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

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.