Selected topics in approximation and computation:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Oxford Univ. Press
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 349 S. graph. Darst. |
| ISBN: | 0195080599 |
Staff View
MARC
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| 100 | 1 | |a Kowalski, Marek A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Selected topics in approximation and computation |c Marek A. Kowalski ; Krzysztof A. Sikorski ; Frank Stenger |
| 264 | 1 | |a New York u.a. |b Oxford Univ. Press |c 1995 | |
| 300 | |a XIV, 349 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Approximation, Théorie de l' |2 ram | |
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| 700 | 1 | |a Sikorski, Krzysztof A. |e Verfasser |4 aut | |
| 700 | 1 | |a Stenger, Frank |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Classical Approximation 1
1.1 General results 1
1.1.1 Exercises 12
1.2 Approximation in unitary spaces 13
1.2.1 Computing the best approximation 17
1.2.2 Completeness of orthogonal systems 20
1.2.3 Examples of orthogonal systems 21
1.2.4 Remarks on convergence of Fourier series ... 34
1.2.5 Exercises 36
1.3 Uniform approximation 39
1.3.1 Chebyshev subspaces 42
1.3.2 Maximal functional 47
1.3.3 The Remez algorithm 56
1.3.4 The Korovkin operators 58
1.3.5 Quality of polynomial approximations 63
1.3.6 Converse theorems in polynomial approximation 66
1.3.7 Projection operators 72
1.3.8 Exercises 83
1.4 Annotations 87
1.5 References 89
2 Splines 93
2.1 Polynomial splines 93
2.1.1 Exercises 102
2.2 B splines 103
2.2.1 General spline interpolation 109
2.2.2 Exercises 110
2.3 General splines Ill
2.3.1 Exercises 114
2.4 Annotations 114
2.5 References 115
jrii CONTENTS
3 Sine Approximation 117
3.1 Basic definitions 117
3.1.1 Exercises 125
3.2 Interpolation and quadrature 126
3.2.1 Exercises 132
3.3 Approximation of derivatives on F 134
3.3.1 Exercises 136
3.4 Sine indefinite integral over F 136
3.4.1 Exercises 139
3.5 Sine indefinite convolution over F 139
3.5.1 Derivation and justification of procedure .... 141
3.5.2 Multidimensional indefinite convolutions .... 146
3.5.3 Two dimensional convolution 147
3.5.4 Exercises 149
3.6 Annotations 150
3.7 References 150
4 Explicit Sine Like Methods 153
4.1 Positive base approximation 153
4.1.1 Exercises 158
4.2 Approximation via elliptic functions 158
4.2.1 Exercises 160
4.3 Heaviside, filter, and delta functions 161
4.3.1 Heaviside function 162
4.3.2 The filter or characteristic function 163
4.3.3 The impulse or delta function 164
4.3.4 Exercises 166
4.4 Annotations 166
4.5 References 166
5 Moment Problems 169
5.1 Duality with approximation 170
5.1.1 Exercises . 175
5.2 The moment problem in the space Cq{D) 175
5.3 Classical moment problems 178
5.3.1 Exercises 185
5.4 Density and determinateness 189
5.4.1 Exercises 203
5.5 A Sine moment problem 205
5.5.1 Exercises 206
5.6 Multivariate orthogonal polynomials 206
5.6.1 Exercises 218
CONTENTS xiii
5.7 Annotations 219
5.8 References 220
6 n Widths and s Numbers 223
6.1 H Widths 223
6.1.1 Relationships between n widths 229
6.1.2 Algebraic versions of an and cn 235
6.1.3 Exercises 236
6.2 s Numbers 237
6.2.1 s Numbers and singular values 240
6.2.2 Relationships between s numbers 246
6.2.3 Exercises 255
6.3 Annotations 255
6.4 References 256
7 Optimal Approximation Methods 259
7.1 A general approximation problem 262
7.1.1 Radius of information—optimal algorithms . .264
7.1.2 Exercises 270
7.2 Linear problems 270
7.2.1 Optimal information 276
7.2.2 Relations to n widths 281
7.2.3 Exercises 285
7.3 Parallel versus sequential methods 286
7.3.1 Exercises 290
7.4 Linear and spline algorithms 291
7.4.1 Spline algorithms 295
7.4.2 Relations to linear Kolmogorov n widths . . . 302
7.4.3 Exercises 304
7.5 s Numbers, minimal errors 304
7.5.1 Exercises 309
7.6 Optimal methods 310
7.6.1 Optimal complexity methods for linear problems312
7.6.2 Exercises 314
7.7 Annotations 314
7.8 References 316
8 Applications 319
8.1 Sine solution of Burgers equation 319
8.2 Signal recovery 321
8.2.1 Formulation of the problem 321
8.2.2 Relations to n widths 322
xiv CONTENTS
8.2.3 Algorithms and their errors 325
8.2.4 Asymptotics of minimal cost 332
8.2.5 Exercises 333
8.3 Bisection method 334
8.3.1 Formulation of the problem 334
8.3.2 Optimality theorem 335
8.3.3 Exercises 340
8.4 Annotations 340
8.5 References 340
Index 343
|
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| id | DE-604.BV010641947 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:28Z |
| institution | BVB |
| isbn | 0195080599 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007100443 |
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| physical | XIV, 349 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Kowalski, Marek A. Verfasser aut Selected topics in approximation and computation Marek A. Kowalski ; Krzysztof A. Sikorski ; Frank Stenger New York u.a. Oxford Univ. Press 1995 XIV, 349 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Approximation, Théorie de l' ram Approximation theory Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s DE-604 Sikorski, Krzysztof A. Verfasser aut Stenger, Frank Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007100443&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kowalski, Marek A. Sikorski, Krzysztof A. Stenger, Frank Selected topics in approximation and computation Approximation, Théorie de l' ram Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4120913-8 |
| title | Selected topics in approximation and computation |
| title_auth | Selected topics in approximation and computation |
| title_exact_search | Selected topics in approximation and computation |
| title_full | Selected topics in approximation and computation Marek A. Kowalski ; Krzysztof A. Sikorski ; Frank Stenger |
| title_fullStr | Selected topics in approximation and computation Marek A. Kowalski ; Krzysztof A. Sikorski ; Frank Stenger |
| title_full_unstemmed | Selected topics in approximation and computation Marek A. Kowalski ; Krzysztof A. Sikorski ; Frank Stenger |
| title_short | Selected topics in approximation and computation |
| title_sort | selected topics in approximation and computation |
| topic | Approximation, Théorie de l' ram Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Approximation, Théorie de l' Approximation theory Approximationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007100443&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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