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Barrett R. — Templates for the solution of linear systems: building blocks for iterative methods
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Название: Templates for the solution of linear systems: building blocks for iterative methodsАвтор: Barrett R. Аннотация: In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1993Количество страниц: 124Добавлена в каталог: 19.06.2005Операции: Положить на полку |
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Предметный указатель
Ad hoc SOR method See method ad Asynchronous method See method asynchronous Bi-CGSTAB method See method Bi-CGSTAB Bi-conjugate gradient stabilized method See method Bi-CGSTAB Bi-orthogonality in BiCG 22 Bi-orthogonality in QMR 23 BiCG method See method BiCG Biconjugate gradient method See method BiCG BLAS 2 73 Block methods 84—85 Breakdown avoiding by look-ahead 22 Breakdown in Bi-CGSTAB 28 Breakdown in BiCG 22 23 Breakdown in CG for indefinite systems 17 CG method See method CG CGNE method See method CGNE CGNR method See method CGNR CGS method See method CGS Chaotic method See method asynchronous Chebyshev iteration See method Chebyshev Codes, FORTRAN 2 Codes, MATLAB 2 Complex systems 57 Conjugate gradient method See method CG Conjugate Gradient Squared method See method CGS Convergence of Bi-CGSTAB 28 Convergence of BiCG 22—23 Convergence of CG 16 Convergence of CGNR and CGNE 18 Convergence of CGS 26 Convergence of Chebyshev iteration 29 Convergence of Gauss — Seidel 10 Convergence of Jacobi 8 9 Convergence of MINRES 17 Convergence of QMR 25 Convergence of SSOR 12 Convergence, irregular 100 Convergence, irregular, of BiCG 22—23 25 Convergence, irregular, of CGS 26 27 Convergence, linear 99 Convergence, smooth 100 Convergence, smooth, of Bi-CGSTAB 28 Convergence, stalled 100 Convergence, stalled, of BiCG 25 Convergence, stalled, of GMRES 19 Convergence, superlinear 99 Convergence, superlinear, of BiCG 29 Convergence, superlinear, of CG 16 Convergence, superlinear, of GMRES 29 Data structures 63—76 Diffusion, artificial 47 Domain decomposition, multiplicative Schwarz 90 91 Domain decomposition, non-overlapping subdomains 88—90 Domain decomposition, overlapping subdomains 87 88 Domain decomposition, Schur complement 86 Domain decomposition, Schwarz 86 Fill-in strategies See preconditioned point FORTRAN codes See codes FORTRAN Gauss — Seidel method See method Gauss Generalized minimal residual method See method GMRES GMRES method See method GMRES Ill-conditioned systems using GMRES on 21 Implementation of Bi-CGSTAB 28 Implementation of BiCG 23 Implementation of CG 16 Implementation of CGS 27 Implementation of Chebyshev iteration 29 Implementation of GMRES 21 Implementation of QMR 25 IMSL 1 Inner products as bottlenecks 16 28—29 Inner products avoiding with Chebyshev 28 29 Irregular convergence See convergence irregular ITPACK 12 Jacobi method See method Jacobi Krylov subspace 15 Lanczos and CG 15 83—84 LAPACK 1 Linear convergence See convergence linear LINPACK 1 MATLAB codes See codes MATLAB Method, ad hoc SOR 14 Method, adaptive Chebyshev 28 29 Method, asynchronous 13 Method, Bi-CGSTAB 3 7 27—28 Method, Bi-CGSTAB2 28 Method, BiCG 3 7 21—23 Method, CG 3 6 11—17 Method, CG, block version 85 Method, CGNE 3 6 18 Method, CGNR 3 6 18 Method, CGS 3 7 25—27 Method, chaotic 13 See asynchronous Method, Chebyshev iteration 3 5 7 28—29 Method, choosing 11—12 Method, comparison with other methods 28—29 Method, domain decomposition 86—91 Method, Gauss — Seidel 3 5 8 9—10 Method, GMRES 3 6 19—21 Method, Jacobi 3 5 8—9 Method, MINRES 3 6 17—18 Method, of simultaneous displacements See method Jacobi Method, of successive displacements See method Gauss Method, QMR 3 7 23—25 Method, relaxation 13 14 Method, SOR 3 6 8 10—12 Method, spectral information required by 28 Method, SSOR 3 6 8 12 Method, SYMMLQ 3 6 17—18 Minimization property in Bi-CGSTAB 28 Minimization property in CG 15 17 Minimization property in MINRES 17 MINRES method See method MINRES Multigrid 91 92 NAG 1 Nonstationary methods 14—29 Normal equations 6 Overrelaxation 11 Parallelism 76 81 Parallelism in BiCG 23 Parallelism in CG 16 Parallelism in Chebyshev iteration 29 Parallelism in GMRES 21 Parallelism in QMR 25 Parallelism, inner products 76—78 Parallelism, matrix-vector products 78 79 Parallelism, vector updates 78 Preconditioners 39 55 Preconditioners, ADI 54 55 Preconditioners, block factorizations 49 52 Preconditioners, block tridiagonal 51 Preconditioners, central differences 46 Preconditioners, cost 39—40 Preconditioners, fast solvers 54 Preconditioners, incomplete factorization 43 52 Preconditioners, left 40 Preconditioners, parallelism in 55 Preconditioners, point incomplete factorizations 44—49 Preconditioners, point incomplete factorizations, fill-in strategies 45 Preconditioners, point incomplete factorizations, modified 46—47 Preconditioners, point incomplete factorizations, parallelism in 48 49 Preconditioners, point incomplete factorizations, vectorization of 47 Preconditioners, point incomplete factorizations, wavefronts in 47—49 Preconditioners, point Jacobi 41 42 Preconditioners, polynomial 52 53 Preconditioners, reduced system 85—86 Preconditioners, right 40 Preconditioners, SSOR 42 Preconditioners, SSOR, parallelism in 42 Preconditioners, symmetric part 53 54 QMR method See method QMR Quasi-Minimal Residual method See method QMR Relaxation method See method relaxation Residuals in BiCG 21 Residuals in CG 14 Residuals in CG, orthogonality of 14 Residuals in SYMMLQ, orthogonality of 17 Restarting in BiCG 23 Restarting in GMRES 19 21 Row projection methods 92 93 Search directions in BiCG 21 Search directions in CG 14 15 Search directions in CG, A-orthogonality of 14 Smooth convergence See convergence smooth Software obtaining 95—96 SOR method See method SOR Sparse matrix storage 64—68 Sparse matrix storage, BCRS 65 Sparse matrix storage, CCS 65 Sparse matrix storage, CDS 65—67 Sparse matrix storage, CRS 64—65 Sparse matrix storage, JDS 67—68 Sparse matrix storage, SKS 68 SSOR method See method SSOR Stalled convergence See convergence stalled Stationary methods 7—14 Stopping criteria 57 63 Successive overrelaxation method See method SOR Super linear convergence See convergence super Symmetric LQ method See method SYMMLQ Symmetric Successive Overrelaxation method See method SSOR SYMMLQ method See method SYMMLQ template 1 Three-term recurrence in CG 15 Two-term recurrence 25 Underrelaxation 11 Wavefronts See preconditioners point wavefront
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