Numerical Analysis Of Wavelet Methods

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Numerical Analysis Of Wavelet Methods

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Author : A. Cohen
language : en
Publisher: Elsevier
Release Date : 2003-04-29

Numerical Analysis Of Wavelet Methods written by A. Cohen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-29 with Mathematics categories.

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 analysisof 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.

Numerical Analysis Of Wavelet Methods

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Author : Albert Cohen
language : en
Publisher: JAI Press
Release Date : 2003-06-26

Numerical Analysis Of Wavelet Methods written by Albert Cohen and has been published by JAI Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with categories.

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.

Wavelet Methods In Numerical Analysis

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Author : Albert Cohen
language : en
Publisher:
Release Date : 2000

Wavelet Methods In Numerical Analysis written by Albert Cohen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Wavelet Analysis

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Author : Ding-Xuan Zhou
language : en
Publisher: World Scientific
Release Date : 2002

Wavelet Analysis written by Ding-Xuan Zhou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.

The International Conference of Computational Harmonic Analysis, held in Hong Kong during the period of June 4 ? 8, 2001, brought together mathematicians and engineers interested in the computational aspects of harmonic analysis. Plenary speakers include W Dahmen, R Q Jia, P W Jones, K S Lau, S L Lee, S Smale, J Smoller, G Strang, M Vetterlli, and M V Wickerhauser. The central theme was wavelet analysis in the broadest sense, covering time-frequency and time-scale analysis, filter banks, fast numerical computations, spline methods, multiscale algorithms, approximation theory, signal processing, and a great variety of applications.This proceedings volume contains sixteen papers from the lectures given by plenary and invited speakers. These include expository articles surveying various aspects of the twenty-year development of wavelet analysis, and original research papers reflecting the wide range of research topics of current interest.

Multiscale Wavelet Methods For Partial Differential Equations

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Author : Wolfgang Dahmen
language : en
Publisher: Elsevier
Release Date : 1997-08-13

Multiscale Wavelet Methods For Partial Differential Equations written by Wolfgang Dahmen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Mathematics categories.

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. - Covers important areas of computational mechanics such as elasticity and computational fluid dynamics - Includes a clear study of turbulence modeling - Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations - Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications

Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations

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Author : Santanu Saha Ray
language : en
Publisher: CRC Press
Release Date : 2018-01-12

Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations written by Santanu Saha Ray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-12 with Mathematics categories.

The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

Adaptive Wavelet Frame Methods For Nonlinear Elliptic Problems

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Author : Jens Kappei
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2012-02-06

Adaptive Wavelet Frame Methods For Nonlinear Elliptic Problems written by Jens Kappei and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-06 with Mathematics categories.

Over the last ten years, adaptive wavelet methods have turned out to be a powerful tool in the numerical treatment of operator equations given on a bounded domain or closed manifold. In this work, we consider semi-nonlinear operator equations, including an elliptic linear operator as well as a nonlinear monotone one. Since the classical approach to construct a wavelet Riesz basis for the solution space is still afflicted with some notable problems, we use the weaker concept of wavelet frames to design an adaptive algorithm for the numerical solution of problems of this type. Choosing an appropriate overlapping decomposition of the given domain, a suitable frame system can be constructed easily. Applying it to the given continuous problem yields a discrete, bi-infinite nonlinear system of equations, which is shown to be solvable by a damped Richardson iteration method. We then successively introduce all building blocks for the numerical implementation of the iteration method. Here, we concentrate on the evaluation of the discrete nonlinearity, where we show that the previously developed auxiliary of tree-structured index sets can be generalized to the wavelet frame setting in a proper way. This allows an effective numerical treatment of the nonlinearity by so-called aggregated trees. Choosing the error tolerances appropriately, we show that our adaptive scheme is asymptotically optimal with respect to aggregated tree-structured index sets, i.e., it realizes the same convergence rate as the sequence of best N-term frame approximations of the solution respecting aggregated trees. Moreover, under the assumption of a sufficiently precise numerical quadrature method, the computational cost of our algorithm stays the same order as the number of wavelets used by it. The theoretical results are widely confirmed by one- and two-dimensional test problems over non-trivial bounded domains.

Wavelet Methods For Elliptic Partial Differential Equations

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Author : Karsten Urban
language : en
Publisher: OUP Oxford
Release Date : 2008-11-27

Wavelet Methods For Elliptic Partial Differential Equations written by Karsten Urban and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.

The origins of wavelets go back to the beginning of the last century and wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have, however, been used successfully in other areas, such as elliptic partial differential equations, which can be used to model many processes in science and engineering. This book, based on the author's course and accessible to those with basic knowledge of analysis and numerical mathematics, gives an introduction to wavelet methods in general and then describes their application for the numerical solution of elliptic partial differential equations. Recently developed adaptive methods are also covered and each scheme is complemented with numerical results, exercises, and corresponding software tools.

Wavelet Solutions For Reaction Diffusion Problems In Science And Engineering

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Author : G. Hariharan
language : en
Publisher: Springer Nature
Release Date : 2019-09-17

Wavelet Solutions For Reaction Diffusion Problems In Science And Engineering written by G. Hariharan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-17 with Mathematics categories.

The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction–diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena. It explores the analytical and numerical approximate solutions obtained by wavelet methods for both classical and fractional-order differential equations; provides comprehensive information on the conceptual basis of wavelet theory and its applications; and strikes a sensible balance between mathematical rigour and the practical applications of wavelet theory. The book is divided into 11 chapters, the first three of which are devoted to the mathematical foundations and basics of wavelet theory. The remaining chapters provide wavelet-based numerical methods for linear, nonlinear, and fractional reaction–diffusion problems. Given its scope and format, the book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.

Wavelets In Soft Computing Second Edition

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Author : Marc Thuillard
language : en
Publisher: World Scientific
Release Date : 2022-09-09

Wavelets In Soft Computing Second Edition written by Marc Thuillard and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-09 with Computers categories.

The comprehensive compendium furnishes a quick and efficient entry point to many multiresolution techniques and facilitates the transition from an idea into a real project. It focuses on methods combining several soft computing techniques (fuzzy logic, neural networks, genetic algorithms) in a multiresolution framework.Illustrated with numerous vivid examples, this useful volume gives the reader the necessary theoretical background to decide which methods suit his/her needs.New materials and applications for multiresolution analysis are added, including notable research topics such as deep learning, graphs, and network analysis.