xxSTABILIZING THE HIERARCHICAL BASIS BY APPROXIMATEWAVELETS , II : IMPLEMENTATION AND NUMERICAL RESULTSPANAYOT

This paper is the second part of a work on stabilizing the classical hierarchical basis (HB) by using wavelet{like basis functions. Implementation techniques are of major concern for the multilevel preconditioners proposed by the authors in the rst part of the work that deals with algorithms and their mathematical theory. Numerical results are presented to connrm the theory established there. A comparison on the performance of a number of multilevel methods is conducted for elliptic problems of three space variables. 1. Introduction In this paper we are concerned with implementation techniques on the wavelet-modiied hierarchical basis method proposed in 16]. As discussed in 16], the method stabilizes the classical hierarchical basis 18] by taking away from each hierarchical basis function its