Orderings for factorized sparse approximate inverse preconditioners

The influence of reorderings on the performance of factorized sparse approx imate inverse preconditioners is considered. Some theoretical results on th e effect of orderings on the fill-in and decay behavior of the inverse fact ors of a sparse matrix are presented. It is shown experimentally that certa in reorderings, like minimum degree and nested dissection, can be very bene ficial. The benefit consists of a reduction in the storage and time require d for constructing the preconditioner, and of faster convergence of the pre conditioned iteration in many cases of practical interest.