Sparse Approximation with Bases
 フォーマット:
 電子ブック
 責任表示:
 by Vladimir Temlyakov ; edited by Sergey Tikhonov
 本文言語:
 英語
 出版情報:
 Basel, Switzerland. 2015. Springer Basel,Imprint: Birkhäuser
 シリーズ:
 Advanced Courses in Mathematics  CRM Barcelona
 概要:
 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 greedytype 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. … 続きを見る
 目次:

Introduction Lebesguetype inequalities for greedy approximation with respect to some classical bases Quasigreedy bases and Lebesguetype inequalities Almost greedy bases and duality Greedy approximation with respect to the trigonometric system Greedy approximation with respect to dictionaries Appendix. Introduction Lebesguetype inequalities for greedy approximation with respect to some classical bases Quasigreedy bases and Lebesguetype inequalities Almost greedy bases and duality Greedy approximation with respect to the trigonometric system Greedy approximation with respect to dictionaries