Factorized sparse approximate inverses for preconditioning and smoothing

In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of || AM-I || in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT A-1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L. We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses that are suited for smoothing in multigrid solvers.