Multiscale Methods for Fredholm Integral Equations

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Multiscale Methods for Fredholm Integral Equations by Zhongying Chen, Charles A. Micchelli, Yuesheng Xu, Cambridge University Press
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Author: Zhongying Chen, Charles A. Micchelli, Yuesheng Xu ISBN: 9781316379509
Publisher: Cambridge University Press Publication: July 16, 2015
Imprint: Cambridge University Press Language: English
Author: Zhongying Chen, Charles A. Micchelli, Yuesheng Xu
ISBN: 9781316379509
Publisher: Cambridge University Press
Publication: July 16, 2015
Imprint: Cambridge University Press
Language: English

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

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The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

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