Numerical Analysis of Wavelet Methods - Couverture rigide

Cohen, A.

Couverture rigide

ISBN 10 : 0444511245 ISBN 13 : 9780444511249

Editeur : JAI Press Inc., 2003

Synopsis

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.

A propos du livre

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.

Revue de presse

"It contains an excellent presentation of the general theory of multiscale decomposition methods based on wavelet bases with a special attention to adaptive approximation."
Teresa Reginska (Warszawa). Zentralblatt Fur Mathematik.

"This book provides a self-contained treatment of the subject. It starts from the theoretical foundations, then it explores the related numerical algorithms, and finally discusses the applications. In particular, the development of adaptive wavelets methods for the numerical treatment of partial differential equations is emphasized."
--A. Cohen

"This extremely well written volume is intended to graduage students and researchers in numerical analysis and applied mathematics."
-NUMERICAL ALGORITHMS, Vol. 38, 2005

Détails de l'édition

• Éditeur: JAI Press Inc.
• Date d'édition: 2003
• ISBN 10: 0444511245
• ISBN 13: 9780444511249
• Reliure: Relié
• Langue: anglais
• Numéro d'édition: 1
• Nombre de pages: 354
• Coordonnées du fabricant: non disponible