S. 149
HPD see “Hermitian positive definite”
Huckle, T. 350
Hypercube 358
Idempotent 9 32
If and only if 3
IFF see “If and only if”
Il'in, V.P. 350
ILQ, factorization 342
ILQ, preconditioning 342
ILU 287—316
ILU(1) 297
ILU(O) 284 287 293—295
ILU(O), algorithm 294
ILU(O), distributed factorization 398
ILU(O), for distributed sparse matrices 397
ILU(O), for red-black ordering 390
ILU, Crout variant 316
ILU, distributed 396
ILU, factorization 287
ILU, factorization, instability in 313 321
| ILU, general algorithm 289
ILU, IKJ version 291
ILU, ILUC 316
ILU, ILUS 314—316
ILU, ILUS, algorithm 316
ILU, modified 305—306
ILU, preconditioner 287
ILU, preconditioner, for Schur complement 479
ILU, reordering 333
ILU, static pattern 292
ILU, with multi-elimination see “ILUM”
ILU, with threshold see “ILUT and ILUTP”
ILU, zero pattern 289
ILUM 394 442
ILUT 306—313
ILUT, algorithm 307
ILUT, analysis 308
ILUT, implementation 310
ILUT, with pivoting see “ILUTP”
ILUTP 312
ILUTP, for normal equations 339
Incomplete factorization 284 287
Incomplete factorization, Gram — Schmidt 342
Incomplete factorization, ILQ 342
Incomplete factorization, QR 342
Incomplete Gram — Schmidt 343
Incomplete LQ see “ILQ”
Incomplete LU see “ILU”
Incomplete orthogonalization algorithm 161
Incomplete orthogonalization method see “K”
Indefinite inner product 220
Independent set orderings 84 442
Independent sets 85 392
Independent sets, maximal 85
Index of an eigenvalue 16
Indirect addressing 75
Induced norm 8
Induced preconditioners 478
Inhomogeneous medium 48
Injection 421
Inner products, B inner product 31
Inner products, indefinite 220
Invariant subspace 10 136
Inverse LU factors 329
IOM 161
IOM, algorithm 162
IOM, direct version 161
Irreducibility 89
Irreducible 26
ISO see “Independent set orderings”
Isometry 7
Iteration matrix 110 111
Jacobi iteration 103
Jacobi iteration, for the normal equations 249
JAD storage format 365
JAD storage format, definition 365
JAD storage format, in level scheduling 372
JAD storage format, matvecs in 366
Jagged diagonal format see “JAD storage format”
Jagged diagonals 365
Jbilou, K. 216
Jea, K.C 196 216
Johnson, C 72
Johnson, C.R. 23
Johnson, O.G. 385
Jordan block 16
Jordan box 16
Jordan canonical form 15
Jordan submatrix 16
Jordan, H. 101
Joukowski mapping 200
Kaczmarz, S. 259
Kamath, C 259
Karp, R.M. 85
Karush, T.I. 375 404
Karypis, G 493
Kernel 9
Kershaw, D.S. 351
Keyes, D.E. 493
Kolotilina, L.Y. 350
Koster, J. 350
Kranoselskii, M.A. 149
Kronsjoe, L. 449
Krylov subspace 152
Krylov subspace, dimension of a 152
Krylov subspace, invariant 153
Krylov subspace, methods 151 217
Krylov subspace, versus multigrid 445
Kumar, V. 375 493
Lanczos algorithm 185 186
Lanczos algorithm, algorithm 186 217
Lanczos algorithm, and orthogonal polynomials 186
Lanczos algorithm, biorthogonalization 217
Lanczos algorithm, breakdown 219
Lanczos algorithm, breakdown, incurable 220
Lanczos algorithm, breakdown, lucky 220
Lanczos algorithm, breakdown, serious 220
Lanczos algorithm, for linear systems 221
Lanczos algorithm, look-ahead version 220
Lanczos algorithm, loss of orthogonality 186
Lanczos algorithm, modified Gram — Schmidt version 186
Lanczos algorithm, nonsymmetric 217
Lanczos algorithm, partial reorthogonalization 186
Lanczos algorithm, practical implementations 220
Lanczos algorithm, selective reorthogonalization 186
Lanczos algorithm, symmetric case 185
Lanczos, C 215 222 243 404
Laplacian see “Laplacian operator”
Laplacian operator 47 60
Laplacian operator, of a graph 486
Least-squares polynomials 383
Least-squares problem 245
Left eigenvector 4
Left versus right preconditioning 272
Leisersen, C.E. 317
Leland, R. 493
LeTallec, P. 493
Leuze, R. 405
Level of fill-in 297
Level scheduling 370—372
Level scheduling, for five-point matrices 370
Level scheduling, for general matrices 370
Level-set orderings 81 487
Lewis, J.G. 375 405
Line relaxation 107
Linear mappings 2
Linear span 9
Linear system 37 103
Linear system, existence of a solution 37
Linear system, right-hand side of a 37
Linear system, singular 37
Linear system, unknown of a 37
Linked lists 93
Liou, K.P. 493
Liu, J.W-H. 94 299 487
Liu, Z.S. 221
Local Schur complement 462
Look-ahead Lanczos algorithm 220
Low frequency modes 407
Lower triangular matrices 4
LQ factorization 342
LQ factorization, algorithm 343
Lucky breakdowns 156
Lusk, E. 359
M-matrix 25 288 338
Manteuffel, T. 198 216 243 351
Marin, J. 350
Mask 348
Matching 335
Mathew, T.P. 493
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