Padé approximants for operators: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1984
|
| Series: | Lecture notes in mathematics
1065 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 138 S. |
| ISBN: | 3540133429 0387133429 |
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MARC
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
List of notations VI
Summary IX
Chapter I: Abstract Pade approximarts in operator theory 1
§ 1. Motivation 1
§ 2. Introduction 1
2.1. Banach spaces and Banach algebra? 1
2.2. Linear and multilinear operators 2
2.3. Frechet derivatives 4
2.4. Abstract polynomials 5
§ 3. Definition 10
3.1. Univariate Pade approximant 10
3.2. Abstract analyticity 11
3.3. Abstract Pade approximant 13
§ 4. Existence of a solution 15
§ 5. Relations between (P,Q) and (P*,Q.) 18
5.1. Order and degree of P.Q.P* and Q^ 18
5.2. Order of F.Q^ P^ 20
§ 6. Covariance properties 24
§ 7. Recurrence relations 27
7.1. Two term identities 27
7.2. The e algorithm 28
7.3. The od algorithm 34
§ 8. Existence of an irreducible form 4 0
§ 9. Finite dimensional spaces 43
§ 10. The abstract Pade table 45
§ 11. Regularity and normality 49
11.1. Definitions 49
11.2. Normality 49
11.3. Regularity 52
11.4. Numerical examples 53
§12. Projection property and product property 53
Chapter II: ^fultivariate Pade approximants 59
§ 1. Motivation 59
§ 2. Existence of a nontrivial solution 60
§ 3. Covariance properties 62
§ 4. Near Toeplitz structure of the homogeneous system 65
4.1. Displacement rank 65
4.2. Numerical examples 68
§ S. Three term identities 69
5.1. Cross ratios 69
5.2. Three term identities 70
§ 6. Accelerating the convergence of a table with multiple entry . . 72
6.1. Table with double entry 72
6.2. Table with multiple entry 72
6.3. Applications 73
§ 7. Comparison with some other types of multivariate Pade approximants 75
7.1. General order Pade type rational approximants
introduced by Levin 76
7.2. Canterbury approximants, Lutterodt approximants and
Karlsson Wallin approximants 77
7.3. Numerical examples 81
7.4. Rational approximations of multiple power series
introduced by Million 88
§ 8. Beta function 89
8.1. Introduction 89
8.2. Numerical values 91
8.3. Figures 92
Chapter III: The solution of nonlinear operator equations .... 94
§ 1. Introduction 94
§ 2. Inverse interpolation 94
§ 3. Direct interpolation 98
§ 4. Systems of nonlinear equations 99
§ 5. Initial value problems 103
§ 6. Boundary value problems 109
§ 7. Partial differential equations 113
§ 8. Nonlinear integral equation of Fredholm type 116
§ 9. Numerical stability of the Palley iteration for the solution of
a system of nonlinear equations 122
9.1. Numerical stability of iterations 122
9.2. The Halley iteration 124
9.3. Example 129
References 133
Subject Index 137
|
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| author | Cuyt, Annie 1956- |
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| dewey-full | 510 511/.4 |
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| dewey-raw | 510 511/.4 |
| dewey-search | 510 511/.4 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:54Z |
| institution | BVB |
| isbn | 3540133429 0387133429 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000143417 |
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| physical | VIII, 138 S. |
| psigel | TUB-nvmb |
| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Cuyt, Annie 1956- Verfasser (DE-588)110252535 aut Padé approximants for operators theory and applications Annie Cuyt Berlin [u.a.] Springer 1984 VIII, 138 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1065 Opérateurs, Théorie des Padé, Approximants de Padé-benaderingen gtt Operator theory Padé approximant Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 s Operatortheorie (DE-588)4075665-8 s DE-604 Padé-Näherungsbruch (DE-588)4173061-6 s Operator (DE-588)4130529-2 s Lecture notes in mathematics 1065 (DE-604)BV000676446 1065 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cuyt, Annie 1956- Padé approximants for operators theory and applications Lecture notes in mathematics Opérateurs, Théorie des Padé, Approximants de Padé-benaderingen gtt Operator theory Padé approximant Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Padé-Näherung (DE-588)4173060-4 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4130529-2 (DE-588)4173060-4 (DE-588)4173061-6 |
| title | Padé approximants for operators theory and applications |
| title_auth | Padé approximants for operators theory and applications |
| title_exact_search | Padé approximants for operators theory and applications |
| title_full | Padé approximants for operators theory and applications Annie Cuyt |
| title_fullStr | Padé approximants for operators theory and applications Annie Cuyt |
| title_full_unstemmed | Padé approximants for operators theory and applications Annie Cuyt |
| title_short | Padé approximants for operators |
| title_sort | pade approximants for operators theory and applications |
| title_sub | theory and applications |
| topic | Opérateurs, Théorie des Padé, Approximants de Padé-benaderingen gtt Operator theory Padé approximant Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Padé-Näherung (DE-588)4173060-4 gnd Padé-Näherungsbruch (DE-588)4173061-6 gnd |
| topic_facet | Opérateurs, Théorie des Padé, Approximants de Padé-benaderingen Operator theory Padé approximant Operatortheorie Operator Padé-Näherung Padé-Näherungsbruch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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