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| Saad Y. — Iterative Methods for Sparse Linear Systems |
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| Предметный указатель |
Idempotent 10 33
If and only if 3
IFF see “If and only if”
ILQ, factorization 315
ILQ, preconditioning 314
ILU 268—297
ILU with multi-elimination see “ILUM”
ILU with threshold see “ILUT and ILUTP”
ILU(0) 265 268 274—276
ILU(0) for distributed sparse matrices 373
ILU(0) for red-black ordering 366
ILU(0), algorithm 275
ILU(0), distributed factorization 374
ILU(1) 278
ILU, distributed 372
ILU, factorization 268
ILU, factorization, instability in 293 297
ILU, general algorithm 270
ILU, IKJ version 272
ILU, ILUS 294—297
ILU, ILUS, algorithm 296
ILU, modified 285—286
ILU, preconditioner 268
ILU, preconditioner for Schur complement 409
ILU, static pattern 273
ILU, zero pattern 270
ILUM 370
ILUT 286—293
ILUT with pivoting see “ILUTP”
ILUT, algorithm 287
ILUT, analysis 288
ILUT, implementation 290
ILUTP 293
ILUTP for normal equations 312
Incomplete factorization 265 268
Incomplete factorization, Gram — Schmidt 315
Incomplete factorization, ILQ 314 315
Incomplete factorization, QR 315
Incomplete Gram — Schmidt 316
Incomplete LQ see “ILQ”
Incomplete LU see “ILU”
Incomplete orthogonalization method see “IOM”
Incomplete, orthogonalization algorithm 154
Indefinite inner product 207
Independent set orderings 79
Independent sets 79 368
Independent sets, maximal 80
Index of an eigenvalue 16 17
Indirect addressing 69
Induced norm 8
Induced preconditioners 407
Inhomogeneous medium 47
Inner products 5
Inner products, indefinite 207
Invariant subspace 10 130
Inverse LU factors 306
IOM 154
IOM, algorithm 154
IOM, direct version 154
Irreducibility 83
Irreducible 27
Isometry 7
Iteration matrix 102 104
j-diagonal 340
Jacobi iteration 95
Jacobi iteration for the normal equations 233
JAD storage format 340
JAD storage format in level scheduling 348
JAD storage format, definition 340
JAD storage format, matvecs in 341
Jagged diagonal format see “JAD storage format”
Jagged diagonals 340
Jordan block 17
Jordan box 17
Jordan canonical form 16
Jordan submatrix 17
Joukowski mapping 188
Kernel 9 10
Krylov subspace 144
Krylov Subspace Methods 204
Krylov subspace, dimension of a 144
Krylov subspace, invariant 145
Krylov subspace, methods 143
Lanczos algorithm 172 173
Lanczos algorithm and orthogonal polynomials 173
Lanczos algorithm for linear systems 208
Lanczos algorithm, algorithm 173 205
Lanczos algorithm, biorthogonalization 204
Lanczos algorithm, breakdown 206
Lanczos algorithm, breakdown, incurable 207
Lanczos algorithm, breakdown, lucky 207
Lanczos algorithm, breakdown, serious 207
Lanczos algorithm, look-ahead version 207
Lanczos algorithm, loss of orthogonality 173
Lanczos algorithm, modified Gram — Schmidt version 173
Lanczos algorithm, nonsymmetric 204
Lanczos algorithm, partial reorthogonalization 173
Lanczos algorithm, practical implementations 207
Lanczos algorithm, selective reorthogonalization 173
Lanczos algorithm, symmetric case 172
Laplacean see “Laplacean operator”
Laplacean operator 46 55
Laplacean operator of a graph 416
Least-squares polynomials 359
Least-squares problem 229
Left eigenvector 4
Left versus right preconditioning 255
Level of fill-in 278
Level scheduling 345—348
Level scheduling for 5-point matrices 345
Level scheduling for general matrices 346
Level set orderings 76 417
Line relaxation 99
Linear mappings 2
Linear span 9
Linear system 38 95
Linear system, existence of a solution 38
Linear system, right-hand side of a 38
Linear system, singular 38
Linear system, unknown of a 38
Linked lists 88
Local Schur complement 393
Look-ahead Lanczos algorithm 207
Lower triangular matrices 5
LQ factorization 314
LQ factorization, algorithm 315
Lucky breakdowns 148
M-matrix 26 269 310
Mask 320
Matrix 1
Matrix, addition 2
Matrix, adjoint of a 7
Matrix, banded 5
Matrix, bidiagonal 5
Matrix, canonical forms 15
Matrix, characteristic polynomial 3
Matrix, diagonal 5
Matrix, diagonal dominant 108
Matrix, diagonal form 16
Matrix, diagonalizable 16
Matrix, hermitian 4 21 24
Matrix, Hessenberg 5
Matrix, irreducible 83
Matrix, Jordan canonical form 16
Matrix, multiplication 2
Matrix, nonnegative 4 26
Matrix, nonsingular 3
Matrix, norm of a 8
Matrix, normal 4 21
Matrix, orthogonal 5
| Matrix, outer product 5
Matrix, positive definite 30—32
Matrix, powers of a 19
Matrix, reduction 15
Matrix, Schur form 17
Matrix, self-adjoint 7 403
Matrix, singular 3
Matrix, skew-Hermitian 4
Matrix, skew-symmetric 4
Matrix, spectral radius 4
Matrix, spectrum 3
Matrix, square 3
Matrix, symmetric 4
Matrix, symmetric positive definite 31 112
Matrix, trace 4
Matrix, transpose 2
Matrix, transpose conjugate 2
Matrix, triangular 5
Matrix, tridiagonal 5
Matrix, unitary 4
Matrix-by-vector product 334
Matrix-by-vector product for distributed matrices 344
Matrix-by-vector product in DIA format 338
Matrix-by-vector product in Ellpack format 339
Matrix-by-vector product in triad form 339
Matrix-by-vector product, dense matrices 334
Mesh generation 61
Mesh size 58
Message passing 328
Min-max theorem 24
Minimal degree ordering 88
Minimal residual iteration 133
Minimal residual iteration, algorithm 134
Minimal residual iteration, convergence 135
Mixed boundary conditions 45 46
MLU 285—286
Modified Gram — Schmidt 148
Modified ILU see “MLU”
Modified Sparse Row storage see “MSR”
Molecule 48
Moment matrix 208
Moment matrix in Lanczos procedure 208
MR iteration see “Minimal residual iteration”
MSR storage format 85
Multi-elimination 368 369
Multicolor orderings 81
Multicoloring 364—368
Multicoloring for general sparse matrices 367
Multifrontal methods 381
Multinode expansion algorithm 420
Multiple eigenvalue 15
Multiple vector pipelines 325
Multiplicative projection process 138
Multiplicative Schwarz preconditioning 399
Multiprocessing 325
Natural ordering 54
Near singularity 40
Nested-dissection ordering 88
Neumann boundary conditions 45 46
Neumann polynomials 355
Nonnegative matrix 4 26
Nonsingular matrix 3
Norm of matrices 8
Norm of vectors 5
Norm, Euclidean 7
Norm, Holder 7
Norm, induced 8
Norm, p-norm 8
Normal derivative 56
Normal equations 229
Normal matrix 4 21
Null space 9 10
Null space of a projector 33
Object oriented programming 334
Oblique projection methods 204
Oblique projector 35
Operator, elliptic 44
Operator, Laplacean 46
Optimality of projection methods 126
Order relation for matrices 26
ORTHODIR 182—184
Orthogonal complement 10
Orthogonal matrix 5
Orthogonal projector 10 35
Orthogonal vectors 10
Orthogonality 10
Orthogonality between vectors 10
Orthogonality of a vector to a subspace 10
ORTHOMIN 182—184
Orthonormal 10
Outer product matrices 5
Over-relaxation 97
Overdetermined systems 229
Overlapping domains 385
p-Norm 8
Packet switching 328
Parallel architectures 326
Parallel sparse techniques 72
Parallelism 324
Parallelism, forms of 324
Partial differential equations 44
Partial Schur decomposition 18
Partition 100
Partition vector 416
Partitioning 384
PDE see “Partial differential equations”
Pe see “Processing element”
Peaceman — Rachford algorithm 117
Peripheral node 417
Permutation matrices 5 73
permutations 72
Perron — Frobenius theorem 27
Perturbation analysis 39
Petrov — Galerkin conditions 122—124
Physical mesh versus graph 72
Pipelining 324
Polynomial approximation 144
Polynomial preconditioning 352 354—364
Positive definite matrix 6 25 30—32
Positive matrix 26
Positive real matrix see “Positive definite matrix”
Positive semidefinite 25
Preconditioned, CG 244
Preconditioned, CG for the normal equations 259
Preconditioned, CG, efficient implementations 248
Preconditioned, CG, left 246
Preconditioned, CG, parallel implementation 330
Preconditioned, CG, split 247
Preconditioned, CG, symmetry in 245
Preconditioned, fixed-point iteration 103
Preconditioned, GMRES 250
Preconditioned, GMRES, comparison 253
Preconditioned, GMRES, flexible variant 255 256
Preconditioned, GMRES, left preconditioning 250
Preconditioned, GMRES, right preconditioning 252
Preconditioned, GMRES, split preconditioning 253
Preconditioner 103
Preconditioning 102 244
Preconditioning and relaxation scheme 103
Preconditioning, EBE 376
Preconditioning, incomplete LU 268
Preconditioning, induced 407
Preconditioning, Jacobi 265
Preconditioning, normalequationsfor normal equations 311
Preconditioning, polynomial 354—364
Preconditioning, polynomial with Chebyshev polynomials 356
Preconditioning, polynomial with least-squares polynomials 359
Preconditioning, polynomial with Neumann polynomials 355
Preconditioning, SOR 265
Preconditioning, SSOR 265
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