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