196	1997	Johan Walden	johan@tdb.uu.se	Filter Bank Subdivisions of Bounded Domains


			Abstract

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.