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Multiscale Methods for Fredholm Integral Equations
Zhongying ChenCharles A. MicchelliYuesheng Xu
出版Cambridge University Press, 2015-07-16
主題Mathematics / GeneralMathematics / CalculusMathematics / Mathematical AnalysisMathematics / Functional AnalysisMathematics / Numerical Analysis
ISBN11071034799781107103474
URLhttp://books.google.com.hk/books?id=tcrSCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.