Convergence of iterations for linear equations
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel u.a.
Birkhäuser
1993
|
| Schriftenreihe: | Lectures in mathematics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Nevanlinna, Olavi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Convergence of iterations for linear equations |c Olavi Nevanlinna |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1993 | |
| 300 | |a VII, 177 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Lectures in mathematics | |
| 650 | 7 | |a Convergence (Mathématiques) |2 ram | |
| 650 | 7 | |a Convergentie (wiskunde) |2 gtt | |
| 650 | 7 | |a Equations - Solutions numériques |2 ram | |
| 650 | 7 | |a Iteratief oplossen |2 gtt | |
| 650 | 7 | |a Itération (Mathématiques) |2 ram | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Convergence | |
| 650 | 4 | |a Equations |x Numerical solutions | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
| 650 | 0 | 7 | |a Lineare Gleichung |0 (DE-588)4234490-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvergenz |0 (DE-588)4032326-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Iteration |0 (DE-588)4123457-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Gleichung |0 (DE-588)4234490-6 |D s |
| 689 | 0 | 1 | |a Iteration |0 (DE-588)4123457-1 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-004627843 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 650f 2001 A 26253 |
|---|---|
| DE-BY-TUM_katkey | 587885 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010505703 |
| _version_ | 1820813056819593216 |
| adam_text | Contents
Preface vii
1. Motivation, problem and notation
1.1 Motivation 1
1.2 Problem formulation 1
1.3 Usual tools 2
1.4 Notation for polynomial acceleration 2
1.5 Minimal error and minimal residual 5
1.6 Approximation of the solution operator 6
1.7 Location of zeros 7
1.8 Heuristics 9
Comments to Chapter 1 11
2. Spectrum, resolvent and power boundedness
2.1 The spectrum 13
2.2 The resolvent 17
2.3 The spectral mapping theorem 22
2.4 Continuity of the spectrum 23
2.5 Equivalent norms 26
2.6 The Yosida approximation 29
2.7 Power bounded operators 30
2.8 Minimal polynomials and algebraic operators 34
2.9 Quasialgebraic operators 41
2.10 Polynomial numerical hull 41
Comments to Chapter 2 44
3. Linear convergence
3.1 Preliminaries 46
3.2 Generating functions and asymptotic convergence factors 47
3.3 Optimal reduction factor 52
3.4 Green s function for Goo 57
3.5 Optimal polynomials for E 63
3.6 Simply connected Goo (i) 72
3.7 Stationary recursions 77
3.8 Simple examples 81
Comments to Chapter 3 85
4. Sublinear convergence
4.1 Introduction 86
4.2 Convergence of Lk{L 1) 88
4.3 Splitting into invariant subspaces 90
4.4 Uniform convergence 95
4.5 Nonisolated singularity and successive approximation 99
4.6 Nonisolated singularity and polynomial acceleration 103
4.7 Fractional powers of operators 111
4.8 Convergence of iterates 113
4.9 Convergence with speed 116
Comments to Chapter 4 123
V
vi
5. Superlinear convergence
5.1 What is superlinear 124
5.2 Introductory examples 125
5.3 Order and type 133
5.4 Finite termination 137
5.5 Lower and upper bounds for optimal polynomials 139
5.6 Infinite products 144
5.7 Almost algebraic operators 145
5.8 Estimates using singular values 157
5.9 Multiple clusters 163
5.10 Approximation with algebraic operators 165
5.11 Locally superlinear implies superlinear 177
Comments to Chapter 5 169
References 171
Definitions 175
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| id | DE-604.BV007222736 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T12:23:07Z |
| institution | BVB |
| isbn | 3764328657 0817628657 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004627843 |
| oclc_num | 27679137 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-824 DE-20 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | VII, 177 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lectures in mathematics |
| spellingShingle | Nevanlinna, Olavi Convergence of iterations for linear equations Convergence (Mathématiques) ram Convergentie (wiskunde) gtt Equations - Solutions numériques ram Iteratief oplossen gtt Itération (Mathématiques) ram Numerieke methoden gtt Convergence Equations Numerical solutions Iterative methods (Mathematics) Lineare Gleichung (DE-588)4234490-6 gnd Konvergenz (DE-588)4032326-2 gnd Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4234490-6 (DE-588)4032326-2 (DE-588)4123457-1 |
| title | Convergence of iterations for linear equations |
| title_auth | Convergence of iterations for linear equations |
| title_exact_search | Convergence of iterations for linear equations |
| title_full | Convergence of iterations for linear equations Olavi Nevanlinna |
| title_fullStr | Convergence of iterations for linear equations Olavi Nevanlinna |
| title_full_unstemmed | Convergence of iterations for linear equations Olavi Nevanlinna |
| title_short | Convergence of iterations for linear equations |
| title_sort | convergence of iterations for linear equations |
| topic | Convergence (Mathématiques) ram Convergentie (wiskunde) gtt Equations - Solutions numériques ram Iteratief oplossen gtt Itération (Mathématiques) ram Numerieke methoden gtt Convergence Equations Numerical solutions Iterative methods (Mathematics) Lineare Gleichung (DE-588)4234490-6 gnd Konvergenz (DE-588)4032326-2 gnd Iteration (DE-588)4123457-1 gnd |
| topic_facet | Convergence (Mathématiques) Convergentie (wiskunde) Equations - Solutions numériques Iteratief oplossen Itération (Mathématiques) Numerieke methoden Convergence Equations Numerical solutions Iterative methods (Mathematics) Lineare Gleichung Konvergenz Iteration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004627843&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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