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| Авторизация |
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| Saad Y. — Iterative Methods for Sparse Linear Systems |
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| Предметный указатель |
probing 409
Processing Element (PE) 325
Profile 79
Projection methods 122
Projection methods, additive 136
Projection methods, approximate problem 123
Projection methods, definitions 122
Projection methods, error bounds 129
Projection methods, general 123
Projection methods, matrix representation 124
Projection methods, multiplicative 138
Projection methods, oblique 122 204
Projection methods, one-dimensional 131
Projection methods, optimality 126
Projection methods, orthogonal 122 124
Projection methods, prototype 124
Projection methods, residual 127
Projection methods, theory 126
Projection operator see “Projector”
Projection, orthogonal to 33
Projection, parallel to 33
Projector 10 32—38 101
Projector, existence 34
Projector, matrix representation 35
Projector, oblique 35
Projector, orthogonal 35
Projector, orthogonal, eigenvalues 37
Projector, orthogonal, properties 37
Prolongation operator 101 398
Property A 112
Pseudo-peripheral node 417
qmr 209—213
QMR, algorithm 212
QMR, approximation 212
QR decomposition 11
Quasi-GMRES 168
Quasi-GMRES, algorithm 168
Quasi-minimal residual see “QMR”
Quasi-Schur form 18
Quick-split, in ILUT 291
Quotient graph 72
RANGE 2 9
Range of a projector 33
Rank 10
Rank, full 10
Rayleigh quotient 23 24
Real Schur form 18
Recursive graph bisection 418
Red-black ordering 364
Reduced system 318 387
Reducible 27
Reduction of matrices 15
Reduction operations 332
reflectors 12
Regular splitting 107
Regularization 241
Relaxation methods, block 98
Relaxation methods, convergence 104
reordering 74
Reordering rows, columns 72
Reorthogonalization 11
Residual norm steepest descent 135
Residual projection methods 127
Restarted FOM 153
Restriction operator 101 397
Reverse communication 333
Right versus left preconditioning 255
Right-hand side 38 95
Right-hand side, multiple 199
Row projection methods 231 378
Row projection methods, parallel 378
Row reordering 74
Row sum 285
Saddle-point problems 238
saxpy 131 301 332
SAXPY, parallel 332
SAXPY, sparse 301
Scatter and gather operations 336—337
Schur complement 387
Schur complement and direct solution 387
Schur complement for finite-element partitionings 392
Schur complement for vertex partitionings 389
Schur complement, approaches 406
Schur complement, local 391
Schur complement, methods 407
Schur complement, properties 388
Schur form 17
Schur form, example 18
Schur form, nonuniqueness 19
Schur form, partial 18
Schur form, quasi 18
Schur form, real 18
Schwarz alternating procedure 385 394
Schwarz alternating procedure, additive 401
Schwarz alternating procedure, algorithm 395
Schwarz alternating procedure, multiplicative 394
Search subspace 122
Section of an operator 145
Self preconditioning 301
Self preconditioning, convergence behavior 303
Self-adjoint 7 403
Semisimple 15
Separators 414
| Set decomposition 100
Shared memory computers 326
Similarity transformation 15
Simple eigenvalue 15
Singular matrix 3
Singular values 9
Sites (in graph partitioning) 420
Skew-Hermitian, matrices 4 21 186
Skew-Hermitian, part 31
Skew-symmetric matrices 4
Skyline solvers 79
SOR 97
SOR for SPD matrices 112
SOR, convergence 112
SOR, iteration 95
SOR, multicolor sweep 368
Span of q vectors 9
sparse 59
Sparse Gaussian elimination 70 88
Sparse matrices, adjacency graph 70 71
Sparse matrices, basic operations 86
Sparse matrices, direct methods 88
Sparse matrices, graph representation 70
Sparse matrices, matrix-by-vector operation 87
Sparse matrices, permutation and reordering 72
Sparse matrices, storage 83—86
Sparse matrix-by-vector product 87
Sparse skyline storage format see “SSK”
Sparse triangular system solution 87
Sparse-sparse mode computations 300
Sparsity 68
SPARSKIT 89—91
SPD see “Symmetric positive definite”
Spectral bisection 416
Spectral radius 4
Spectrum of a matrix 3
Splitting 97
Square matrices 3
SSK storage format 295
SSOR 97
Steepest descent 131
Stencil 48
Stereographic projection 415
Stieljes algorithm 174
Stiffness matrix 59 61
Stokes problem 240
Storage format, COO 84
Storage format, CSC 85
Storage format, CSR 85 272
Storage format, ELL 86
Storage format, MSR 85
Storage format, SSK 295
Storage of sparse matrices 83—86
Structured sparse matrix 69
Subdomain 373
subspace 9
Subspace of approximants 122
Subspace of constraints 122
Subspace, direct sum 10
Subspace, orthogonal 10
Subspace, sum 10
Successive over-relaxation see “SOR”
Symbolic factorization 88
Symmetric Gauss — Seidel 97
Symmetric matrices 4
Symmetric positive definite 31 112
Symmetric SOR see “SSOR”
Symmetric squaring 315
Symmetry in preconditioned CG 245
Test problems 88
TFQMR 219
TFQMR, algorithm 224
Topological sorting 346
Trace 4
Transpose-Free QMR see “TFQMR”
Triad operation 339
Triangular systems 344
Triangular systems, distributed 375
Triangular systems, level scheduling 346
Triangular systems, sparse 344
Tridiagonal matrices 5
Unassembled matrix 60
Under-determined 230
Undirected graph 71
Unitary matrices 4
Unstructured sparse matrix 69
Upper triangular matrices 5
Upwind schemes 51
Uzawa’s algorithm 239
Variable preconditioner 25
Vector of unknowns 95
Vector, computers 325
Vector, operations 331
Vector, orthogonality 10
Vector, processors 325
Vector, updates 131 332
Vector, updates, parallel 332
Vertex (in a graph) 71
Wavefronts 346
Weak formulation 56
Weakly diagonally dominant matrix 109
Winget regularization 377
Zarantonello’s lemma 189
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