Does the ordering affect to sparse approximate inverse preconditioners?

Abstract

We experimentally study how the reordering techniques affect the rate of convergence of preconditioned Krylov subspace methods for nonsymmetric 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 requirement and computations for a given accuracy. These properties are illustrated with a numerical experiment taken from the discretization of PDE by a finite element method.