Filter bank subdivisions of bounded domains (Q1971375)

Filter bank transforms that are adapted to bounded domains are constructed. The transforms are constructed with the aim of solving partial differential equations together with finite difference methods, and the properties important for this kind of application are analyzed. As the filter banks do not need to correspond to wavelets, short filters can be used. The price to be paid is an extra growth factor in the number of coefficients and in the error, compared to the multiresolution analysis approach. However, these factors are small. Upper bounds of the growth factors are presented. Numerical examples for an interval, a three-dimensional box, and a triangle are showed. Examples of fast differentiation and other operations on thresholded expansions are discussed.