GMRES PRECONDICIONADO CON WAVELETS. UN ALGORITMO DE SELECCIÓN DEL UMBRAL PARA LA OBTENCIÓN DEL PATRÓN DE DISPERSIÓN

Abstract

In order to use the GMRES method to solve dense linear equations systems in iterations, the building of a preconditioner using
the no singular sparse approximation of a dense linear equations systems matrix is proposed. The sparse approximation is obtained by wavelet compression, using Haar and Daubechies wavelets basis. The novelty of this work is the proposed strategy to automatic
selection of the threshold to obtain the sparse matrix from the original dense matrix, which is based on statistics concept of percentile and another contribution is the cost analysis that was done. A broad numerical experimentation allowed to evaluate the qualit y of the preconditioner related to some parameters like problem dimension, used wavelet base and number of non zero elements of the sparse matrix.