Non-uniform multiresolution analysis with supercompact multiwavelets

This work is devoted to a generalization of the framework presented in Beam and Warming (2000) [6], where a multiresolution analysis scheme with supercompact multiwavelets was presented. The approach considers uniform partitions of a nested grid hierarchy in the framework of Harten’s multi-scale representations. In this paper we study the non-uniform case. The non-uniform analysis is well adapted to more realistic contexts and makes it possible to improve the approximation.