Ridge functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
205 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | X, 207 S. |
| ISBN: | 9781107124394 |
Internformat
MARC
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| 035 | |a (OCoLC)929457357 | ||
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| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
| 300 | |a X, 207 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 205 | |
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-028335766 | ||
Datensatz im Suchindex
| _version_ | 1804175203855499264 |
|---|---|
| adam_text | Contents
Preface page vii
Glossary of Selected Symbols ix
1 Introduction 1
1.1 Motivation 1
1.2 Organization 6
1.3 Notation 8
2 Smoothness 12
2.1 Ridge Function Smoothness 12
2.2 Smoothness in the Multivariate Setting 15
3 Uniqueness 19
3.1 Ridge Function Uniqueness 19
3.2 Uniqueness in the Multivariate Setting 24
4 Identifying Functions and Directions 28
4.1 Known Directions 28
4.2 Unknown Directions 30
4.3 The Multivariate Setting 33
5 Polynomial Ridge Functions 36
5.1 Homogeneous Polynomials 36
5.2 Algebraic Polynomials 46
5.3 Waring’s Problem for Polynomials 48
5.4 Generalized Ridge Polynomials 56
6 Density and Representation 60
6.1 Density with Fixed Directions 60
6.2 Generalized Ridge Function Density 64
6.3 Density with Variable Directions 66
6.4 Representation 69
6.5 Ridgelet Density 73
v
Contents
vi
7 Closure
7.1 General Closure Results in Lp 78
7.2 Counterexamples ^0
7.3 More General Closure Results
7.4 Closure in C(K) ^7
8 Existence and Characterization of Best Approximations 90
8.1 General Results 90
8.2 LP(K)9pe( l,oo) 92
8.3 Examples 95
8.4 C(K) 98
9 Approximation Algorithms 105
9.1 Fixed Directions in Hilbert Space 106
9.2 A Greedy-Type Algorithm 123
9.3 Fixed Directions in Smooth Banach Spaces 130
9.4 The Diliberto-Straus Algorithm 135
10 Integral Representations 141
10.1 Gegenbauer Ridge Polynomials 142
10.2 Ridgelets 147
11 Interpolation at Points 152
11.1 General Results 153
11.2 Closed Paths: r = 2 157
11.3 Difference Commensurable Points 160
12 Interpolation on Lines 168
12.1 Interpolation on a Set 169
12.2 Interpolation from Л4 (a) 173
12.3 Interpolation from Л^а1, a2) on Two Straight Lines 174
12.4 First-Order Difference Equations and Interpolation from
-Mia1, a2) 186
References 196
Supplemental References 202
Author Index 205
Subject Index 207
|
| any_adam_object | 1 |
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| author_facet | Pinkus, Allan 1946- |
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| dewey-full | 515.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
| dewey-search | 515.73 |
| dewey-sort | 3515.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV042907855 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:12:34Z |
| institution | BVB |
| isbn | 9781107124394 |
| language | English |
| lccn | 2015014539 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028335766 |
| oclc_num | 929457357 |
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| owner | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| physical | X, 207 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Pinkus, Allan 1946- Verfasser (DE-588)110369297 aut Ridge functions Allan Pinkus 1. publ. Cambridge Cambridge Univ. Press 2015 X, 207 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 205 Includes bibliographical references and indexes Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 s Mehrere Variable (DE-588)4277015-4 s DE-604 Cambridge tracts in mathematics 205 (DE-604)BV000000001 205 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028335766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pinkus, Allan 1946- Ridge functions Cambridge tracts in mathematics Funktion Mathematik (DE-588)4071510-3 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4071510-3 (DE-588)4277015-4 |
| title | Ridge functions |
| title_auth | Ridge functions |
| title_exact_search | Ridge functions |
| title_full | Ridge functions Allan Pinkus |
| title_fullStr | Ridge functions Allan Pinkus |
| title_full_unstemmed | Ridge functions Allan Pinkus |
| title_short | Ridge functions |
| title_sort | ridge functions |
| topic | Funktion Mathematik (DE-588)4071510-3 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Funktion Mathematik Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028335766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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