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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