Hyper-power methods for the computation of outer inverses

In this paper, we propose new iterative schemes for the computation of outer inverse which reduce the total number of matrix multiplications per iteration. In particular, we consider how the hyper-power method of orders 5 and 9 can be accelerated such that they require 4 and 5 matrix multiplications per iteration, respectively. These improvements are tested against quadratically convergent Schultz’ method and fastest Horner scheme hyper-power method of order three. Numerical results show the superiority and practical applicability of the proposed methods. Finally, it is shown that a possibly more efficient method should have the order at least r≥14r≥14, making it useless for practical applications.