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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:

This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science.


Язык: en

Рубрика: Математика/Численные методы/Численная линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition with corrections

Год издания: 2000

Количество страниц: 447

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Additive projection procedure      136
ADI      116
ADI, Peaceman — Rachford algorithm      117
Adjacency graph      71
Adjacency graph of PDE matrices      71
Adjoint of a matrix      7
Algebraic multiplicity      15
Alternating Direction Implicit      see “ADI”
Angle between a vector and a subspace      130
Anisotropic medium      47
Approximate inverse preconditioners      297
Approximate inverse preconditioners for improving a preconditioner      308
Approximate inverse preconditioners, column-oriented      300
Approximate inverse preconditioners, global iteration      298
Approximate inverse techniques      375
Arnoldi’s method      146—157
Arnoldi’s method for linear systems      151
Arnoldi’s method with Householder orthogonalization      149
Arnoldi’s method with modified Gram — Schmidt      148
Arnoldi’s method, basic algorithm      146
Arnoldi’s method, breakdown of      148
Arnoldi’s method, lucky breakdown      148
Arnoldi’s method, practical implementation      148
Arrow — Hurwicz’s algorithm      241
Assembled matrix      60
Assembly process      59
Banded matrices      5
Bandwidth of a bus      327
Bandwidth of a matrix      5
Basis of a subspace      10
BCG      209—213
BCG, algorithm      210
BCG, transpose-free variants      213—226
BICGSTAB      216
Biconjugate Gradient      see “BCG”
Bidiagonal matrices      5
Bilinear form      56
Biorthogonal bases      35
Biorthogonal vectors      35 205
Biorthogonalization      204
Bipartite graph      82 112
Block Arnoldi, algorithm      196
Block Arnoldi, Ruhe’s variant      197
Block diagonal matrices      5
Block FOM      199
Block Gaussian elimination      385—388
Block Gaussian elimination, algorithm      388
Block GMRES      199—200
Block GMRES, multiple right-hand sides      199
Block Gram — Schmidt      197
Block Jacobi      102
Block Jacobi as a preconditioner      353
Block Krylov subspace methods      144 196–200
Block preconditioners      309
Block relaxation      98
Block tridiagonal matrices      5 309
Block tridiagonal matrices, preconditioning      309
boundary conditions      45 46
Boundary conditions, Dirichlet      46
Boundary conditions, mixed      46
Boundary conditions, Neumann      46
Cache memory      327
Canonical form      15
Canonical form, Jordan      16
Canonical form, Schur      17
Cauchy — Schwartz inequality      6 8
Cayley — Hamilton theorem      144
Cell-centered scheme      64
Cell-vertex scheme      64
Centered difference approximation      48
Centered difference formula      48
Centerpoint      415
CG algorithm      see “Conjugate gradient algorithm”
CG for normal equations      236 237
CGNE      237
CGNE, algorithm      238
CGNE, optimality      238
CGNR      236
CGNR, algorithm      236
CGNR, optimality      236
cgs      214—216
CGS, algorithm      216
Characteristic polynomial      3
Chebyshev polynomials      186—192 194 356—364
Chebyshev polynomials and ellipses      188
Chebyshev polynomials for preconditioning      356
Chebyshev polynomials, complex      188 203
Chebyshev polynomials, optimality      189—191
Chebyshev polynomials, real      187
Chebyshev, acceleration      358
Cimmino’s method      233
Circuit switching      328
Coarse-grain      353
Coefficient matrix      95
Coloring vertices      81
Column reordering      74
Compressed Sparse Column storage      see “CSC”
Compressed Sparse Row storage      see “CSR”
Concus, Golub and Widlund algorithm      260
Condition number      40
Condition number for normal equation systems      230
Condition numbers and CG      180
Conjugate gradient algorithm      174—181
Conjugate gradient algorithm for the normal equations      236
Conjugate gradient algorithm, algorithm      178
Conjugate gradient algorithm, alternative formulations      178
Conjugate gradient algorithm, convergence      191 192
Conjugate gradient algorithm, derivation      174 177
Conjugate gradient algorithm, eigenvalue estimates      180
Conjugate gradient algorithm, preconditioned      244
Conjugate gradient squared      see “CGS”
Conjugate Residual algorithm      181
Consistent matrix norms      8
Consistent orderings      112—116
Control volume      63
Convection-diffusion equation      47
Convergence of GMRES      193
Convergence of relaxation methods      104
Convergence of Schwarz procedures      402
Convergence of the Minimal Residual method      135
Convergence, factor      105
Convergence, factor, general      105
Convergence, factor, specific      105
Convergence, rate      105
COO storage scheme      84
Coordinate storage format      see “COO”
Courant characterization      26
Craig’s method      238
CRAY T3D      329
CSC storage format      85
CSC storage format, matvecs in      335
CSR storage format      85 272
CSR storage format, matvecs in      335
Cut-edges      416
Cuthill — McKee ordering      77
Data coherence      327
Data-parallel      326
Defective eigenvalue      15
Derogatory      15
Determinant      3
DIA storage format      85 338
DIA storage format, matvecs in      338
Diagonal compensation      285
Diagonal dominance      108 109
Diagonal form of matrices      16
Diagonal matrices      5
Diagonal storage format      see “DIA”
Diagonalizable matrix      16
Diagonally dominant matrix      109
Diagonally structured matrices      85
Diameter of a graph      417
Diameter of a triangle      58
DIOM      154—157 175
DIOM, algorithm      156
Direct IOM      see “DIOM”
Direct sum of subspaces      10 33
Directed graph      71
Dirichlet boundary conditions      45 46
Distributed, computing      325
Distributed, ILU      372
Distributed, memory      328
Distributed, sparse matrices      341 373
Divergence of a vector      46
Divergence operator      46
Domain decomposition and direct solution      387
Domain decomposition, convergence      402
Domain decomposition, full matrix methods      411
Domain decomposition, induced preconditioners      407
Domain decomposition, Schur complement approaches      406
Domain decomposition, Schwarz alternating procedure      394
Domain sweep      396
Double orthogonalization      148
Double-striping      418
DQGMRES      168—172 258
DQGMRES, algorithm      169
EBE preconditioner      376
EBE regularization      377
Edge in a graph      71
Eigenspace      10
Eigenvalues      3
Eigenvalues from CG iteration      180
Eigenvalues of an orthogonal projector      37
Eigenvalues, definition      3
Eigenvalues, index      16 17
Eigenvector      3
Eigenvector, left      4
Eigenvector, right      4
Eisenstat’s implementation      248 263
Eisenstat’s trick      see “Eisenstat’s implementation”
Element-By-Element preconditioner      see “EBE preconditioner”
ELL storage format      86
ELL storage format, matvecs in      339
Elliptic operators      44
Ellpack-Itpack storage format      see “ELL storage format”
Energy norm      32 236 238
Error projection methods      129
Euclidean inner product      6
Euclidean norm      7
Faber — Manteuffel theorem      184
Factored approximate inverse      306
Fast solvers      47 383
FGMRES      255—258
FGMRES, algorithm      256
Fictitious domain methods      387
Fiedler vector      416
Field of values      23
Fill-in elements      275
Fine-grain algorithms      353
Finite difference scheme      47
Finite difference scheme for 1-D problems      50
Finite difference scheme for 2-D problems      54
Finite difference scheme for the Laplacean      49
Finite difference scheme, upwind schemes      51
Finite element method      44 55
Finite volume method      63
Flexible GMRES      see “FGMRES”
Flexible iteration      255
Flux vector      63
FOM      151
FOM with restarting      153
FOM, algorithm      152
Frobenius norm      8
Frontal methods      60 376
Full matrix methods      411–413
Full Orthogonalization Method      see “FOM”
Galerkin conditions      124
Gastinel’s method      139
Gather operation      336
Gauss — Seidel iteration      95
Gauss — Seidel iteration for normal equations      231
Gauss — Seidel iteration for normal equations in parallel      378
Gauss — Seidel iteration, backward      97
Gauss — Seidel iteration, symmetric      97
Gaussian elimination      60 176 269—273 278 282 283 285—287 368 369 383
Gaussian elimination in IOM and DIOM      156
Gaussian elimination in Lanczos process      176
Gaussian elimination in skyline format      295
Gaussian elimination, block      385
Gaussian elimination, frontal methods      376
Gaussian elimination, IKJ variant      271
Gaussian elimination, parallel      409
Gaussian elimination, parallelism in      71
Gaussian elimination, reordering in      75
Gaussian elimination, sparse      70
GCR      182—184
Generalized Conjugate Residual      see “GCR”
Geometric multiplicity      15
Gershgorin discs      110
Gershgorin’s theorem      109
Global iteration      298—300 305
Global reduction operations      332
gmres      157—172 184 193—196
GMRES with polynomial preconditioning      363
GMRES with restarting      167
GMRES, algorithm      158
GMRES, block algorithm      199
GMRES, breakdown      163 164
GMRES, convergence      193
GMRES, flexible variant      250 255—258
GMRES, Householder version      158
GMRES, lucky breakdown      164
GMRES, parallel implementation      331
GMRES, practical implementation      160
GMRES, relation with FOM      164 166
GMRES, stagnation      167
GMRES, truncated      168
Grade of a vector      144
Gram — Schmidt algorithm      11—12 314
Gram — Schmidt algorithm, block      197
Gram — Schmidt algorithm, cancellations in      148
Gram — Schmidt algorithm, modified      11
Gram — Schmidt algorithm, standard      11
Graph      71
Graph, bipartite      82
Graph, coloring      81
Graph, directed      71
Graph, edges      71
Graph, Laplacean of a      416
Graph, partitioning      382 413
Graph, partitioning, geometric      414
Graph, partitioning, graph theory techniques      417
Graph, partitioning, spectral techniques      416
Graph, partitioning, type      384
Graph, undirected      71
Graph, vertices      71
Hankel matrix      208
Harmonic functions      46
Harwell — Boeing collection      89 90
Hausdorff’s convex hull theorem      23
Heap-sort, in ILUT      291
Hermitian inner product      6
Hermitian matrices      4 24
Hermitian positive definite      31
Hessenberg matrices      5
Holder norms      7
Householder algorithm      12
Householder orthogonalization in Arnoldi’s method      149
Householder reflectors      12
HPD      see “Hermitian positive definite”
Hypercube      329
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