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Numerical Analysis of Wavelet Methods

2003-04-29 Mathematics
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Release : 2003-04-29
Genre : Mathematics
Kind : eBook
Book Rating : 855/5 ( reviews)

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Book Synopsis Numerical Analysis of Wavelet Methods by : A. Cohen

Download or read book Numerical Analysis of Wavelet Methods written by A. Cohen. This book was released on 2003-04-29. Available in PDF, EPUB and Kindle. Book excerpt: 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

2003-06-26
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Release : 2003-06-26
Genre :
Kind : eBook
Book Rating : 277/5 ( reviews)

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Book Synopsis Numerical Analysis of Wavelet Methods by : Albert Cohen

Download or read book Numerical Analysis of Wavelet Methods written by Albert Cohen. This book was released on 2003-06-26. Available in PDF, EPUB and Kindle. Book excerpt: 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 Numerical Method and Its Applications in Nonlinear Problems

2021-03-09 Technology & Engineering
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Release : 2021-03-09
Genre : Technology & Engineering
Kind : eBook
Book Rating : 435/5 ( reviews)

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Book Synopsis Wavelet Numerical Method and Its Applications in Nonlinear Problems by : You-He Zhou

Download or read book Wavelet Numerical Method and Its Applications in Nonlinear Problems written by You-He Zhou. This book was released on 2021-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

2018-01-12 Mathematics
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Release : 2018-01-12
Genre : Mathematics
Kind : eBook
Book Rating : 210/5 ( reviews)

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Book Synopsis Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations by : Santanu Saha Ray

Download or read book Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations written by Santanu Saha Ray. This book was released on 2018-01-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wavelet Methods In Mathematical Analysis And Engineering

2010-09-21 Mathematics
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Release : 2010-09-21
Genre : Mathematics
Kind : eBook
Book Rating : 058/5 ( reviews)

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Book Synopsis Wavelet Methods In Mathematical Analysis And Engineering by : Alain Damlamian

Download or read book Wavelet Methods In Mathematical Analysis And Engineering written by Alain Damlamian. This book was released on 2010-09-21. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective.The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.

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