Sparse approximation with bases [electronic resource] / Vladimir Temlyakov ; editor for this volume: Sergey Tikhonov.
2015
QA221
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Title
Sparse approximation with bases [electronic resource] / Vladimir Temlyakov ; editor for this volume: Sergey Tikhonov.
ISBN
9783034808903 electronic book
3034808909 electronic book
9783034808897
3034808909 electronic book
9783034808897
Published
Basel : Birkhäuser, 2015.
Language
English
Description
1 online resource (xi, 261 pages).
Item Number
10.1007/978-3-0348-0890-3 doi
Call Number
QA221
Dewey Decimal Classification
511/.4
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 3, 2015).
Added Author
Tikhonov, Sergey, 1976- editor.
Series
Advanced courses in mathematics. CRM Barcelona.
Available in Other Form
Print version: 9783034808897
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Table of Contents
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.
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.