A new approach to compute sparse approximate inverse factors of a matrix

The FSAI algorithm is among the most effective preconditioners for solving large and sparse linear system of equations. But its main disadvantage is the need to prescribe the sparsity pattern of the approximate inverse factors in advance. In this paper a new method is proposed by combining the FSAI preconditioner with approximating the sparse solution of a sparse linear system by sparse–sparse iterations. The new method does not require that the sparsity pattern be known in advance. Moreover, it retains the inherent parallelism of the FSAI algorithm. Some numerical experiments on test matrices from Harwell–Boeing collection are presented.