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| Авторизация |
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| Saad Y. — Iterative methods for sparse linear systems |
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| Предметный указатель |
A-norm 31 133 204
Adams, L.M. 101 404
Additive projection procedure 143
ADI 124
ADI, Peaceman — Rachford algorithm 124
Adjacency graph 75
Adjacency graph, of PDE matrices 76
Adjoint of a matrix 6
AINV 331
Algebraic multigrid 437—445
Algebraic multigrid, coarsening 437
Algebraic multiplicity 14
Aliga, J.I. 243
Allen, M.C 375
Alternating Direction Implicit see “ADI”
AMG see “Algebraic multigrid”
Amoldi's method 153—164
Amoldi's method, basic algorithm 154
Amoldi's method, breakdown of 155
Amoldi's method, for linear systems 159
Amoldi's method, lucky breakdown 156
Amoldi's method, practical implementation 156
Amoldi's method, with Householder orthogonalization 156
Amoldi's method, with modified Gram — Schmidt 156
Anderson, E. 375
Angle between a vector and a subspace 137
Anisotropic medium 48
Approximate inverse see “AINV”
Approximate inverse preconditioners 320
Approximate inverse preconditioners, column-oriented 323
Approximate inverse preconditioners, for improving a preconditioner 331
Approximate inverse preconditioners, global iteration 321
Approximate inverse techniques 399
Arnoldi, W.E. 153
Arrow — Hurwicz's algorithm 256
Assembled matrix 65
Assembly process 64
Axelsson, O. 72 216 280 349 350
Bakhvalov, N.S. 449
Banded matrices 5
Bandwidth, of a bus 356
Bandwidth, of a matrix 5
Bank, R. 449
Barker, V.A. 72 350
Barth, T.J. 243
Basis of a subspace 9
BCG 222—226
BCG, algorithm 223
BCG, transpose-free variants 228—240
BCR see “Block cyclic reduction”
Benantar, M. 101
Benzi, M. 331 337 350
BFS see “Breadth first search”
BICGSTAB 231
Biconjugate Gradient see “BCG”
Bidiagonal matrices 5
Bilinear form 61
binary search trees 317
Biorthogonal bases 34
Biorthogonal vectors 34 218
Biorthogonalization 217
Bipartite graph 87 119 335
Bipartite matching 335
Bipartite transversal 335
Birkhoff, G 126
Bjoerk, A. 259
Bjorstad, P. 492
Block Arnoldi, algorithm 208
Block Arnoldi, Ruhe's variant 209
Block cyclic reduction 57
Block cyclic reduction, Buneman's variant 58
Block diagonal matrices 5
Block FOM 210—211
Block Gaussian elimination 453—457
Block Gaussian elimination, algorithm 456
Block GMRES 210—212
Block GMRES, multiple right-hand sides 211
Block Gram — Schmidt 208
Block independent sets 443
Block Jacobi 110
Block Jacobi, as a preconditioner 378
Block Krylov subspace methods 152 208—212
Block preconditioners 337
Block relaxation 106
Block tridiagonal matrices 5 337
Block tridiagonal matrices, preconditioning 337
Bodewig, E. 349
Boley, D.L. 243
Bollhefer, M 350
Bottleneck transversal 336
boundary conditions 46 47
Boundary conditions, Dirichlet 47
Boundary conditions, mixed 47
Boundary conditions, Neumann 47
Brakhage, H. 449
Brakkee, W. 493
Bramble, J.H. 493
Bramley, R. 259
Brandt, A. 449
BREADTH FIRST SEARCH 81
Brezinski, C 243 244
Brinkkemper, S. 350
Brown, P.N. 178 181 216 228
Buleev, N.I. 350
Buneman's algorithm 58
Buneman, O. 58
Cache memory 357
Canonical form 14
Canonical form, Jordan 15
Canonical form, Schur 16
Cauchy — Schwarz inequality 6 7
Cayley — Hamilton theorem 152
Cell-centered scheme 69
Cell-vertex scheme 69
Centered difference approximation 49
Centered difference formula 49
Centerpoint 485
Cesari, L. 349 404
CG algorithm see “Conjugate gradient algorithm”
CG for normal equations 252 253
CGNE 253
CGNE, algorithm 254
CGNE, optimality 254
CGNR 252
CGNR, algorithm 252
CGNR, optimality 252
cgs 229—231
CGS, algorithm 231
CGW algorithm 278
Chan, T.R 243 467 480 493
Characteristic polynomial 3
Chebyshev acceleration 382
Chebyshev polynomials 199—204 206 381—388
Chebyshev polynomials, and ellipses 200
Chebyshev polynomials, complex 200 216
Chebyshev polynomials, for preconditioning 381
Chebyshev polynomials, optimality 201—203
Chebyshev polynomials, real 199
Cheney, C.C 200
Chow, E. 316 350
Ciarlet, P.G. 72
Cimmino's method 249
Cimmino, G. 259
Circuit switching 357
Coarse-grain 378
Coarse-grid correction 425
Coarsening 437 442
Coefficient matrix 103
Coloring vertices 87
Column reordering 78
| Complex GMRES 184
Compressed Sparse Column storage see “CSC”
Compressed Sparse Row storage see “CSR”
Concus, Golub, and Widlund algorithm see “CGW algorithm”
Concus, P. 278 350
Condition number 38
Condition number, for normal equations systems 246
Condition numbers and CG 192
Conjugate gradient algorithm 187—194
Conjugate gradient algorithm, algorithm 190
Conjugate gradient algorithm, alternative formulations 191
Conjugate gradient algorithm, convergence 203 204
Conjugate gradient algorithm, derivation 187 190
Conjugate gradient algorithm, eigenvalue estimates 192
Conjugate gradient algorithm, for the normal equations 251
Conjugate gradient algorithm, preconditioned 262
Conjugate gradient squared see “CGS”
Conjugate Residual algorithm 194
Consistent matrix norms 8
Consistent orderings 119—123
Control volume 68
Convection diffusion equation 48
Convergence, factor 113
Convergence, factor, general 113
Convergence, factor, specific 113
Convergence, of GMRES 205
Convergence, of relaxation methods 112
Convergence, of Schwarz procedures 473
Convergence, of the minimal residual method 141
Convergence, rate 113
Coordinate storage format 89
Cormen.T.H. 317
Cosgrove, J.D.R 350
Courant characterization 25
Craig's method 254
CSC storage format 90
CSC storage format, matvecs in 362
CSR storage format 90 291
CSR storage format, matvecs in 362
Cullum, J. 179
Cuthill — McKee ordering 81
Cuthill — McKee ordering, queue implementation 82
Dahlquist, G. 449
Data coherence 357
Data-parallel 355
Datta, B.N. 43
Davis, T.A. 405
Defective eigenvalue 15
Delong, M.A. 405
Demmel, J. 43
Derogatory 15
Determinant 3
Deuflhard, P. 244
Diagonal storage format 91 364
Diagonal storage format, matvecs in 364
Diagonal, compensation 305
Diagonal, dominance 116 117
Diagonal, form of matrices 15
Diagonal, matrices 4
Diagonalizable matrix 15
Diagonally dominant matrix 117
Diagonally structured matrices 91
Diameter of a graph 299 487
Diameter of a triangle 62
Diaz, J.C 350
Difference equation 464
DIOM 161—164 188
DIOM, algorithm 163
Direct IOM see “DIOM”
Direct sum of subspaces 9 32
Directed graph 75
Dirichlet boundary conditions 46 47
Distributed, computing 355
Distributed, ILU 396
Distributed, memory 357
Distributed, sparse matrices 366 396
Divergence of a vector 47
Divergence operator 47
Domain decomposition, and direct solution 456
Domain decomposition, convergence 473
Domain decomposition, full matrix methods 481
Domain decomposition, induced preconditioners 478
Domain decomposition, Schur complement approaches 477
Domain decomposition, Schwarz alternating procedure 465
Domain sweep 467
Double orthogonalization 156
Double-striping 488
DQGMRES 172—177 181 276
DQGMRES, algorithm 174
Dryja, M. 477
Duff, I.S. 96 101 350 405
EBE preconditioner 399
EBE regularization 401
Edge cuts 486
Edge in a graph 75
Eigenspace 10
Eigenvalues 2
Eigenvalues, definition 3
Eigenvalues, from CG iteration 192
Eigenvalues, index 16
Eigenvalues, of an orthogonal projector 36
Eigenvector 3
Eigenvector, left 4
Eigenvector, right 4
Eisenstat's implementation 266 280
Eisenstat's trick see “Eisenstat's implementation”
Eisenstat, S.C. 280 319
Element-By-Element preconditioner see “EBE preconditioner”
Elfving, T. 259
Elliptic operators 46
Ellpack — Itpack storage format 91 364
Ellpack — Itpack storage format, matvecs in 364
Elman, H.C 350 405
Energy norm 31 133 252 254
Erisman, A.M 101
Error projection methods 135
Euclidean inner product 6
Euclidean norm 7
Faber — Manteuffel theorem 196
Faber.V. 198 216
FACR 59
Factored approximate inverse 329
Fan, K. 288
Fan-in in multigrid 422
Fan-out in multigrid 422
Farhat, C 493
Fast Poisson solvers 48 55—59 452
Fast Poisson solvers, block cyclic reduction 57
Fast Poisson solvers, Buneman's algorithm 58
Fast Poisson solvers, FACR 59
Fast Poisson solvers, FFT based 56 57
Fedorenko, R.R 449
FFT 57 465
FFT solvers 55
FGMRES 273—275
FGMRES, algorithm 273
Fictitious domain methods 455
Fiedler vector 486
Field of values 22
fill factor 334
Fill path 298
Fill-in elements 293
Fine-grain algorithms 378
Finite difference scheme 48
Finite difference scheme, for 1-D problems 51
Finite difference scheme, for 2-D problems 54
Finite difference scheme, for the Laplacian 50
Finite difference scheme, upwind schemes 52
Finite element method 45 60
Finite volume method 68
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