Filter bank subdivisions of bounded domains Original Research Article

We construct filter bank transforms that are adapted to bounded domains. The transforms are constructed with the aim of solving PDEs 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 paid is extra growth factors in the number of coefficients and in the error, compared to the multiresolution analysis approach. However, these factors are small. We give upper bounds of the growth factors, and show numerical examples for an interval, a three-dimensional box, and a triangle. We also show examples of fast differentiation and other operations on thresholded expansions.