Multiscale methods for Fredholm integral equations /
Zhongying Chen, Charles A. Micchelli, Yuesheng Xu.
- Cambridge : Cambridge University Press, 2015.
- 1 online resource (xiii, 536 pages) : digital, PDF file(s).
- Cambridge monographs on applied and computational mathematics ; 28 .
- Cambridge monographs on applied and computational mathematics ; 28. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.