The Nonsingularity of Sparse Approximate Inverse Preconditioning and Its Performance Based on Processor

In this paper, we analyze the properties of the sparse approximate inverse precon-ditioner, and prove that for a strictly diagonally dominant M matrix, the computed preconditioning matrix can be guaranteed to be nonsingular if it is nonnegative. Then we investigate the use of the processor virtualization technique to parallelize the sparse approximate inverse solver. Numerical experiments on a distributed memory parallel computer show that the eciency of the resulting preconditioner can be improved by virtualization