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| Авторизация |
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| Saad Y. — Iterative methods for sparse linear systems |
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| Предметный указатель |
Matrix 1
Matrix norm 8
Matrix, addition 2
Matrix, adjoint of a 6
Matrix, banded 5
Matrix, bidiagonal 5
Matrix, canonical forms 14
Matrix, characteristic polynomial 3
Matrix, diagonal 4
Matrix, diagonal dominant 116
Matrix, diagonal form 15
Matrix, diagonalizable 15
Matrix, hermitian 4 20 23
Matrix, Hessenberg 5
Matrix, irreducible 89
Matrix, Jordan canonical form 15
Matrix, M- 25
Matrix, multiplication 2
Matrix, nonnegative 4 25
Matrix, nonsingular 3
Matrix, norm of a 7
Matrix, normal 4 20
Matrix, orthogonal 4
Matrix, outer product 5
Matrix, positive definite 29—31
Matrix, powers of a 18
Matrix, reduction 14
Matrix, Schur form 16
Matrix, self-adjoint 6 473
Matrix, singular 3
Matrix, skew-Hermitian 4
Matrix, skew-symmetric 4
Matrix, spectral radius 3
Matrix, spectrum 3
Matrix, square 2
Matrix, symmetric 4
Matrix, symmetric positive definite 30 119
Matrix, trace 3
Matrix, transpose 2
Matrix, transpose conjugate 2
Matrix, triangular 4
Matrix, tridiagonal 5
Matrix, unitary 4
Matrix-by-vector product 361
Matrix-by-vector product, dense matrices 361
Matrix-by-vector product, for distributed matrices 368
Matrix-by-vector product, in diagonal format 364
Matrix-by-vector product, in Ellpack format 365
Matrix-by-vector product, in triad form 364
Maximum transversal 335
McCormick, S.R 449
Meijerink, J.A. 280 349
Mesh generation 66
Mesh refinement 66
Mesh size 62
Message passing 358
Meurant, G.A. 350
Meyer, C.D. 43
MG see “Multigrid”
Micchelli, C.A. 385
Miller, G.L. 484 485
MILU 305—306
Min-max theorem 23
Minimal residual iteration 140
Minimal residual iteration, algorithm 140
Minimal residual iteration, convergence 141
Minimal residual smoothing 181—184 228
Minimum degree ordering 93 333
Mixed boundary conditions 46 47
Modified Gram — Schmidt 156
Modified ILU see “MILU”
Modified Sparse Row storage see “MSR”
Molecule 49
Moment matrix 221
Moment matrix, in Lanczos procedure 221
Moment of intertia 484
MR iteration see “Minimal residual iteration”
MRS see “Minimal residual smoothing”
MSR storage format 90
Multi-elimination 392 393
Multicolor orderings 87
Multicoloring 389—392
Multicoloring, for general sparse matrices 391
Multifrontal methods 405
Multigrid methods 407—446
Multigrid methods, algebraic multigrid see “AMG”
Multigrid methods, AMG 437
Multigrid methods, FMG 429
Multigrid methods, full multigrid see “FMG”
Multigrid methods, Galerkin projection 423
Multigrid methods, nested iteration 424 429
Multigrid methods, V-cycle 427
Multigrid methods, W-cycle 427
Multinode expansion algorithm 488
Multiple eigenvalue 14
Multiple vector pipelines 355
Multiplicative projection process 145
Multiplicative Schwarz preconditioning 470
Multiprocessing 355
Munksgaard, N. 350
Nachtigal, N.M. 176 216 243
Natural ordering 54
Near singularity 38
Nested dissection 333
Nested dissection ordering 93
Nested iteration 424 429
Neumann boundary conditions 46 47
Neumann polynomials 380
Nonnegative matrix 4 25
Nonsingular matrix 3
Norm, A-norm, energy norm 31
Norm, energy norm, A-norm 133
Norm, Euclidean 7
Norm, Hoelder 7
Norm, induced 8
Norm, of matrices 7
Norm, of vectors 5
Norm, p-norm 8
Normal derivative 60
Normal equations 245
Normal matrix 4 20
Notay, Y. 281
Null space 9
Null space, of a projector 32
Numerical radius 22
O'Leary, D. 216
Oblique projection methods 129 133
Oblique projector 34
Operator, elliptic 46
Operator, Laplacian 47
Optimality of projection methods 133
Order relation for matrices 25
Ortega, J. 280
Ortega, J.M. 101 404
ORTHODIR 194—196
Orthogonal bases 10
Orthogonal, complement 10
Orthogonal, Matrix 4
Orthogonal, projector 10 34
Orthogonal, vectors 10
Orthogonality 10
Orthogonality, between vectors 10
Orthogonality, of a vector to a subspace 10
ORTHOMIN 194—196
Orthonormal 10
Orthonormal bases 10
Oscillatory modes 407
Osterby.O. 101 350
Outer product matrices 5
Overdetermined systems 245
| Overlapping domains 455
Overrelaxation 105
Overton, ML. 281
p-Norm 8
Packet switching 357
Paige, C.C 189 216
Parallel architectures 355
Parallel sparse techniques 77
Parallelism 354
Parallelism, forms of 354
Parlett, B.N. 156 186 220 221
Partial differential equations 45
Partial Schur decomposition 17
Partition 108
Partition vector 486
Partitioning 453
Pasciak, J.E. 493
Paul, G 385
PDE see “Partial differential equations”
Pe see “Processing element”
Peaceman — Rachford algorithm 124
Peaceman, D. 124 126 128
Peierls, T. 317
Peripheral node 487
Permutation matrices 5 78
permutations 77
Perron — Frobenius theorem 26
Perturbation analysis 38
Petrov — Galerkin conditions 129—131
Peyton, B.W. 405
Physical mesh versus graph 77
Pipelining 354
Polynomial approximation 152
Polynomial preconditioning 377 379—388
Poole, E.L. 101 405
Positive definite matrix 5 24 29—31
Positive matrix 25
Positive real matrix see “Positive definite matrix”
Positive semidefinite 24
Pothen, A. 405 493
Preconditioned, CG 262
Preconditioned, CG, efficient implementations 265
Preconditioned, CG, for the normal equations 276
Preconditioned, CG, left 263
Preconditioned, CG, parallel implementation 359
Preconditioned, CG, split 264
Preconditioned, CG, symmetry in 262
Preconditioned, fixed-point iteration 111
Preconditioned, GMRES 267
Preconditioned, GMRES, comparison 271
Preconditioned, GMRES, flexible variant 272 273
Preconditioned, GMRES, left preconditioning 268
Preconditioned, GMRES, right preconditioning 269
Preconditioned, GMRES, split preconditioning 270
Preconditioner 111
Preconditioning 110 172 261
Preconditioning, and relaxation scheme 111
Preconditioning, approximate inverse 320
Preconditioning, block 337
Preconditioning, by ILQ 342
Preconditioning, EBE 399
Preconditioning, for normal equations 339
Preconditioning, incomplete LU 287
Preconditioning, induced 478
Preconditioning, Jacobi 284
Preconditioning, left 261
Preconditioning, polynomial 379—388
Preconditioning, polynomial, with Chebyshev polynomials 381
Preconditioning, polynomial, with least-squares polynomials 383
Preconditioning, polynomial, with Neumann polynomials 380
Preconditioning, right 261
Preconditioning, SOR 284
Preconditioning, split 261
Preconditioning, SSOR 284
probing 480
Processing element 355
Profile 84
Projection methods 129
Projection methods, additive 143
Projection methods, approximate problem 130
Projection methods, definitions 129
Projection methods, error bounds 135
Projection methods, general 130
Projection methods, matrix representation 131
Projection methods, multiplicative 145
Projection methods, oblique 129 217
Projection methods, one-dimensional 137
Projection methods, optimality 133
Projection methods, orthogonal 129 131
Projection methods, prototype 131
Projection methods, residual 134
Projection methods, theory 132
Projection, operator see “Projector”
Projection, orthogonal to 32
Projection, parallel to 32
Projector 9 32—36 109
Projector, existence 33
Projector, matrix representation 34
Projector, oblique 34
Projector, orthogonal 34
Projector, orthogonal, eigenvalues 36
Projector, orthogonal, properties 36
Prolongation operator 109 468
Property A 119
Propkopov, G.P. 216
Przemieniecki, J.S. 492
Pseudo-peripheral node 487
qmr 222—226
QMR, algorithm 225
QMR, approximation 225
QMR, from residual smoothing 228
QMR, peaks and plateaus of residuals 228
QMRS see “Quasi-minimal residual smoothing”
QR decomposition 11
Quasi-GMRES 172—173
Quasi-GMRES, algorithm 172
Quasi-GMRES, direct version 172
Quasi-GMRES, DQGMRES 172
Quasi-minimal residual see “QMR”
Quasi-minimal residual smoothing 184 228
Quasi-residual norm 174
Quasi-residual smoothing 228
Quasi-Schur form 17
Quick-split, in ILUT 311
Quotient graph 77
Rachford, H. 124 126 128
RANGE 2 9
Range, of a projector 32
Rank 9
Rank, full 10
Rapid elliptic solvers see “Fast Poisson solvers”
Rayleigh quotient 22 23
RCM 333
Real Schur form 17
Recursive graph bisection 487
Red-black ordering 389
Redivo Zaglia, M. 243
Reduced system 346 456
Reducible 26
Reduction of matrices 14
Reduction operations 361
refinement 66
reflectors 11
Regular splitting 115
Regularization 257
Reid, J.K. 101 216
Relaxation methods, block 106
Relaxation methods, convergence 112
reordering 78 333
Reordering rows, columns 77
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