A contemporary study of iterative methods: convergence, dynamics and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London, United Kingdom
Elsevier, Academic Press
[2018]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiv, 385 Seiten Illustrationen, Diagramme |
| ISBN: | 9780128092149 |
Internformat
MARC
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| 245 | 1 | 0 | |a A contemporary study of iterative methods |b convergence, dynamics and applications |c Á. Alberto Magreñán, Ioannis K. Argyros |
| 264 | 1 | |a London, United Kingdom |b Elsevier, Academic Press |c [2018] | |
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Datensatz im Suchindex
| _version_ | 1804178474232971264 |
|---|---|
| adam_text | Contents
1. The majorization method in the Kantorovich theory
1.1 Introduction 1
1.2 Semilocal convergence 6
1.3 Local convergence 12
1.4 Applications 14
1.5 Examples 18
References 24
2. Directional Newton methods
2.1 Introduction 27
2.2 Semilocal convergence analysis 29
References 35
3. Newton s method
3.1 Introduction 37
3.2 Convergence analysis 40
3.3 Numerical examples 42
References 46
4. Generalized equations
4.1 Introduction 49
4.2 Preliminaries 49
4.3 Local convergence 50
4.4 Special cases 55
4.5 Numerical example 56
References 57
5. Gauss-Newton method
5.1 Introduction 61
5.2 Local convergence analysis 62
• •
vn
viiî Contents
5.3 Numerical examples 64
References 66
6. Gauss-Newton method for convex optimization
6.1 Introduction 69
6.2 Gauss-Newton algorithm and quasi-regularity condition 70
6.2.1 Gauss-Newton algorithm 70
6.2.2 Quasi-regularity 71
6.3 Semilocal convergence 72
6.4 Numerical example 77
References 78
7. Proximal Gauss-Newton method
7.1 Introduction 81
7.2 Background 82
7.3 Local convergence analysis of the proximal Gauss-Newton
method 83
7.4 Numerical examples 85
References 87
8. Multistep modified Newton-Hermitian and
Skew-Hermitian Splitting method
8.1 Introduction 89
8.2 Semilocal convergence 90
8.3 Numerical examples 98
References 102
9. Secant-like methods in chemistry
9.1 Introduction 105
9.2 Convergence analysis of the secant method 107
9.2.1 Semilocal example 1 116
9.2.2 Semiiocal Example 2 119
9.3 Local convergence of the secant method 122
9.3.1 Local example 1 127
9.3.2 Local example 2 129
References 131
10. Robust convergence of Newton s method for cone
inclusion problem
10.1 Introduction 135
10.2 Semilocal analysis for Newton s method 1 36
10.3 Special cases and a numerical example 142
Contents ix
References 146
11. Gauss-Newton method for convex composite
optimization
11.1 Introduction 149
11.2 The Gauss-Newton algorithm 150
11.2.1 Regularity 150
11.3 Semiloca! convergence 152
11.4 Special cases and examples 157
References 162
12. Domain of parameters
12.1 Introduction 165
12.2 Convergence analysis 167
12.3 Numerical examples 179
References 182
13. Newton s method for solving optimal shape design
problems
13.1 Introduction 185
13.2 The mesh independence principle 186
References 196
14. Osada method
14.1 Introduction 197
14.2 Auxiliary results 199
14.3 Local convergence 201
14.4 Numerical example 206
References 207
15. Newton s method to solve equations with solutions of
multiplicity greater than one
15.1 Introduction 209
15.2 Auxiliary results 211
15.3 Ball of convergence 213
15.4 Numerical examples 219
References 221
16. Laguerre-Hke method for multiple zeros
16.1 Introduction 223
16.2 Auxiliary results 224
x Contents
16.3 Local convergence 226
16.4 Numerical examples 231
References 232
17. Traub s method for multiple roots
17.1 Introduction 233
17.2 Auxiliary results 234
17.3 Local convergence 236
17.4 Numerical examples 241
References 242
18. Shadowing lemma for operators with chaotic behavior
18.1 Introduction 243
18.2 The shadowing lemma 243
References 248
19. Inexact two-point Newton-like methods
19.1 Introduction 249
19.2 Convergence analysis for method (19.1.2) 250
19.3 Numerical examples 259
References 261
20. Two-step Newton methods
20.1 Introduction 265
20.2 Majorizing sequences for two-step Newton s method (20.1.4) 269
20.3 Majorizing sequences for two-step Newton s method (20.1.3) 277
20.4 Semilocal convergence of two-step Newton s method (20.1.4) 281
20.5 Local convergence of two-step Newton s method (20.1.4) 284
20.6 Numerical examples 286
References 291
21. Introduction to complex dynamics
21.1 Basic dynamical concepts 295
21.2 Julia and Fatou sets 301
21.3 Topological conjugations 302
21.4 Parameter planes 303
References 309
22. Convergence and the dynamics of Chebyshev-Halley
type methods
22.1 Introduction 311
Contents xi
22.2 Local convergence 313
22.3 Dynamical study of the method (22.1.2) 321
22.4 Numerical example 326
References 331
23. Convergence planes of Iterative methods
23.1 Introduction 333
23.2 Local convergence 334
23.3 Convergence planes of the method (23.1.2) applied to the
quadratic polynomial p(z) — z2 — 1 341
23.4 Numerical examples 342
References 344
24. Convergence and dynamics of a higher order family of
iterative methods
24.1 Introduction 347
24.2 Semilocal convergence 348
24.3 Local convergence 350
24.4 Dynamical Study 352
References 364
25. Convergence of iterative methods for multiple zeros
25.1 Introduction 367
25.2 Auxiliary results 370
25.3 Local convergence 371
25.4 Numerical examples 377
References 378
Index
381
A CONTEMPORARY STUDY
OF ITERATIVE METHODS
Convergence, Dynamics and Applications
Á. Alberto Magreñán and loannis K. Argyros
A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications
evaluates and compares advances in iterative techniques, also discussing their numerous
applications in applied mathematics, engineering, mathematical economics, mathematical
biology, and other applied sciences. It uses the popular iteration technique in generating
the approximate solutions of complex nonlinear equations that is suitable for aiding in the
solution of advanced problems in engineering, mathematical economics, mathematical
biology, and other applied sciences. Iteration methods are also applied for solving
optimization problems. In such cases the iteration sequences converge to an optimal
solution of the problem at hand.
Key Features
• Contains recent results on the convergence analysis of numerical algorithms in both
finite-and infinite-dimensional spaces
• Encompasses the dynamic analysis for iterative methods, including developments in
polynom iog ra phy
• Explores computation using iterative methods across nonlinear analysis
• Uniquely places discussion of derivative-free methods in the context of other
discoveries, aiding comparison and contrast between options
Professor Dr. Ángel Alberto Magreñán works in the Engineering School, Universidad
Internacional de La Rioja (UNIR) in Spain. Dr. Magreñán has published more than 65
articles and 10 books and chapters of books. He works in operator theory, computational
mathematics, iterative methods, dynamical study, computation, and image processing.
Professor Dr. loannis Argyros works in the Department of Mathematical Sciences Cameron
University, Lawton, Oklahoma, USA. He has published more than 950 articles and 25 books.
Dr. Argyros is interested in theories of inequalities, operators, computational mathematics
and iterative methods, as well as Banach spaces.
|
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| isbn | 9780128092149 |
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| spelling | Magreñán, Ángel Alberto Verfasser (DE-588)1158693869 aut A contemporary study of iterative methods convergence, dynamics and applications Á. Alberto Magreñán, Ioannis K. Argyros London, United Kingdom Elsevier, Academic Press [2018] xiv, 385 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Iteration (DE-588)4123457-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Iteration (DE-588)4123457-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Argyros, Ioannis K. Verfasser (DE-588)14160820X aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305217&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305217&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Magreñán, Ángel Alberto Argyros, Ioannis K. A contemporary study of iterative methods convergence, dynamics and applications Iteration (DE-588)4123457-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4128130-5 |
| title | A contemporary study of iterative methods convergence, dynamics and applications |
| title_auth | A contemporary study of iterative methods convergence, dynamics and applications |
| title_exact_search | A contemporary study of iterative methods convergence, dynamics and applications |
| title_full | A contemporary study of iterative methods convergence, dynamics and applications Á. Alberto Magreñán, Ioannis K. Argyros |
| title_fullStr | A contemporary study of iterative methods convergence, dynamics and applications Á. Alberto Magreñán, Ioannis K. Argyros |
| title_full_unstemmed | A contemporary study of iterative methods convergence, dynamics and applications Á. Alberto Magreñán, Ioannis K. Argyros |
| title_short | A contemporary study of iterative methods |
| title_sort | a contemporary study of iterative methods convergence dynamics and applications |
| title_sub | convergence, dynamics and applications |
| topic | Iteration (DE-588)4123457-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Iteration Numerisches Verfahren |
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