Matrix preconditioning techniques and applications
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
19 |
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| Online-Zugang: | Inhaltsverzeichnis |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 650f 2005 A 7445 |
|---|---|
| DE-BY-TUM_katkey | 1516331 |
| DE-BY-TUM_location | 01 |
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| _version_ | 1820859283995099136 |
| adam_text | MATRIX PRECONDITIONING TECHNIQUES AND APPLICATIONS KE CHEN READER IN
MATHEMATICS DEPARTMENT OF MATHEMATICAL SCIENCES THE UNIVERSITY OF
LIVERPOOL CAMBRIDGE UNIVERSITY PRESS 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 E-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 VN 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 [TL]: DIRECT
APPROXIMATION OF A NXN 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~ XKN 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 OT A NXH ANA A~ 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 M 3 AND ITERATIVE
SOLUTION 384 11.2 THE LOW WAVENUMBER CASE OF A HELMHOLTZ EQUATION 397
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.I 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 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 513 C.I 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 WITH FORTRAN OR C 519 C.6 DEBUGGING A MFILE 521 C.7 RUNNING A
MATLAB SCRIPT AS A BATCH JOB 521 C.8 SYMBOLIC COMPUTING 521 APPENDIX D:
LIST OF SUPPLIED M-FLLES AND PROGRAMS 523 APPENDIX E: LIST OF SELECTED
SCIENTIFIC RESOURCES ON INTERNET 525 E.I 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 564
|
| any_adam_object | 1 |
| author | Chen, Ke |
| author_facet | Chen, Ke |
| author_role | aut |
| author_sort | Chen, Ke |
| author_variant | k c kc |
| building | Verbundindex |
| bvnumber | BV019856956 |
| callnumber-first | Q - Science |
| callnumber-label | QA188 |
| callnumber-raw | QA188 |
| callnumber-search | QA188 |
| callnumber-sort | QA 3188 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 910 |
| classification_tum | MAT 650f |
| ctrlnum | (OCoLC)255072611 (DE-599)BVBBV019856956 |
| dewey-full | 512.9434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9434 |
| dewey-search | 512.9434 |
| dewey-sort | 3512.9434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV019856956 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T18:17:36Z |
| institution | BVB |
| isbn | 0521838282 9780521838283 |
| language | English |
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| oclc_num | 255072611 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-703 DE-634 DE-355 DE-BY-UBR DE-1050 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-703 DE-634 DE-355 DE-BY-UBR DE-1050 |
| physical | XXIII, 568 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge monographs on applied and computational mathematics |
| series2 | Cambridge monographs on applied and computational mathematics |
| spellingShingle | Chen, Ke Matrix preconditioning techniques and applications Cambridge monographs on applied and computational mathematics Analyse numérique matricielle Itération (Mathématiques) Matrices éparses Équations différentielles - Solutions numériques - Informatique Équations intégrales - Solutions numériques - Informatique Datenverarbeitung Differential equations Numerical solutions Data processing Integral equations Numerical solutions Data processing Iterative methods (Mathematics) Data processing Sparse matrices Data processing Iteration (DE-588)4123457-1 gnd Integralgleichung (DE-588)4027229-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4027229-1 (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4139030-1 (DE-588)4056053-3 |
| title | Matrix preconditioning techniques and applications |
| title_auth | Matrix preconditioning techniques and applications |
| title_exact_search | Matrix preconditioning techniques and applications |
| title_full | Matrix preconditioning techniques and applications Ke Chen |
| title_fullStr | Matrix preconditioning techniques and applications Ke Chen |
| title_full_unstemmed | Matrix preconditioning techniques and applications Ke Chen |
| title_short | Matrix preconditioning techniques and applications |
| title_sort | matrix preconditioning techniques and applications |
| topic | Analyse numérique matricielle Itération (Mathématiques) Matrices éparses Équations différentielles - Solutions numériques - Informatique Équations intégrales - Solutions numériques - Informatique Datenverarbeitung Differential equations Numerical solutions Data processing Integral equations Numerical solutions Data processing Iterative methods (Mathematics) Data processing Sparse matrices Data processing Iteration (DE-588)4123457-1 gnd Integralgleichung (DE-588)4027229-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd |
| topic_facet | Analyse numérique matricielle Itération (Mathématiques) Matrices éparses Équations différentielles - Solutions numériques - Informatique Équations intégrales - Solutions numériques - Informatique Datenverarbeitung Differential equations Numerical solutions Data processing Integral equations Numerical solutions Data processing Iterative methods (Mathematics) Data processing Sparse matrices Data processing Iteration Integralgleichung Differentialgleichung Numerisches Verfahren Computerunterstütztes Verfahren Schwach besetzte Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013181533&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011073737 |
| work_keys_str_mv | AT chenke matrixpreconditioningtechniquesandapplications |