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Sparse approximation with bases

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Sparse approximation with bases

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sparse approximation with basesby Vladimir Temlyakov ; edited by Sergey Tikhonov.
Author:	Temlyakov, Vladimir.
other author:	Tikhonov, Sergey.
Published:	Basel :Springer Basel :2015.
Description:	xi, 261 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Approximation theory.
Online resource:	http://dx.doi.org/10.1007/978-3-0348-0890-3
ISBN:	9783034808903 (electronic bk.)

Sparse approximation with bases
Temlyakov, Vladimir.

Sparse approximation with bases[electronic resource] /by Vladimir Temlyakov ; edited by Sergey Tikhonov. - Basel :Springer Basel :2015. - xi, 261 p. :ill., digital ;24 cm. - Advanced courses in mathematics, CRM Barcelona,2297-0304. - Advanced courses in mathematics, CRM Barcelona..

Introduction -- Lebesgue-type inequalities for greedy approximation with respect to some classical bases -- Quasi-greedy bases and Lebesgue-type inequalities -- Almost greedy bases and duality -- Greedy approximation with respect to the trigonometric system -- Greedy approximation with respect to dictionaries -- Appendix.

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.

ISBN: 9783034808903 (electronic bk.)

Standard No.: 10.1007/978-3-0348-0890-3doiSubjects--Topical Terms:

185327
Approximation theory.

LC Class. No.: QA221

Dewey Class. No.: 511.4

Sparse approximation with bases
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245 1 0 $a Sparse approximation with bases $h [electronic resource] / $c by Vladimir Temlyakov ; edited by Sergey Tikhonov.
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300 $a xi, 261 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advanced courses in mathematics, CRM Barcelona, $x 2297-0304
505 0 $a Introduction -- Lebesgue-type inequalities for greedy approximation with respect to some classical bases -- Quasi-greedy bases and Lebesgue-type inequalities -- Almost greedy bases and duality -- Greedy approximation with respect to the trigonometric system -- Greedy approximation with respect to dictionaries -- Appendix.
520 $a 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.
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