The effect of orderings on sparse approximate inverse preconditioners for non-symmetric problems

Abstract

We experimentally study how reordering techniques affect the rate of convergence of preconditioned Krylov subspace methods for non-symmetric sparse linear systems, where the preconditioner is a sparse approximate inverse. In addition, we show how the reordering reduces the number of entries in the approximate inverse and thus, the amount of storage and computation required for a given accuracy. These properties are illustrated with several numerical experiments taken from the discretization of PDEs by a finite element method and from a standard matrix collection.