Greedy approximation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Series: | Cambridge monographs on applied and computational mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 418 S. |
| ISBN: | 9781107003378 |
Staff View
MARC
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| 245 | 1 | 0 | |a Greedy approximation |c Vladimir Temlyakov |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page
ix
Greedy approximation with regard to bases
Introduction
Schauder
bases in Banach spaces
Greedy bases
Quasi-greedy and almost greedy bases
Weak Greedy Algorithms with respect to bases
Thresholding and minimal systems
Greedy approximation with respect to the trigonometric
system
Greedy-type bases; direct and inverse theorems
Some further results
Systems
L p
-equivalent to the
Haar
basis
Open problems
Greedy approximation with respect to dictionaries:
Hilbert spaces
Introduction
Convergence
Rate of convergence
Greedy algorithms for systems that are not dictionaries
Greedy approximation with respect to
λ
-quasi-orthogonal
dictionaries
Lebesgue-type inequalities for greedy approximation
Saturation property of greedy-type algorithms
Some further remarks
Open problems
Entropy
Introduction: definitions and some simple properties
vi
Contents
3.2
Finite
dimensional
spaces
144
3.3
Trigonometric polynomials and volume estimates
151
3.4
The function classes
165
3.5
General inequalities
168
3.6
Some further remarks
175
3.7
Open problems
182
4
Approximation in learning theory
183
4.1
Introduction
183
4.2
Some basic concepts of probability theory
189
4.3
Improper function learning; upper estimates
206
4.4
Proper function learning; upper estimates
235
4.5
The lower estimates
253
4.6
Application of greedy algorithms in learning theory
270
5
Approximation in compressed sensing
277
5.1
Introduction
277
5.2
Equivalence of three approximation properties of the
compressed sensing matrix
283
5.3
Construction of a good matrix
287
5.4
Dealing with noisy data
294
5.5
First results on exact recovery of sparse signals;
the Orthogonal Greedy Algorithm
298
5.6
Exact recovery of sparse signals; the Subspace Pursuit
Algorithm
305
5.7
On the size of incoherent systems
314
5.8
Restricted Isometry Property for random matrices
327
5.9
Some further remarks
330
5.10
Open problems
332
6
Greedy approximation with respect to dictionaries:
Banach spaces
334
6.1
Introduction
334
6.2
The Weak Chebyshev Greedy Algorithm
340
6.3
Relaxation; co-convex approximation
347
6.4
Free relaxation
350
6.5
Fixed relaxation
354
6.6
Thresholding algorithms
359
6.7
Greedy expansions
363
6.8
Relaxation; X-greedy algorithms
378
6.9
Incoherent dictionaries and exact recovery
381
6.10
Greedy algorithms with approximate evaluations
and restricted search
385
Contents
vii
6.11 An
application
of greedy algorithms for the discrepancy
estimates
390
6.12
Open problems
404
References
405
Index
415
|
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| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV039700452 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:09:17Z |
| institution | BVB |
| isbn | 9781107003378 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024549013 |
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| physical | XIV, 418 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge monographs on applied and computational mathematics |
| series2 | Cambridge monographs on applied and computational mathematics |
| spelling | Temlyakov, Vladimir 1953- Verfasser (DE-588)102386116X aut Greedy approximation Vladimir Temlyakov Cambridge [u.a.] Cambridge Univ. Press 2011 XIV, 418 S. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on applied and computational mathematics 20 Nichtlineare Approximation (DE-588)4127922-0 gnd rswk-swf Approximationsalgorithmus (DE-588)4500954-5 gnd rswk-swf Greedy-Algorithmus (DE-588)4331446-6 gnd rswk-swf Greedy-Algorithmus (DE-588)4331446-6 s Approximationsalgorithmus (DE-588)4500954-5 s Nichtlineare Approximation (DE-588)4127922-0 s DE-604 Cambridge monographs on applied and computational mathematics 20 (DE-604)BV011073737 20 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024549013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Temlyakov, Vladimir 1953- Greedy approximation Cambridge monographs on applied and computational mathematics Nichtlineare Approximation (DE-588)4127922-0 gnd Approximationsalgorithmus (DE-588)4500954-5 gnd Greedy-Algorithmus (DE-588)4331446-6 gnd |
| subject_GND | (DE-588)4127922-0 (DE-588)4500954-5 (DE-588)4331446-6 |
| title | Greedy approximation |
| title_auth | Greedy approximation |
| title_exact_search | Greedy approximation |
| title_full | Greedy approximation Vladimir Temlyakov |
| title_fullStr | Greedy approximation Vladimir Temlyakov |
| title_full_unstemmed | Greedy approximation Vladimir Temlyakov |
| title_short | Greedy approximation |
| title_sort | greedy approximation |
| topic | Nichtlineare Approximation (DE-588)4127922-0 gnd Approximationsalgorithmus (DE-588)4500954-5 gnd Greedy-Algorithmus (DE-588)4331446-6 gnd |
| topic_facet | Nichtlineare Approximation Approximationsalgorithmus Greedy-Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024549013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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