Sparse Approximation with Bases

  • Vladimir Temlyakov
  • Sergey Tikhonov

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vladimir Temlyakov
    Pages 1-19
  3. Vladimir Temlyakov
    Pages 61-102
  4. Vladimir Temlyakov
    Pages 103-119
  5. Vladimir Temlyakov
    Pages 187-228
  6. Vladimir Temlyakov
    Pages 229-256
  7. Back Matter
    Pages 257-261

About this book


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.


Banach spaces Greedy algorithms Lebesgue-type inequalities nonlinear approximation sparse approximation

Authors and affiliations

  • Vladimir Temlyakov
    • 1
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA

Editors and affiliations

  • Sergey Tikhonov
    • 1
  1. 1.ICREA and CRMBarcelonaSpain

Bibliographic information