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Advanced Courses in Mathematics - CRM Barcelona

Sparse Approximation with Bases

Authors: Temlyakov, Vladimir

Editors: Tikhonov, Sergey (Ed.)

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  • Features a thorough introduction into a new area of research (greedy approximation)
  • Deals with numerous applications
  • Recent fundamental results are combined with previous results to build the theory of greedy approximation​
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eBook 23,79 €
price for Spain (gross)
  • ISBN 978-3-0348-0890-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 31,19 €
price for Spain (gross)
  • ISBN 978-3-0348-0889-7
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book systematically presents recent fundamental results on greedy approximation with respect to bases.

Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. 

The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.

Reviews

“This book mainly deals with a kind of interesting and current nonlinear approximation called m-term approximation, or sparse approximation, with bases. … The book is based on numerous research papers of the author and is recommended to researchers working in approximation theory, numerical analysis, harmonic analysis and functional analysis. Also, it could be used for various graduate courses in the above mentioned topics.” (Sorin Gheorghe Gal, zbMATH 1317.41019, 2015)


Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Pages 1-19

    Temlyakov, Vladimir

  • Lebesgue-type Inequalities for Greedy Approximation with Respect to Some Classical Bases

    Pages 21-60

    Temlyakov, Vladimir

  • Quasi-greedy Bases and Lebesgue-type Inequalities

    Pages 61-102

    Temlyakov, Vladimir

  • Almost Greedy Bases and Duality

    Pages 103-119

    Temlyakov, Vladimir

  • Greedy Approximation with Respect to the Trigonometric System

    Pages 121-186

    Temlyakov, Vladimir

Buy this book

eBook 23,79 €
price for Spain (gross)
  • ISBN 978-3-0348-0890-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 31,19 €
price for Spain (gross)
  • ISBN 978-3-0348-0889-7
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Sparse Approximation with Bases
Authors
Editors
  • Sergey Tikhonov
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0890-3
DOI
10.1007/978-3-0348-0890-3
Softcover ISBN
978-3-0348-0889-7
Series ISSN
2297-0304
Edition Number
1
Number of Pages
XI, 261
Topics