Laurent series and their Padé approximations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston
Birkhäuser Verlag
1987
|
| Series: | Operator theory
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 274 Seiten |
| ISBN: | 3764319402 0817619402 |
Staff View
MARC
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| 100 | 1 | |a Bultheel, Adhemar |4 aut | |
| 245 | 1 | 0 | |a Laurent series and their Padé approximations |
| 264 | 1 | |a Basel ; Boston |b Birkhäuser Verlag |c 1987 | |
| 300 | |a xi, 274 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 27 | |
| 650 | 4 | |a Laurent, Séries de | |
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| 650 | 4 | |a Padé approximant | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface ix
2. Introduction 1
2.1 Classical Pade approximation 1
2.2 Toeplitz and Hankel systems 2
2.3 Continued fractions 3
2.4 Orthogonal polynomials 4
2.5 Rhombus algorithms and convergence 5
2.6 Block, structure 5
2.7 Laurent Pade approximants 6
2.8 The projection method 7
2.9 Applications 7
2.10 Outline 10
3. Moebius transforms, continued fractions and Pade
approximants 11
3.1 Moebius transforms 11
3.2 How graphs 14
3.3 Continued fractions (CF) 18
3.4 Formal series 22
3.5 Pade approximants 24
4. Two algorithms 29
4.1 Algorithm 1 29
4.2 Algorithm 2 32
5. All kinds of Pade Approximants . 37
5.1 Pade approximants 37
5.2 Laurent Pade approximants 39
5.3 Two point Pade approximants 43
6. Continued fractions 47
6.1 General observations 47
6.2 Some special cases 49
7. Moebius transforms 55
7.1 General observations 55
7.2 Some special cases 57
8. Rhombus algorithms 65
vi CONTENTS
8.1 The ab parameters (sawtooth path) 65
8.2 The FG parameters (row path) 72
8.3 A staircase path 73
8.4 pa paramaters (diagonal path) 75
8.5 Some dual results 77
8.6 Relation with classical algorithms 81
9. Biorthogonal polynomials, quadrature and reproducing
kernels 83
9.1 Biorthogonal polynomials 83
9.2 Interpolatory quadrature methods 90
9.3 Reproducing kernels 94
9.4 Other orthogonality relations 98
10. Determinant expressions and matrix interpretations 103
10.1 Determinant expressions 103
10.2 Matrix interpretations 112
10.2.1 Toeplitz matrices 112
10.2.2 Hankel matrices 122
10.2.3 Tridiagonal matrices 127
11. Symmetry Properties 132
11.1 Symmetry for F(z) and F(z) = F(l/z) 132
11.2 Symmetry for F(z) and G(z)= /F(z) 136
12. Block structures 141
12.1 Pade forms, Laurent Pade forms and two point Pade
forms 141
12.2 The Stable 143
12.3 The Pade, Laurent Pade, and two point Pade tables 149
13. Meromorphic functions and asymptotic behaviour . . 155
13.1 The function F(z) 155
13.2 Asymptotics for finite Toeplitz determinants 156
13.3 Asymptotics for infinite Toeplitz determinants 159
13.4 Consequences for the T table 163
14. Montessus de Ballore theorem for Laurent Pade
approximants 167
14.1 Semi infinite Laurent series 167
14.2 Bi infinite Laurent series 170
15. Determination of poles 173
15.1 Rutishauser polynomials of type 1 and type 2 173
15.2 Rutishauser polynomials of type 3 179
15.3 Rutishauser polynomials and Laurent series 181
CONTENTS vii
15.4 Convergence of parameters 183
16. Determination of zeros 187
16.1 Dual Rutishauser polynomials and semi infinite
series 187
16.2 From semi infinite to bi infinite series 189
16.3 Convergence of parameters 193
17. Convergence in a row of the Laurent Pade table 195
17.1 Toeplitz operators and the projection method 197
17.2 Convergence of the denominator 199
17.3 Convergence of the numerator 203
18. The positive definite case and applications 207
18.1 Function classes 207
18.2 Connection with the previous results 212
18.3 Stochastic processes and systems 219
18.4 Lossless inverse scattering and transmission lines 224
18.5 Laurent Pade approximation and ARMA filtering 230
18.6 Concluding remarks 231
19. Examples 233
19.1 Example 1 233
19.2 Example 2 248
19.3 Example 3 253
References 257
List of symbols 263
Subject index 271
|
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| id | DE-604.BV000725878 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:18:28Z |
| institution | BVB |
| isbn | 3764319402 0817619402 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000454020 |
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| physical | xi, 274 Seiten |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Bultheel, Adhemar aut Laurent series and their Padé approximations Basel ; Boston Birkhäuser Verlag 1987 xi, 274 Seiten txt rdacontent n rdamedia nc rdacarrier Operator theory 27 Laurent, Séries de Padé, Approximants de Laurent series Padé approximant Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Laurent-Reihe (DE-588)4192933-0 gnd rswk-swf Laurent-Entwicklung (DE-588)4224176-5 gnd rswk-swf Laurent-Reihe (DE-588)4192933-0 s Padé-Näherung (DE-588)4173060-4 s DE-604 Laurent-Entwicklung (DE-588)4224176-5 s Erscheint auch als Online-Ausgabe 978-3-0348-9306-0 Operator theory 27 (DE-604)BV000000970 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bultheel, Adhemar Laurent series and their Padé approximations Operator theory Laurent, Séries de Padé, Approximants de Laurent series Padé approximant Padé-Näherung (DE-588)4173060-4 gnd Laurent-Reihe (DE-588)4192933-0 gnd Laurent-Entwicklung (DE-588)4224176-5 gnd |
| subject_GND | (DE-588)4173060-4 (DE-588)4192933-0 (DE-588)4224176-5 |
| title | Laurent series and their Padé approximations |
| title_auth | Laurent series and their Padé approximations |
| title_exact_search | Laurent series and their Padé approximations |
| title_full | Laurent series and their Padé approximations |
| title_fullStr | Laurent series and their Padé approximations |
| title_full_unstemmed | Laurent series and their Padé approximations |
| title_short | Laurent series and their Padé approximations |
| title_sort | laurent series and their pade approximations |
| topic | Laurent, Séries de Padé, Approximants de Laurent series Padé approximant Padé-Näherung (DE-588)4173060-4 gnd Laurent-Reihe (DE-588)4192933-0 gnd Laurent-Entwicklung (DE-588)4224176-5 gnd |
| topic_facet | Laurent, Séries de Padé, Approximants de Laurent series Padé approximant Padé-Näherung Laurent-Reihe Laurent-Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT bultheeladhemar laurentseriesandtheirpadeapproximations |