A parallel algorithm to approximate inverse factors of a matrix via sparse–sparse iterations

摘要

In [D.K. Salkuyeh, F. Toutounian, A block version algorithm to approximate inverse factors, Appl. Math. Comput., 162 (2005) 1499–1509], the authors proposed the BAIB algorithm to approximate inverse factors of a matrix. In this paper a parallel version of the BAIB algorithm is presented. In this method the BAIB algorithm is combined with computing the sparse approximate solution of a sparse linear system by sparse–sparse iterations. The new method does not require that the sparsity pattern be known in advance. Some numerical experiments on test matrices from Harwell–Boeing collection are presented to show the efficiency of the new method and comparing to the AIB algorithm.