Advances in the efficiency of computational methods and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 546 S. |
| ISBN: | 9810243367 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
ADVANCES IN THE EFFICIENCY
OF COMPUTATIONAL METHODS AND APPLICATIONS
IOANNIS K. ARGYROS DEPARTMENT OF MATHEMATICS CAMERON UNIVERSITY USA
L ^ WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG
IMAGE 2
CONTENTS
PREFACE VII
CHAPTER 1 DIVIDED DIFFERENCES 1
1.1 PARTIALLY ORDERED TOPOLOGICAL SPACES 1
1.2 DIVIDED DIFFERENCE IN A LINEAR SPACE 4
1.3 DIVIDED DIFFERENCES IN A BANACH SPACE 5
1.4 DIVIDED DIFFERENCES AND MONOTONE CONVERGENCE 11
1.5 DIVIDED DIFFERENCES AND FRECHET-DERIVATIVES 16
1.6 EXERCISES 21
CHAPTER 2 CONSTANTS AND FUNCTIONS APPEARING IN NUMERICAL METHODS 29
2.1 PRELIMINARIES 29
2.2 LIPSCHITZ CONDITIONS AND NORM ESTIMATE 34
2.3 LIPSCHITZ CONDITIONS FOR URYSON OPERATORS 36
2.4 THE CASE X = C 39
2.5 THE CASE X = LQO 41
2.6 THE CASE X = L P , 1 P 2 43
2.7 THE CASE X = LP, 2 P OO 44
2.8 EXERCISES 46
CHAPTER 3 CONVERGENCE AND ERROR ANALYSIS FOR ITERATIVE METH ODS 57
3.1 PRELIMINARIES 59
IX
IMAGE 3
X CONTENTS
3.2 A UNIFIED APPROACH FOR CONSTRUCTING INEXACT NEWTON-LIKE METHODS 61
3.3 SEMILOCAL CONVERGENCE RESULTS FOR NEWTON-LIKE METHODS . .. 80 3.4 A
FIXED POINT PROOF FOR EXTENDED NEWTON-LIKE METHODS . .. 90
3.5 A GENERALIZATION OF EDELSTEIN S THEOREM ON FIXED POINTS . .. 97
3.6 WEAK CONDITIONS FOR THE CONVERGENCE OF ITERATIONS 102
3.7 MONOTONE CONVERGENCE OF IMPLICIT NEWTON-LIKE METHODS . . . 108 3.8
GENERAL WAYS OF CONSTRUCTING ACCELERATING NEWTON-LIKE ITERA TIONS 113
3.9 A GENERALIZATION OF OSTROWSKI S THEOREM ON FIXED POINTS . . . 117
3.10 EXERCISES 120
CHAPTER 4 SPECIAL TOPICS 155
4.1 CONVERGENCE RATES FOR INEXACT NEWTON-LIKE METHODS AT SINGU LAR
POINTS 155
4.2 SMOOTHNESS AND INEXACT NEWTON-LIKE METHODS 171
4.3 CONVERGENCE DOMAINS USING OUTER OR GENERALIZED INVERSES . . 185 4.4
EXERCISES 203
CHAPTER 5 CONVERGENCE IN GENERALIZED BANACH SPACES 207
5.1 CONVERGENCE OF INEXACT NEWTON-LIKE METHODS WITH A CONVER GENCE
STRUCTURE 207
5.2 IMPROVING THE RATE OF CONVERGENCE 218
5.3 CONTROLLING THE RESIDUAIS OF INEXACT NEWTON-LIKE METHODS . . 222 5.4
EXERCISES 231
CHAPTER 6 DISCRETIZATION OF NEWTON-LIKE METHODS 247
6.1 THE MESH INDEPENDENCE PRINCIPLE FOR INEXACT NEWTON-LIKE METH ODS
247
6.2 A NEW NEWTON-MYSOVSKII-TYPE THEOREM 275
6.3 INEXACT NEWTON-GALERKIN-LIKE METHODS 296
6.4 EXERCISES 317
CHAPTER 7 CONVERGENCE ANALYSIS BASED ON THE SECOND FRECHET-DERIVATIVE
323
7.1 A NEW CONVERGENCE THEOREM BASED ON THE SECOND FRECHETDERIVATIVE 323
7.2 IMPROVED ERROR BOUNDS 331
IMAGE 4
CONTENTS XI
7.3 A NEW KANTOROVICH-TYPE THEOREM INVOLVING FIRST AND SECOND
DERIVATIVES 340
7.4 NEWTON-LIKE METHODS USING TWICE FRECHET DIFFERENTIABLE OP ERATORS
347
7.5 THE CONVERGENCE OF NEWTON S METHOD FOR POLYNOMIAL EQUATIONS 356 7.6
UNIFORM-LIKE CONTINUITY CONDITIONS 368
7.7 A GLOBAL CONVERGENCE THEOREM 376
7.8 SEMILOCAL CONVERGENCE THEOREMS I 381
7.9 SEMILOCAL CONVERGENCE THEOREMS II 390
7.10 LOCAL CONVERGENCE THEOREMS 397
7.11 MONOTONE CONVERGENCE AND DIVIDED DIFFERENCES OF ORDER TWO . 406
7.12 EXERCISES 412
CHAPTER 8 FORCING SEQUENCES AND THE SECOND FREENET-DERI VATIVE 419
8.1 RELATIONS BETWEEN FORCING SEQUENCES AND INEXACT NEWTON ITERATES419
8.2 AFFINE INVARIANT LOCAL CONVERGENCE THEOREMS FOR INEXACT NEWTONLIKE
METHODS 432
8.3 THE RADIUS OF CONVERGENCE OF NEWTON S METHOD 444
8.4 LOCAL CONVERGENCE INVOLVING THE SECOND FRECHET-DERIVATIVE . . 455
8.5 CHOOSING FORCING SEQUENCES 463
8.6 ROUNDING ERRORS 472
8.7 CONVERGENCE AND RESIDUAIS 478
8.8 RELATIONS BETWEEN FORCING SEQUENCES AND INEXACT NEWTON-LIKE ITERATES
487
8.9 EXERCISES 495
APPENDIX A NUMERICAL ALGORITHMS 503
REFERENCES 527
GLOSSARY OF SYMBOLS 543
INDEX 545
|
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| author | Argyros, Ioannis K. |
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| callnumber-raw | QA297.8 |
| callnumber-search | QA297.8 |
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| ctrlnum | (OCoLC)123123435 (DE-599)BVBBV013869215 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:28Z |
| institution | BVB |
| isbn | 9810243367 |
| language | English |
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| physical | XI, 546 S. |
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| spelling | Argyros, Ioannis K. Verfasser (DE-588)14160820X aut Advances in the efficiency of computational methods and applications Ioannis K. Argyros Singapore [u.a.] World Scientific 2000 XI, 546 S. txt rdacontent n rdamedia nc rdacarrier Iterative methods (Mathematics) Mathematical optimization Iteration (DE-588)4123457-1 gnd rswk-swf Iteration (DE-588)4123457-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486593&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Argyros, Ioannis K. Advances in the efficiency of computational methods and applications Iterative methods (Mathematics) Mathematical optimization Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4123457-1 |
| title | Advances in the efficiency of computational methods and applications |
| title_auth | Advances in the efficiency of computational methods and applications |
| title_exact_search | Advances in the efficiency of computational methods and applications |
| title_full | Advances in the efficiency of computational methods and applications Ioannis K. Argyros |
| title_fullStr | Advances in the efficiency of computational methods and applications Ioannis K. Argyros |
| title_full_unstemmed | Advances in the efficiency of computational methods and applications Ioannis K. Argyros |
| title_short | Advances in the efficiency of computational methods and applications |
| title_sort | advances in the efficiency of computational methods and applications |
| topic | Iterative methods (Mathematics) Mathematical optimization Iteration (DE-588)4123457-1 gnd |
| topic_facet | Iterative methods (Mathematics) Mathematical optimization Iteration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486593&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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