Optimal solution of nonlinear equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 238 S. graph. Darst. |
| ISBN: | 0195106903 |
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Record in the Search Index
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|---|---|
| adam_text | OPTIMAL SOLUTION OF NONLINEAR EQUATIONS KRZYSZTOF A. SIKORSKI V. OXFORD
UNIVERSITY PRESS 2001 CONTENTS 1 INTRODUCTION 3 1.1 BASIC CONCEPTS 3 1.2
FORMULATION OF THE PROBLEM 7 1.2.1 COMPUTATIONAL METHODS 8 1.2.2 OPTIMAL
COMPLEXITY METHODS 16 1.2.3 ASYMPTOTIC SETTING 18 1.2.4 EXERCISES 18 1.3
ANNOTATIONS 19 BIBLIOGRAPHY 20 2 NONLINEAR EQUATIONS 23 2.1 UNIVARIATE
PROBLEMS 25 2.1.1 OPTIMALITY OF THE BISECTION METHOD 27 2.1.2 ROOT
CRITERION IN C 34 2.1.3 RESIDUAL CRITERION IN W 37 2.1.4 GENERAL
ERROR CRITERION IN C AND W* . . . . 44 2.1.5 POLYNOMIAL EQUATIONS 46
2.1.6 ASYMPTOTIC OPTIMALITY OF THE BISECTION METHOD 56 2.1.7 EXERCISES
70 2.2 MULTIVARIATE PROBLEMS 71 2.2.1 FUNCTIONS WITH NONZERO TOPOLOGICAL
DEGREE . . 71 2.2.2 LIPSCHITZ FUNCTIONS 83 2.2.3 EXERCISES 97 2.3
ANNOTATIONS 98 2.3.1 OVERVIEW AND BRIEF HISTORY 98 2.3.2 SPECIFIC
COMMENTS 106 BIBLIOGRAPHY 108 XI XII CONTENTS 3 FIXED POINTS-CONTRACTIVE
FUNCTIONS 121 3.1 UNIVARIATE PROBLEMS 122 3.1.1 RELATIVE ERROR CRITERION
123 3.1.2 ABSOLUTE ERROR CRITERION 137 3.1.3 EXERCISES 138 3.2
MULTIVARIATE PROBLEMS 139 3.2.1 A CONSTRUCTIVE LEMMA 140 3.2.2 BALL
ITERATION 142 3.2.3 ELLIPSOID ITERATION 144 3.2.4 CENTROID METHOD 155
3.2.5 NUMERICAL TESTS 157 3.2.6 EXERCISES 162 3.3 ANNOTATIONS 162 3.3.1
SPECIFIC COMMENTS 163 BIBLIOGRAPHY 165 4 FIXED POINTS-NONCONTRACTIVE
FUNCTIONS 171 4.1 UNIVARIATE PROBLEMS 173 4.1.1 MINIMAL CARDINALITY
NUMBER 173 4.1.2 THE FPE-A METHOD 175 4.1.3 EXERCISES 177 4.2
MULTIVARIATE PROBLEMS 178 4.2.1 ABSOLUTE ERROR CRITERION 178 4.2.2
EXERCISES 187 4.3 ANNOTATIONS 188 4.3.1 GENERAL COMMENTS 188 4.3.2
RESIDUAL ERROR CRITERION 188 4.3.3 SPECIFIC COMMENTS 190 BIBLIOGRAPHY
190 5 TOPOLOGICAL DEGREE COMPUTATION 193 5.1 TWO-DIMENSIONAL LIPSCHITZ
FUNCTIONS 194 5.1.1 BASIC DEFINITIONS 195 5.1.2 LOWER BOUND ON THE
MINIMAL CARDINALITY NUM- BER 196 5.1.3 MINIMAL CARDINALITY NUMBER 199
5.1.4 COMPLEXITY OF THE PROBLEM 207 5.1.5 NUMERICAL EXPERIMENTS 208
5.1.6 EXERCISES 211 5.2 LIPSCHITZ FUNCTIONS IN D DIMENSIONS 211 CONTENTS
XIII 5.2.1 BASIC DEFINITIONS 212 5.2.2 INFORMATION N* 213 5.2.3
ALGORITHM * USING INFORMATION N* 214 5.2.4 LOWER BOUND ON THE MINIMAL
217 5.2.5 EXERCISES 226 5.3 ANNOTATIONS 226 5.3.1 SPECIFIC COMMENTS 227
BIBLIOGRAPHY 228 INDEX 233
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| isbn | 0195106903 |
| language | English |
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| physical | XIII, 238 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
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| spelling | Sikorski, Krzysztof A. Verfasser aut Optimal solution of nonlinear equations Krzysztof A. Sikorski Oxford [u.a.] Oxford Univ. Press 2001 XIII, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nichtlineare Gleichung - Lösung <Mathematik> - Numerisches Verfahren Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Gleichung (DE-588)4455337-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009351689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sikorski, Krzysztof A. Optimal solution of nonlinear equations Nichtlineare Gleichung - Lösung <Mathematik> - Numerisches Verfahren Nichtlineare Gleichung (DE-588)4455337-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4455337-7 (DE-588)4128130-5 |
| title | Optimal solution of nonlinear equations |
| title_auth | Optimal solution of nonlinear equations |
| title_exact_search | Optimal solution of nonlinear equations |
| title_full | Optimal solution of nonlinear equations Krzysztof A. Sikorski |
| title_fullStr | Optimal solution of nonlinear equations Krzysztof A. Sikorski |
| title_full_unstemmed | Optimal solution of nonlinear equations Krzysztof A. Sikorski |
| title_short | Optimal solution of nonlinear equations |
| title_sort | optimal solution of nonlinear equations |
| topic | Nichtlineare Gleichung - Lösung <Mathematik> - Numerisches Verfahren Nichtlineare Gleichung (DE-588)4455337-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Nichtlineare Gleichung - Lösung <Mathematik> - Numerisches Verfahren Nichtlineare Gleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009351689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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