Orderings for Factorized Sparse Approximate Inverse Preconditioners

The innuence of reorderings on the performance of factorized sparse approximate inverse preconditioners is considered. Some theoretical results on the eeect of orderings on the ll-in and decay behavior of the inverse factors of a sparse matrix are presented. It is shown experimentally that certain reorderings, like Minimum Degree and Nested Dissection, can be very beneecial both in the preconditioner construction phase and in terms of the rate of convergence of the preconditioned iteration.