Sparse Approximate Inverses in Preconditioning Distributed Linear Systems

Abstract

Using a direct approximation of sparse matrix inverse in preconditioning is viewed as a good alternative to the preconditioning techniques that require a matrix factorization. A sparse approximate inverse is easy to compute and apply, and it is suitable for parallel implementations. For distributed linear systems of varying difficulty, approximate block LU preconditioning using sparse approximate inverse techniques and an incomplete LU factorization used in Block-Jacobi preconditioning are compared.