Convergence Acceleration of Iterative Methods for Inverting Real Matrices Using Frobenius Norm Minimization

Abstract

The Schulz-type methods for computing generalizedmatrix inverses are a family of iterative methods that are popular for their high order of convergence (≥ 2). We propose two new scaled acceleration techniques for such type of iterative methods for real matrices (based on Frobenius norm minimization) andlay out efficient algorithms to implement these techniques. Testresults show one of our techniques to be most effective for densematrices but also works for sparse cases as well.