Introduction to numerical continuation methods:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
Soc. for Industrial and Applied Mathematics
2003
|
| Edition: | Unabridged republ. |
| Series: | Classics in applied mathematics
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Ausg. u.d.T.: Allgower, Eugene L.: Numerical continuation methods |
| Physical Description: | XXV, 388 S. graph. Darst. |
| ISBN: | 089871544X |
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| 245 | 1 | 0 | |a Introduction to numerical continuation methods |c Eugene L. Allgower ; Kurt Georg |
| 250 | |a Unabridged republ. | ||
| 264 | 1 | |a Philadelphia, PA |b Soc. for Industrial and Applied Mathematics |c 2003 | |
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| adam_text | INTRODUCTION TO NUMERICAL CONTINUATION METHODS EUGENE L. ALLGOWER KURT
GEORG SIAJN. SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA
IX TABLE OF CONTENTS TABLE OF PSEUDO CODES XIII PREFACE TO THE CLASSICS
EDITION XV FOREWORD XXIII 1 INTRODUCTION 1 2 THE BASIC PRINCIPLES OF
CONTINUATION METHODS 7 2.1 IMPLICITLY DEFINED CURVES 7 2.2 THE BASIC
CONCEPTS OF PC METHODS 13 2.3 THE BASIC CONCEPTS OF PL METHODS 15 3
NEWTON S METHOD AS CORRECTOR 17 3.1 MOTIVATION 17 3.2 THE MOORE-PENROSE
INVERSE IN A SPECIAL CASE 18 3.3 A NEWTON S STEP FOR UNDERDETERMINED
NONLINEAR SYSTEMS ... 20 3.4 CONVERGENCE PROPERTIES OF NEWTON S METHOD
22 4 SOLVING THE LINEAR SYSTEMS 28 4.1 USING A QR DECOMPOSITION 29 4.2
GIVENS ROTATIONS FOR OBTAINING A QR DECOMPOSITION 30 4.3 ERROR ANALYSIS
31 4.4 SCALING OF THE DEPENDENT VARIABLES 34 4.5 USING LU DECOMPOSITIONS
35 5 CONVERGENCE OF EULER-NEWTON-LIKE METHODS 37 5.1 AN APPROXIMATE
EULER-NEWTON METHOD 37 5.2 A CONVERGENCE THEOREM FOR PC METHODS 38 6
STEPLENGTH ADAPTATIONS FOR THE PREDICTOR 44 6.1 STEPLENGTH ADAPTATION BY
ASYMPTOTIC EXPANSION 45 6.2 THE STEPLENGTH ADAPTATION OF DEN HEIJER &
RHEINBOLDT 50 6.3 STEPLENGTH STRATEGIES INVOLVING VARIABLE ORDER
PREDICTORS .... 55 7 PREDICTOR-CORRECTOR METHODS USING UPDATING 61 7.1
BROYDEN S GOOD UPDATE FORMULA 61 7.2 BROYDEN UPDATES ALONG A CURVE 68
X 8 DETECTION OF BIFURCATION POINTS ALONG A CURVE 75 8.1 SIMPLE
BIFURCATION POINTS 75 8.2 SWITCHING BRANCHES VIA PERTURBATION 84 8.3
BRANCHING OFF VIA THE BIFURCATION EQUATION 87 9 CALCULATING SPECIAL
POINTS OF THE SOLUTION CURVE 91 9.1 INTRODUCTION 91 9.2 CALCULATING ZERO
POINTS F(C(S)) = 0 92 9.3 CALCULATING EXTREMAL POINTS RNIN F((C(S)) 94
10 LARGE SCALE PROBLEMS 96 10.1 INTRODUCTION 96 10.2 GENERAL LARGE SCALE
SOLVERS 97 10.3 NONLINEAR CONJUGATE GRADIENT METHODS AS CORRECTORS 101
11 NUMERICALLY IMPLEMENTABLE EXISTENCE PROOFS 112 11.1 PRELIMINARY
REMARKS 112 11.2 AN EXAMPLE OF AN IMPLEMENTABLE EXISTENCE THEOREM 114
11.3 SEVERAL IMPLEMENTATIONS FOR OBTAINING BROUWER FIXED POINTS 118 11.4
GLOBAL NEWTON AND GLOBAL HOMOTOPY METHODS 123 11.5 MULTIPLE SOLUTIONS
128 11.6 POLYNOMIAL SYSTEMS 132 11.7 NONLINEAR COMPLEMENTARITY 141 11.8
CRITICAL POINTS AND CONTINUATION METHODS 145 12 PL CONTINUATION METHODS
151 12.1 INTRODUCTION 151 12.2 PL APPROXIMATIONS 156 12.3 A PL ALGORITHM
FOR TRACING H(U) = 0 159 12.4 NUMERICAL IMPLEMENTATION OF A PL
CONTINUATION ALGORITHM .. 163 12.5 INTEGER LABELING 168 12.6 TRUNCATION
ERRORS 171 13 PL HOMOTOPY ALGORITHMS 173 13.1 SET-VALUED MAPS 173 13.2
MERRILL S RESTART ALGORITHM 181 13.3 SOME TRIANGULATIONS AND THEIR
IMPLEMENTATIONS 186 13.4 THE HOMOTOPY ALGORITHM OF EAVES & SAIGAL 194
13.5 MIXING PL AND NEWTON STEPS 196 13.6 AUTOMATIC PIVOTS FOR THE
EAVES-SAIGAL ALGORITHM 201 14 GENERAL PL ALGORITHMS ON PL MANIFOLDS 203
14.1 PL MANIFOLDS 203 14.2 ORIENTATION AND INDEX 211 14.3 LEMKE S
ALGORITHM FOR THE LINEAR COMPLEMENTARITY PROBLEM . 214 14.4 VARIABLE
DIMENSION ALGORITHMS 218 14.5 EXPLOITING SPECIAL STRUCTURE 229 XI 15
APPROXIMATING IMPLICITLY DEFINED MANIFOLDS 233 15.1 INTRODUCTION 233
15.2 NEWTON S METHOD AND ORTHOGONAL DECOMPOSITIONS REVISITED . 235 15.3
THE MOVING FRAME ALGORITHM 236 15.4 APPROXIMATING MANIFOLDS BY PL
METHODS 238 15.5 APPROXIMATION ESTIMATES 245 16 UPDATE METHODS AND THEIR
NUMERICAL STABILITY 252 16.1 INTRODUCTION 252 16.2 UPDATES USING THE
SHERMAN-MORRISON FORMULA 253 16.3 QR FACTORIZATION 256 16.4 LU
FACTORIZATION 262 PI A SIMPLE PC CONTINUATION METHOD 266 P2 A PL
HOMOTOPY METHOD 273 P3 A SIMPLE EULER-NEWTON UPDATE METHOD 288 P4 A
CONTINUATION ALGORITHM FOR HANDLING BIFURCATION 296 P5 A PL SURFACE
GENERATOR 312 P6 SCOUT * SIMPLICIAL CONTINUATION UTILITIES 326 P6.1
INTRODUCTION 326 P6.2 COMPUTATIONAL ALGORITHMS 328 P6.3 INTERACTIVE
TECHNIQUES 333 P6.4 COMMANDS 335 P6.5 EXAMPLE: PERIODIC SOLUTIONS TO A
DIFFERENTIAL DELAY EQUATION 337 BIBLIOGRAPHY 346 INDEX AND NOTATION 383
|
| any_adam_object | 1 |
| author | Allgower, Eugene L. 1935- Georg, Kurt 1942-2003 |
| author_GND | (DE-588)128607270 (DE-588)172094879 |
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| discipline | Mathematik |
| edition | Unabridged republ. |
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| indexdate | 2024-07-09T19:15:19Z |
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| language | English |
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| series2 | Classics in applied mathematics |
| spelling | Allgower, Eugene L. 1935- Verfasser (DE-588)128607270 aut Numerical continuation methods Introduction to numerical continuation methods Eugene L. Allgower ; Kurt Georg Unabridged republ. Philadelphia, PA Soc. for Industrial and Applied Mathematics 2003 XXV, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in applied mathematics 45 Frühere Ausg. u.d.T.: Allgower, Eugene L.: Numerical continuation methods 1990 Continuation methods Erweiterung (DE-588)4128080-5 gnd rswk-swf Fortsetzungsmethode (DE-588)4246522-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Erweiterung (DE-588)4128080-5 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Fortsetzungsmethode (DE-588)4246522-9 s Georg, Kurt 1942-2003 Verfasser (DE-588)172094879 aut Reproduktion von Berlin : Springer, 1990 3-540-12760-7 (DE-604)BV003607364 Classics in applied mathematics 45 (DE-604)BV008258410 45 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010384027&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Allgower, Eugene L. 1935- Georg, Kurt 1942-2003 Introduction to numerical continuation methods Classics in applied mathematics Continuation methods Erweiterung (DE-588)4128080-5 gnd Fortsetzungsmethode (DE-588)4246522-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4128080-5 (DE-588)4246522-9 (DE-588)4042805-9 |
| title | Introduction to numerical continuation methods |
| title_alt | Numerical continuation methods |
| title_auth | Introduction to numerical continuation methods |
| title_exact_search | Introduction to numerical continuation methods |
| title_full | Introduction to numerical continuation methods Eugene L. Allgower ; Kurt Georg |
| title_fullStr | Introduction to numerical continuation methods Eugene L. Allgower ; Kurt Georg |
| title_full_unstemmed | Introduction to numerical continuation methods Eugene L. Allgower ; Kurt Georg |
| title_short | Introduction to numerical continuation methods |
| title_sort | introduction to numerical continuation methods |
| topic | Continuation methods Erweiterung (DE-588)4128080-5 gnd Fortsetzungsmethode (DE-588)4246522-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Continuation methods Erweiterung Fortsetzungsmethode Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010384027&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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