Numerical analysis of wavelet methods /
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurate...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Amsterdam ; Boston :
Elsevier,
2003.
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| Edition: | 1st ed. |
| Series: | Studies in mathematics and its applications ;
v. 32. |
| Subjects: | |
| Online Access: | CONNECT |
| Summary: | Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies. |
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| Item Description: | ScienceDirect eBook - Mathematics pre-2007 (Elsevier and Woodhead) |
| Physical Description: | 1 online resource (xviii, 336 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 321-333) and index. |
| ISBN: | 9780444511249 0444511245 9780080537856 0080537855 1281279579 9781281279576 9786611279578 6611279571 |
| ISSN: | 0168-2024 ; |
