Multiresolution analysis with non-nested spaces

Two multiresolution analyses (MRA) intended to be used in scientific visualization, and that are both bared on a non-nested set of approximating spaces, are presented. The notion of approximated refinement is introduced to deal with non nested spaces. The first MRA scheme, referred to as BLaC (Blending of Linear and Constant) wavelets is based on a one parameter family of wavelet bases that realizes a blend between the Haar and the linear wavelet bases. The approximated refinement is applied in the last part to build a second MRA scheme for data defined on an arbitrary planar triangular mesh.