An Efficient Schulz-type Method to Compute the Moore-Penrose Inverse

A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.