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Sparse Approximation with Bases / by Vladimir Temlyakov ; edited by Sergey Tikhonov.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Temlyakov, Vladimir., Author.
- Series:
- Advanced Courses in Mathematics - CRM Barcelona, 2297-0304
- Language:
- English
- Subjects (All):
- Approximation theory.
- Functional analysis.
- Algorithms.
- Approximations and Expansions.
- Functional Analysis.
- Local Subjects:
- Approximations and Expansions.
- Functional Analysis.
- Algorithms.
- Physical Description:
- 1 online resource (XI, 261 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Basel : Springer Basel : Imprint: Birkhäuser, 2015.
- Language Note:
- English
- 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.
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-0348-0890-9
- OCLC:
- 1066196746
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