On finding robust approximate inverses for large sparse matrices

Abstract

This paper presents a method based on matrix-matrix multiplication concepts for determining the approximate (sparse) inverses of sparse matrices. The suggested method is a development on the well-known Schulz iteration and it can successfully be combined with iterative solvers and sparse approximation techniques as well. A detailed discussion on the convergence rate of this scheme is furnished. Results of numerical experiments are also reported to illustrate the performance of the proposed method.