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文件名称:matrix preconditioning techniques and applications
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更新时间:2012-11-09 09:33:13
矩阵 预处理 应用
不可多得的矩阵预处理方面的专著,程序代码,相关软件资源详尽。把散见在浩如烟海的论文中矩阵预处理技术系统的总结。下载下来就知道贵得值,此书在当当上要一千七百多元呢。
Contents
Preface page xiii
Nomenclature xxi
1 Introduction 1
1.1 Direct and iterative solvers, types of preconditioning 2
1.2 Norms and condition number 4
1.3 Perturbation theories for linear systems and eigenvalues 9
1.4 The Arnoldi iterations and decomposition 11
1.5 Clustering characterization, field of values and
-pseudospectrum 16
1.6 Fast Fourier transforms and fast wavelet transforms 19
1.7 Numerical solution techniques for practical equations 41
1.8 Common theories on preconditioned systems 61
1.9 Guide to software development and the supplied Mfiles 62
2 Direct methods 66
2.1 The LU decomposition and variants 68
2.2 The Newton–Schulz–Hotelling method 75
2.3 The Gauss–Jordan decomposition and variants 76
2.4 The QR decomposition 82
2.5 Special matrices and their direct inversion 85
2.6 Ordering algorithms for better sparsity 100
2.7 Discussion of software and the supplied Mfiles 106
3 Iterative methods 110
3.1 Solution complexity and expectations 111
3.2 Introduction to residual correction 112
3.3 Classical iterative methods 113
3.4 The conjugate gradient method: the SPD case 119
vii
viii Contents
3.5 The conjugate gradient normal method: the unsymmetric case 130
3.6 The generalized minimal residual method: GMRES 133
3.7 The GMRES algorithm in complex arithmetic 141
3.8 Matrix free iterative solvers: the fast multipole methods 144
3.9 Discussion of software and the supplied Mfiles 162
4 Matrix splitting preconditioners [T1]: direct approximation
of An×n 165
4.1 Banded preconditioner 166
4.2 Banded arrow preconditioner 167
4.3 Block arrow preconditioner from DDM ordering 168
4.4 Triangular preconditioners 171
4.5 ILU preconditioners 172
4.6 Fast circulant preconditioners 176
4.7 Singular operator splitting preconditioners 182
4.8 Preconditioning the fast multipole method 185
4.9 Numerical experiments 186
4.10 Discussion of software and the supplied Mfiles 187
5 Approximate inverse preconditioners [T2]: direct
approximation of A−1
n×n 191
5.1 How to characterize A−1 in terms of A 192
5.2 Banded preconditioner 195
5.3 Polynomial preconditioner pk (A) 195
5.4 General and adaptive sparse approximate inverses 199
5.5 AINV type preconditioner 211
5.6 Multi-stage preconditioners 213
5.7 The dual tolerance self-preconditioning method 224
5.8 Near neighbour splitting for singular integral equations 227
5.9 Numerical experiments 237
5.10 Discussion of software and the supplied Mfiles 238
6 Multilevel methods and preconditioners [T3]: coarse grid
approximation 240
6.1 Multigrid method for linear PDEs 241
6.2 Multigrid method for nonlinear PDEs 259
6.3 Multigrid method for linear integral equations 263
6.4 Algebraic multigrid methods 270
6.5 Multilevel domain decomposition preconditioners for
GMRES 279
6.6 Discussion of software and the supplied Mfiles 286
Contents ix
7 Multilevel recursive Schur complements
preconditioners [T4] 289
7.1 Multilevel functional partition: AMLI approximated Schur 290
7.2 Multilevel geometrical partition: exact Schur 295
7.3 Multilevel algebraic partition: permutation-based Schur 300
7.4 Appendix: the FEM hierarchical basis 305
7.5 Discussion of software and the supplied Mfiles 309
8 Sparse wavelet preconditioners [T5]: approximation
of ˜A n×n and ˜A−1
n×n 310
8.1 Introduction to multiresolution and orthogonal wavelets 311
8.2 Operator compression by wavelets and sparsity patterns 320
8.3 Band WSPAI preconditioner 323
8.4 New centering WSPAI preconditioner 325
8.5 Optimal implementations and wavelet quadratures 335
8.6 Numerical results 336
8.7 Discussion of software and the supplied Mfiles 338
9 Wavelet Schur preconditioners [T6] 340
9.1 Introduction 341
9.2 Wavelets telescopic splitting of an operator 342
9.3 An exact Schur preconditioner with level-by-level wavelets 346
9.4 An approximate preconditioner with level-by-level wavelets 352
9.5 Some analysis and numerical experiments 357
9.6 Discussion of the accompanied Mfiles 363
10 Implicit wavelet preconditioners [T7] 364
10.1 Introduction 365
10.2 Wavelet-based sparse approximate inverse 368
10.3 An implicit wavelet sparse approximate inverse
preconditioner 369
10.4 Implementation details 371
10.5 Dense problems 374
10.6 Some theoretical results 376
10.7 Combination with a level-one preconditioner 379
10.8 Numerical results 380
10.9 Discussion of the supplied Mfile 381
11 Application I: acoustic scattering modelling 383
11.1 The boundary integral equations for the Helmholtz equation in
R3 and iterative solution 384
11.2 The low wavenumber case of a Helmholtz equation 397
x Contents
11.3 The high wavenumber case of a Helmholtz equation 398
11.4 Discussion of software 399
12 Application II: coupled matrix problems 400
12.1 Generalized saddle point problems 401
12.2 The Oseen and Stokes saddle point problems 403
12.3 The mixed finite element method 405
12.4 Coupled systems from fluid structure interaction 407
12.5 Elasto-hydrodynamic lubrication modelling 410
12.6 Discussion of software and a supplied Mfile 413
13 Application III: image restoration and inverse problems 415
13.1 Image restoration models and discretizations 416
13.2 Fixed point iteration method 429
13.3 Explicit time marching schemes 436
13.4 The Primal-dual method 436
13.5 Nonlinear multigrids for optimization 439
13.6 The level set method and other image problems 442
13.7 Numerical experiments 446
13.8 Guide to software and the supplied Mfiles 447
14 Application IV: voltage stability in electrical power systems 449
14.1 The model equations 450
14.2 Fold bifurcation and arc-length continuation 454
14.3 Hopf bifurcation and solutions 458
14.4 Preconditioning issues 473
14.5 Discussion of software and the supplied Mfiles 473
15 Parallel computing by examples 475
15.1 A brief introduction to parallel computing and MPI 476
15.2 Some commonly used MPI routines 478
15.3 Example 1 of a parallel series summation 481
15.4 Example 2 of a parallel power method 483
15.5 Example 3 of a parallel direct method 489
15.6 Discussion of software and the supplied MPI Fortran files 502
Appendix A: a brief guide to linear algebra 504
A.1 Linear independence 504
A.2 Range and null spaces 505
A.3 Orthogonal vectors and matrices 505
A.4 Eigenvalues, symmetric matrices and diagonalization 505
A.5 Determinants and Cramer’s rule 506
Contents xi
A.6 The Jordan decomposition 507
A.7 The Schur and related decompositions 509
Appendix B: the Harwell–Boeing (HB) data format 511
Appendix C: a brief guide to MATLAB r 513
C.1 Vectors and matrices 513
C.2 Visualization of functions 514
C.3 Visualization of sparse matrices 516
C.4 The functional Mfile and string evaluations 517
C.5 Interfacing MATLAB r with Fortran or C 519
C.6 Debugging a Mfile 521
C.7 Running a MATLAB r script as a batch job 521
C.8 Symbolic computing 521
Appendix D: list of supplied M-files and programs 523
Appendix E: list of selected scientific resources on Internet 525
E.1 Freely available software and data 525
E.2 Other software sources 527
E.3 Useful software associated with books 527
E.4 Specialized subjects, sites and interest groups 528
References 530
Author Index 556
Subject Index
网友评论
- 这是一本好书 深入浅出讲了矩阵预条件理论
- 讲解很详细,谢谢分享这么好的资源。唯一的缺点是书中的代码要自己到书中给的网站上下载。
- preconditioning method内容讲解很全面 希望能找到ILU分解的相关内容 后附的代码要是C就好了
- 这是我目前看到的一本关于preconditioning method最详细可靠的一本书,解了燃眉之急,感谢CSDN提供资源!