An improved Schulz-type iterative method for matrix inversion with application

Abstract

In this paper, we present an algorithm which could be considered an improvement to the well-known Schulz iteration for finding the inverse of a square matrix iteratively. The convergence of the proposed method is proved and its computational complexity is analysed. The extension of the scheme to generalized outer inverses will be treated. In order to validate the new scheme, we apply it to large sparse matrices alongside the application to preconditioning of practical problems.