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| Saad Y. — Iterative methods for sparse linear systems |
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| Предметный указатель |
Reordering, for ILU 333
Reorthogonalization 10
Residual norm steepest descent 142
Residual projection methods 134
Residual smoothing 181 182
Restarted FOM 160
Restriction 421
Restriction operator 109 468
Reverse Cuthill — McKee ordering see “RCM”
Richardson's iteration 114 250 412
Right versus left preconditioning 272
Right-hand side 37 103
Right-hand side, multiple 211
Rivest, R.L. 317
Rivlin, T.J. 201
Rose — Tarjan theorem 298
Roux, J.X. 493
Row projection methods 247 401
Row projection methods, parallel 401
Row reordering 78
Row sum 305
Ruge, A. 449
Ruhe, A. 209
Rutishauser, H. 404
Saddle-point problems 254
Sadok, H. 216 243
Saltz, J. 375
Sameh, A. 259
Saunders, M.A. 189
saxpy 137 324 360
SAXPY, parallel 360
SAXPY, sparse 324
Scatter and gather operations 362—363
Schoenauer, W. 216 243
Schultz, M.H. 319
Schur complement 456
Schur complement, and direct solution 456
Schur complement, approaches 477
Schur complement, for finite element partitionings 460
Schur complement, for model problems 463
Schur complement, for vertex partitionings 458
Schur complement, local 460
Schur complement, methods 477
Schur complement, properties 457
Schur form 16
Schur form, example 17
Schur form, nonuniqueness 18
Schur form, partial 17
Schur form, quasi 17
Schur form, real 17
Schwarz alternating procedure 455 465
Schwarz alternating procedure, additive 472
Schwarz alternating procedure, algorithm 465
Schwarz alternating procedure, multiplicative 465
Schwarz, H.A. 492
Search subspace 129
Section of an operator 153
Self-adjoint 6 473
Self-preconditioning 324
Self-preconditioning, convergence behavior 326
Semisimple 15
Separators 484
Set decomposition 108
Shared memory computers 356
Sherman, A.H. 319
Sidi, A. 244
Similarity transformation 14
Simon, H.D. 350 375 493
Simoncini, V. 216 243
Simple eigenvalue 14
Singular matrix 3
Singular values 9
Sites (in graph partitioning) 488
Skew — Hermitian, matrices 4 20 198
Skew — Hermitian, part 30
Skew-symmetric matrices 4
Skjellum, A. 359
Skyline solvers 84
Smith, B. 493
Smooth modes 407
Smoother 423
Smoothing operator 423
Smoothing property 435
Sonneveld, P. 229 243
SOR 105
SOR, convergence 119
SOR, for SPD matrices 119
SOR, iteration 103
SOR, multicolor sweep 392
Span of q-vectors 9
sparse 63
Sparse Gaussian elimination 75 93
Sparse matrices, adjacency graph 75
Sparse matrices, basic operations 92
Sparse matrices, direct methods 93
Sparse matrices, graph representation 75
Sparse matrices, matrix-by-vector operation 92
Sparse matrices, permutation and reordering 77
Sparse matrices, storage 89—92
Sparse matrix-by-vector product 92
Sparse skyline storage format see “SSK”
Sparse triangular system solution 93
Sparse-sparse mode computations 323
Sparsity 73
SPARSKIT 94—97
SPD see “Symmetric positive definite”
Spectral bisection 486
Spectral radius 3
Spectrum of a matrix 3
Split preconditioning 262
Splitting 105
| Square matrices 2
SSK storage format 314
SSOR 105
Steepest descent 138
Stencil 49
Stereographic projection 485
Stewart, G.W. 43
Stewart, W.J. 449
Stiefel, E.L. 215 380 404
Stieltjes algorithm 187
Stiffness matrix 64 65
Stokes problem 256
Storage format, coordinate 89
Storage format, CSC 90
Storage format, CSR 90 291
Storage format, Ellpack — Itpack 91
Storage format, MSR 90
Storage format, SSK 314
Storage of sparse matrices 89—92
Strang, G. 72
Structural nonsingularity 336
Structured sparse matrix 73
Stueben, K. 449
Subdomain 397
subspace 9
Subspace, direct sum 9
Subspace, of approximants 129
Subspace, of constraints 129
Subspace, orthogonal 10
Subspace, sum 9
Successive overrelaxation see “SOR”
Swartzrauber, P.N. 59
Sweet, R. 72
Symbolic factorization 93
Symmetric Gauss — Seidel 105
Symmetric matrices 4
Symmetric positive definite 30 119
Symmetric SOR see “SSOR”
Symmetric squaring 342
Symmetry in preconditioned CG 262
Szyld, D.B. 281 350
Tang, W.P. 350
Taylor, D.R. 220 221
Teng, S.H. 484 485
Tensor product 411
Tensor sum 411
Test problems 94
TFQMR 234
TFQMR, algorithm 239
Topological sorting 370
Trace 3
Transpose-Free QMR see “TFQMR”
Transversal 335
Triad operation 364
Triangular systems 369
Triangular systems, distributed 399
Triangular systems, level scheduling 370
Triangular systems, sparse 369
Tridiagonal matrices 5
Trottenberg, U. 449
Tuma.M.T. 331 337 350
Unassembled matrix 65
Underdetermined 246
Undirected graph 75
Unitary matrices 4
Unstructured sparse matrix 73
Upper triangular matrices 4
Upwind schemes 52
Uzawa's method 254 255
van der Vorst, H.A. 233 243 280 349 375
Varga, R.S. 43 121 126 128 350 405
Variable preconditioner 273
Vassilevski, P. 280
Vavasis, S.A. 484 485
Vector, computers 355
Vector, of unknowns 103
Vector, operations 360
Vector, orthogonality 10
Vector, processors 355
Vector, updates 137 360
Vector, updates, parallel 360
Vertex (in a graph) 75
Vinsome.R K.W. 216
Voevodin, V.V. 216
Wachspress, E.L. 128
Wagner, C 449
Walker, H.R 156 183 216 228 244
Walter, A. 244
Wang, X. 345 351
Wathens, A.J. 350
Watts, J.W 350
Wave-fronts 370
Weak formulation 61
Weakly diagonally dominant matrix 116
Weiss, R. 182 216 243
Wesseling, P. 243 449
Widlund, O.B. 278 477
Wigton, L.B. 350
Wilders, P. 493
Wilkinson, B. 375
Wilkinson, J.H. 216 220
Winget regularization 401
Wu, C.H. 101
Xu, J. 477 493
Ye, Q. 281
Yeremin, A.Y 350
Young, D.M. 121 123 126 128 196 405
Young, D.P. 350
Zarantonello's lemma 201
Zhou, L. 183 216 228 244
Zlatev.Z. 101 350
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