A fourth-order iterative method for computing the moore-penrose inverse

In this study, a new fourth-order method to compute the Moore-Penrose inverse is proposed. Convergence analysis along with the error estimates of the method is investigated. Every iteration of the method involves four matrix multiplications. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.