Asymptotics and extrapolation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
Akad.-Verl.
1996
|
| Edition: | 1. ed. |
| Series: | Mathematical research
88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 308 - 328 |
| Physical Description: | 330 S. |
| ISBN: | 3055017323 |
Staff View
MARC
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| 100 | 1 | |a Walz, Guido |e Verfasser |0 (DE-588)124600107 |4 aut | |
| 245 | 1 | 0 | |a Asymptotics and extrapolation |c Guido Walz |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1996 | |
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| 500 | |a Literaturverz. S. 308 - 328 | ||
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| 650 | 4 | |a Extrapolation | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction 11
Part I: Asymptotic Expansions
1. Asymptotic Systems and Expansions 15
1.1 Basic Definitions and Examples 15
1.2 Problems 19
2. Geometric Asymptotic Expansions 21
2.1 Asymptotic Behavior of Iteration Processes 22
2.2 Eigenvalue Expansions 29
2.2.1 One Step Matrix Iteration 29
2.2.2 The Power Method 31
2.3 Problems 37
3. Logarithmic Asymptotic Expansions 39
3.1 Some Introductory Examples 40
3.1.1 Numerical Computation of n 40
3.1.2 Continued Fractions of Poincare Type 41
3.1.3 Numerical Differentiation 43
3.1.4 Asymptotic Expansions for the Error of Best
Uniform Polynomial Approximation 44
3.2 Euler s Summation Formula and Riemann s
Zeta Function 47
3.2.1 Bernoulli Polynomials 48
3.2.2 Euler s Summation Formula 52
3.2.3 Asymptotic Expansion for the Partial Sums
of Riemann s Zeta Function 55
3.2.4 Generalization to Other Infinite Series 58
3.3 Asymptotic Expansions with a Prescribed
Limit Function 61
3.3.1 Partial Products of Infinite Products 61
8 Table of Contents
3.3.2 Use of Taylor s Expansion 65
3.3.3 Elliptic Functions and Elliptic Integrals 71
3.4 Numerical Quadrature Rules 76
3.4.1 The Classical Case: Sufficiently Smooth
Integrands 76
3.4.2 Integrands with an Endpoint Singularity 82
3.4.3 Integrands with a Singularity in the Interior
of the Integration Range 93
3.4.4 Multivariate Integration 101
3.5 Divided Differences and Numerical Differentiation.
The E Method 103
3.5.1 Classical Divided Differences 104
3.5.2 Generalized Divided Differences 109
3.5.3 The E Method 118
3.6 Discretization Methods for Ordinary Differential
Equations 128
3.6.1 One Step Methods for First Order Problems ... 130
3.6.2 Runge Kutta Methods and Generalized
Trapezoidal Rules 140
3.6.3 Linear Multistep Methods 153
3.6.4 Existence of Asymptotic Expansions 163
3.6.5 Miscellanea 180
3.7 Problems 185
Part II: Linear Extrapolation Methods
4. Fundamental Concepts and General Philosophy 193
4.1 Geometric Extrapolation 194
4.1.1 The General Situation 194
4.1.2 Extrapolation of Special Geometric
Asymptotic Expansions 200
4.1.3 Extrapolation of Supergeometric
Asymptotic Expansions 205
4.2 Logarithmic Extrapolation 208
Table of Contents 9
4.2.1 Extrapolation of Logarithmic
Asymptotic Expansions: The Procedure 209
4.2.2 Numerical Examples 211
4.2.3 The Name Extrapolation ; Generalization
to Other Index Sequences 216
4.3 Some Specific Numerical Methods as Special Cases
of Logarithmic Extrapolation 224
4.3.1 Romberg Quadrature 224
4.3.2 Richardson Extrapolation and Gragg s Method . 234
4.3.3 Numerical Computation of the Matrix Exponential 240
4.4 Problems 241
5. Error Bounds, Stopping Rules and Monotonicity 244
5.1 Asymptotic Error Bounds and Inclusions 244
5.1.1 Some Remarks on Exact Error Bounds 245
5.1.2 Asymptotic Error Bounds for Logarithmic
Extrapolation 247
5.2 Error Bounds and Stopping Rules for Normal Expansions 257
5.2.1 A Priori Error Bounds 260
5.2.2 Stopping Rules 262
5.2.3 Examples 268
5.3 Miscellanea 279
5.3.1 Propagation of Rounding Errors 279
5.3.2 Monotonicity Preserving Extrapolation 283
5.4 Problems 287
6. Generalizations and Final Remarks 289
6.1 Triangular Recursion Schemes 289
6.2 A Quite General Extrapolation Algorithm 296
6.3 Problems 302
Historical Notes 303
References 308
Index 329
|
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| ctrlnum | (OCoLC)35038720 (DE-599)BVBBV010669188 |
| discipline | Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV010669188 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:56:57Z |
| institution | BVB |
| isbn | 3055017323 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007122043 |
| oclc_num | 35038720 |
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| owner_facet | DE-12 DE-703 DE-824 DE-91G DE-BY-TUM DE-521 DE-83 DE-11 DE-188 |
| physical | 330 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Walz, Guido Verfasser (DE-588)124600107 aut Asymptotics and extrapolation Guido Walz 1. ed. Berlin Akad.-Verl. 1996 330 S. txt rdacontent n rdamedia nc rdacarrier Mathematical research 88 Literaturverz. S. 308 - 328 Asymptotic expansions Extrapolation Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Extrapolation (DE-588)4153421-9 gnd rswk-swf Extrapolation (DE-588)4153421-9 s DE-604 Asymptotische Entwicklung (DE-588)4112609-9 s Mathematical research 88 (DE-604)BV000008585 88 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007122043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walz, Guido Asymptotics and extrapolation Mathematical research Asymptotic expansions Extrapolation Asymptotische Entwicklung (DE-588)4112609-9 gnd Extrapolation (DE-588)4153421-9 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4153421-9 |
| title | Asymptotics and extrapolation |
| title_auth | Asymptotics and extrapolation |
| title_exact_search | Asymptotics and extrapolation |
| title_full | Asymptotics and extrapolation Guido Walz |
| title_fullStr | Asymptotics and extrapolation Guido Walz |
| title_full_unstemmed | Asymptotics and extrapolation Guido Walz |
| title_short | Asymptotics and extrapolation |
| title_sort | asymptotics and extrapolation |
| topic | Asymptotic expansions Extrapolation Asymptotische Entwicklung (DE-588)4112609-9 gnd Extrapolation (DE-588)4153421-9 gnd |
| topic_facet | Asymptotic expansions Extrapolation Asymptotische Entwicklung |
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