Multiscale Methods for Fredholm Integral Equations

Description

Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. Abstract: The authors present the state of the art in fast multiscale methods, from traditional numerical methods to the recently developed wavelet-based approach. Theorems of functional analysis used throughout the book are summarised in an appendix. Selected chapters are suitable for a one-semester course for advanced undergraduates or beginning graduates.  Read more... Content: A review of the Fredholm approach -- Fredholm equations and projection theory -- Conventional numerical methods -- Multiscale basis functions -- Multiscale Galerkin methods -- Multiscale Petrov -- Galerkin methods -- Multiscale collocation methods -- Numerical integrations and error control -- Fast solvers for discrete systems -- Multiscale methods for nonlinear integral equations -- Multiscale methods for ill-posed integral equations -- Eigen-problems of weakly singular integral operators.