Projection methods for systems of equations:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier
1997
|
| Schriftenreihe: | Studies in computational mathematics
7 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007944047&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VII, 400 S. |
| ISBN: | 0444827773 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | PROJECTION METHODS FOR SYSTEMS OF EQUATIONS CLAUDE BREZINSKI UNIVERSITE
DES SCIENCES ET TECHNOLOGIES DE LILLE VILLENEUVE D ASCQ, FRANCE 1997
ELSEVIER AMSTERDAM - LAUSANNE - NEW YORK - OXFORD - SHANNON - SINGAPORE
- TOKYO CONTENTS INTRODUCTION 1 1 PRELIMINARIES 17 1.1 PROJECTIONS AND
PROJECTION METHODS 17 1.1.1 PROJECTIONS 18 1.1.2 PROJECTION METHODS 23
1.2 EXTRAPOLATION METHODS 26 1.3 BEST APPROXIMATION 28 1.4 ALGORITHMS
FOR RECURSIVE PROJECTION 31 1.4.1 THE GENERAL INTERPOLATION PROBLEM 35
1.4.2 RECURSIVE PROJECTION 36 1.5 SOLVING LINEAR SYSTEMS BY
EXTRAPOLATION 38 1.5.1 THE TOPOLOGICAL E-ALGORITHM 40 1.5.2 THE
5/3-ALGORITHM 43 1.5.3 VECTOR PADE APPROXIMANTS 45 1.5.4 VECTOR 0-TYPE
TRANSFORMATIONS 46 2 BIORTHOGONALITY 61 2.1 GENERALITIES 62 2.2
BIORTHOGONAL POLYNOMIALS 68 2.3 HANKEL AND TOEPLITZ SYSTEMS . . .-- 70
2.3.1 HANKEL MATRICES 72 2.3.2 TOEPLITZ MATRICES 78 2.4
BIORTHOGONALIZATION PROCESSES 81 3 PROJECTION METHODS FOR LINEAR SYSTEMS
93 3.1 VARIATIONAL FORMULATION 94 3.2 PROJECTION ITERATIVE METHODS 99
3.2.1 METHOD OF CONJUGATE DIRECTIONS 108 3.2.2 THE CONJUGATE GRADIENTS
ALGORITHM ILL 3.2.3 ROW PROJECTION METHODS 123 VI CONTENTS 3.3
PROJECTION ACCELERATION PROCEDURES 124 3.4 PRECONDITIONED STEEPEST
DESCENT ALGORITHMS 130 3.5 ACCELERATED DESCENT METHODS 132 4
LANCZOS-TYPE METHODS 141 4.1 EXTRAPOLATION AND PROJECTION METHODS 141
4.2 VOROBYEV S METHOD OF MOMENTS 154 4.3 THE METHOD OF LANCZOS 164 4.4
GENERALIZATIONS OF LANCZOS METHOD 171 4.4.1 ORTHORES 174 4.4.2
LANCZOS/ORTHORES 178 4.5 THE METHOD OF ARNOLDI 180 5 HYBRID PROCEDURES
183 5.1 THE BASIC PROCEDURE 184 5.2 RECURSIVE USE OF THE PROCEDURE 187
5.3 CONVERGENCE ACCELERATION 193 5.4 MULTIPLE HYBRID PROCEDURES 203 5.5
MULTIPARAMETER HYBRID PROCEDURES 217 5.6 CHANGING THE MINIMIZATION
CRITERION 218 6 SEMI-ITERATIVE METHODS 223 6.1 SEMI-ITERATIVE HYBRID
PROCEDURES 224 6.2 MORE PROJECTION METHODS 226 6.3 STATIONARY ITERATIVE
METHODS 229 6.4 NONSTATIONARY ITERATIVE METHODS 236 6.5 THE MINIMAL
RESIDUAL SMOOTHING METHOD 241 6.6 A HYBRID MINIMAL RESIDUAL SMOOTHING
METHOD 242 7 AROUND RICHARDSON S PROJECTION 247 7.1 THE BASIC IDEA 247
7.2 CHOICE OF THE SEARCH DIRECTION 250 7.3 CHOICE OF THE PRECONDITIONER
258 7.3.1 CONSTANT PRECONDITIONER 260 7.3.2 LINEAR ITERATIVE
PRECONDITIONER 260 7.3.3 QUADRATIC ITERATIVE PRECONDITIONER 262 7.3.4
DIRECT PRECONDITIONER 264 7.3.5 A SPARSE PRECONDITIONER 266 7.4
NUMERICAL EXAMPLES 268 7.5 ANOTHER CHOICE FOR THE SEARCH DIRECTION 271
CONTENTS VII 7.6 TWO-STEP METHODS 273 7.7 SPLITTING-UP METHODS 273 7.8
MULTIPARAMETER EXTENSIONS 276 7.9 THE SYMMETRIC POSITIVE DEFINITE CASE
284 8 SYSTEMS OF NONLINEAR EQUATIONS 287 8.1 INTRODUCTION 287 8.2
QUASI-NEWTON METHODS 289 8.2.1 A PRECONDITIONED NEWTON S METHOD 294
8.2.2 BARNES SECANT METHOD 294 8.2.3 BROYDEN METHODS 296 8.2.4 THE
E-ALGORITHMS 298 8.2.5 THE METHOD OF HENRICI 300 8.2.6 THE METHOD OF
WOLFE 302 8.3 EXTENSION OF NEWTON S METHOD 303 8.4 NONLINEAR HYBRID
PROCEDURES 308 8.4.1 THE BASIC PROCEDURE 309 8.4.2 A VECTOR SEQUENCE
TRANSFORMATION 310 8.4.3 APPLICATION TO FIXED POINT PROBLEMS 312 8.5
SOME FIXED POINT METHODS 313 8.5.1 THE METHOD OF LEMARECHAL 313 8.5.2
THE METHOD OF MARDER-WEITZNER 317 8.5.3 THE A K METHOD 318 8.5.4 A MORE
STABLE MW-TYPE SCHEME 323 8.5.5 THE METHODS OF BARZILAI-BORWEIN 325 8.6
A CHOICE FOR THE SEARCH DIRECTION 328 8.7 A MULTIPARAMETER A K METHOD
332 8.7.1 DEFINITION OF THE MULTIPARAMETER SCHEME 334 8.7.2 MINIMIZING
THE RESIDUAL 335 APPENDIX 337 SCHUR S COMPLEMENT 337 SYLVESTER S AND
SCHWEINS IDENTITIES . 338 BIBLIOGRAPHY 341 INDEX 391
|
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| author | Brezinski, Claude 1941- |
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| author_variant | c b cb |
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| bvnumber | BV011771856 |
| callnumber-first | Q - Science |
| callnumber-label | QA214 |
| callnumber-raw | QA214 |
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| callnumber-sort | QA 3214 |
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| classification_rvk | SK 915 |
| ctrlnum | (OCoLC)37928481 (DE-599)BVBBV011771856 |
| dewey-full | 512.9/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/42 |
| dewey-search | 512.9/42 |
| dewey-sort | 3512.9 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011771856 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:18:21Z |
| institution | BVB |
| isbn | 0444827773 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007944047 |
| oclc_num | 37928481 |
| open_access_boolean | |
| owner | DE-29T DE-384 DE-703 DE-11 |
| owner_facet | DE-29T DE-384 DE-703 DE-11 |
| physical | VII, 400 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Elsevier |
| record_format | marc |
| series | Studies in computational mathematics |
| series2 | Studies in computational mathematics |
| spellingShingle | Brezinski, Claude 1941- Projection methods for systems of equations Studies in computational mathematics Lineaire vergelijkingen gtt Projectiemethoden (wiskunde) gtt Equations, Simultaneous Numerical solutions Iterative methods (Mathematics) Projektionsverfahren (DE-588)4175879-1 gnd Gleichungssystem (DE-588)4128766-6 gnd |
| subject_GND | (DE-588)4175879-1 (DE-588)4128766-6 |
| title | Projection methods for systems of equations |
| title_auth | Projection methods for systems of equations |
| title_exact_search | Projection methods for systems of equations |
| title_full | Projection methods for systems of equations Claude Brezinski |
| title_fullStr | Projection methods for systems of equations Claude Brezinski |
| title_full_unstemmed | Projection methods for systems of equations Claude Brezinski |
| title_short | Projection methods for systems of equations |
| title_sort | projection methods for systems of equations |
| topic | Lineaire vergelijkingen gtt Projectiemethoden (wiskunde) gtt Equations, Simultaneous Numerical solutions Iterative methods (Mathematics) Projektionsverfahren (DE-588)4175879-1 gnd Gleichungssystem (DE-588)4128766-6 gnd |
| topic_facet | Lineaire vergelijkingen Projectiemethoden (wiskunde) Equations, Simultaneous Numerical solutions Iterative methods (Mathematics) Projektionsverfahren Gleichungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007944047&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001895633 |
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