RAPID MATRIX-VECTOR PRODUCTS USING WAVELE T TRANSFORM - APPLICATION TO NUMERICAL-SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS

Some matrix-vector products can be efficiently computed using the wave let transform. In this article, we compare two methods: the standard m ethod, which simply wavelet transforms the system, and the BCR method. These algorithms and tile practical implementation of the two methods are explained in detail and improvements are given for the shift-inva riant operator case. These methods are applied to the numerical soluti on of heat equation and advection equation for a periodic one-dimensio nal domain : computing time comparisons are given, demonstrating the s uperiority of the standard method in terms of computational cost.