Multivariate polynomial approximation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
2003
|
| Series: | International series of numerical mathematics
144 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 358 S. Ill., graph. Darst. |
| ISBN: | 3764316381 |
Staff View
MARC
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| 100 | 1 | |a Reimer, Manfred |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multivariate polynomial approximation |c Manfred Reimer |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a X, 358 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of numerical mathematics |v 144 | |
| 650 | 7 | |a Análise multivariada |2 larpcal | |
| 650 | 7 | |a Aproximação por polinomios |2 larpcal | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Polynomials | |
| 650 | 0 | 7 | |a Multivariates Polynom |0 (DE-588)4645038-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Polynomapproximation |0 (DE-588)4197097-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Multivariate Approximation |0 (DE-588)4314108-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Polynomapproximation |0 (DE-588)4197097-4 |D s |
| 689 | 0 | 1 | |a Multivariates Polynom |0 (DE-588)4645038-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Multivariate Approximation |0 (DE-588)4314108-0 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-010441735 | ||
Record in the Search Index
| _version_ | 1804130160924950528 |
|---|---|
| adam_text | Contents
Preface
ix
I Introduction
1
1
Basic Principles and Facts
3
1.1
Preliminaries
.............................. 3
1.2
Existence of a Reproducing Kernel Function
............. 4
1.3
Rotation-Invariant Spaces
....................... 5
1.4
Rotation Principles,
Т
-Kernels....................
8
1.5
Averages and
Т
-Kernel Projections
.................. 10
1.6
Reproducing Kernels in C^S7 1)
................... 16
1.7
Problems
................................ 18
2 Gegenbauer
Polynomials
19
2.1
Generating Function
.......................... 19
2.2
Differential Equation
.......................... 23
2.3
Orthogonality
.............................. 25
2.4
Bessel Functions
............................ 28
2.5
Asymptotics
............................... 31
2.6
Asymptotics of the
Gegenbauer
Zeros
................ 35
2.7
Problems
................................ 37
II Approximation Means
39
3
Multivariate Polynomials
41
3.1
The Zoo of Multivariate Polynomiak
................. 41
3.2
Polynomials on Subsets
........................ 64
3.3
Problems
................................ 65
vi
Contents
4
Polynomials on Sphere and Ball
67
4.1
The Rotation-Invariant Subspaces of Fr (S7-1)
........... 67
4.2
Biorthonormal Systems on the Sphere
................ 81
4.3
Biorthonormal Systems on the Ball
.................. 98
4.4
The Image of G^+/t(a ·) under
Т
-Kernel Projections
........ 104
4.5
Problems
................................ 108
III Multivariate Approximation
109
5
Approximation Methods 111
5.1
Bounded Linear Operators
.......................
Ill
5.2
Bernstein Polynomials and the Theorem of
Weierstrass
....... 119
5.3
Best Approximation and Projections
................. 122
5.4
Interpolatory
Projections in C(D)
................... 130
5.5
Extremal Bases and Extremal Fundamental Systems
........ 136
5.6
Quadrature
............................... 149
5.7
Best Approximation in the Maximum Norm
............. 158
5.8
Examples
................................ 164
5.9
Problems
................................ 176
6
Approximation on the Sphere
179
6.1
Orthogonal Projections and Laplace Series
.............. 179
6.2
Minimal Projection in the Uniform Norm
.............. 182
6.3
Interpolation on the Sphere
...................... 192
6.4
Quadrature on the Sphere
....................... 203
6.5
Geometry of Nodes and Weights in a Positive Quadrature
..... 217
6.6
Hyperinterpolation on the Sphere
................... 226
6.7
Summation of Laplace Series
..................... 230
6.8
Generalized Hyperinterpolation
.................... 244
6.9
Moduli of Continuity and the Approximation Order
........ 247
6.10
Truncated Generalized Hyperinterpolation
.............. 254
6.11
Problems
................................ 262
7
Approximation on the Ball
263
7.1
Orthogonal Projections and
Appell
Series
.............. 263
7.2
Summation of
Appell
Series
...................... 265
7.3
Interpolation on the Ball
........................ 269
7.4
Quadrature on Sphere and Ball are Related Topics
......... 276
7.5
Hyperinterpolation and Generalized Hyperinterpolation
...... 280
7.6
Evaluation of Multivariate Orthogonal Expansions
......... 280
7.7
Problems
................................ 282
Contents
vii
IV
Applications 283
8
Tomography
285
8.1 Radon
Transform
............................ 286
8.2
Adjoint Operator and the Inverse
................... 288
8.3
Reconstruction by Approximation
.................. 292
8.4
Complexity and Stability
....................... 297
8.5
k-Plane Transform
........................... 301
8.6
Problems
................................ 303
Appendix
305
A Legendre Basis
307
В
Zeros of the Kernel Function
311
С
Newman-Shapiro Operators
313
D
Reconstruction
317
E
Solutions
323
Bibliography
345
Index
351
|
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)52728783 (DE-599)BVBBV017323154 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.4 |
| dewey-search | 511/.4 |
| dewey-sort | 3511 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017323154 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:16:37Z |
| institution | BVB |
| isbn | 3764316381 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010441735 |
| oclc_num | 52728783 |
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| owner_facet | DE-20 DE-824 DE-703 DE-739 DE-706 DE-634 DE-355 DE-BY-UBR DE-11 |
| physical | X, 358 S. Ill., graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series | International series of numerical mathematics |
| series2 | International series of numerical mathematics |
| spelling | Reimer, Manfred Verfasser aut Multivariate polynomial approximation Manfred Reimer Basel [u.a.] Birkhäuser 2003 X, 358 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of numerical mathematics 144 Análise multivariada larpcal Aproximação por polinomios larpcal Approximation theory Multivariate analysis Polynomials Multivariates Polynom (DE-588)4645038-5 gnd rswk-swf Polynomapproximation (DE-588)4197097-4 gnd rswk-swf Multivariate Approximation (DE-588)4314108-0 gnd rswk-swf Polynomapproximation (DE-588)4197097-4 s Multivariates Polynom (DE-588)4645038-5 s DE-604 Multivariate Approximation (DE-588)4314108-0 s International series of numerical mathematics 144 (DE-604)BV035415862 144 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reimer, Manfred Multivariate polynomial approximation International series of numerical mathematics Análise multivariada larpcal Aproximação por polinomios larpcal Approximation theory Multivariate analysis Polynomials Multivariates Polynom (DE-588)4645038-5 gnd Polynomapproximation (DE-588)4197097-4 gnd Multivariate Approximation (DE-588)4314108-0 gnd |
| subject_GND | (DE-588)4645038-5 (DE-588)4197097-4 (DE-588)4314108-0 |
| title | Multivariate polynomial approximation |
| title_auth | Multivariate polynomial approximation |
| title_exact_search | Multivariate polynomial approximation |
| title_full | Multivariate polynomial approximation Manfred Reimer |
| title_fullStr | Multivariate polynomial approximation Manfred Reimer |
| title_full_unstemmed | Multivariate polynomial approximation Manfred Reimer |
| title_short | Multivariate polynomial approximation |
| title_sort | multivariate polynomial approximation |
| topic | Análise multivariada larpcal Aproximação por polinomios larpcal Approximation theory Multivariate analysis Polynomials Multivariates Polynom (DE-588)4645038-5 gnd Polynomapproximation (DE-588)4197097-4 gnd Multivariate Approximation (DE-588)4314108-0 gnd |
| topic_facet | Análise multivariada Aproximação por polinomios Approximation theory Multivariate analysis Polynomials Multivariates Polynom Polynomapproximation Multivariate Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
| work_keys_str_mv | AT reimermanfred multivariatepolynomialapproximation |