Sparse Approximation with Bases

Erscheinungsjahr 2015
ISBN: 978-3-0348-0889-7
Verlag: Birkhäuser

Buch, Englisch, 261 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 523 g

Reihe: Advanced Courses in Mathematics - CRM Barcelona

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Temlyakov, Vladimir

Tikhonov, Sergey

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.