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Saad Y. — Iterative methods for sparse linear systems
Saad Y. — Iterative methods for sparse linear systems

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Название: Iterative methods for sparse linear systems

Автор: Saad Y.

Аннотация:

Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best methods available today.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2

Год издания: 2003

Количество страниц: 547

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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