Multiresolution and wavelets

Abstract

Wavelets may possibly provide a useful basis for the numerical solution of differential or integral equations, in particular when they model processes which operate on very different space- or time-scales (turbulence, boundary layers, shocks, for instance). Our aim in this report is to provide a self-contained introduction to the basic theory of multiresolution and wavelets, accessible to the numerical analyst who knows nothing of signal processing, quantum theory, or any of the other established fields of application.