An efficient quadratically convergent iterative method to find the Moore-Penrose inverse

In this paper, we propose a new Schulz-type method to find the pseudo-inverse (also known as the Moore-Penrose inverse) of a singular or rectangular real (or complex) matrix. It is proved that the method converges quadratically. A wide set of numerical comparisons of our method with nine higher order methods shows that the average number of matrix-matrix multiplications and the average CPU time of proposed method are considerably less than those of other methods. So, our new method can be considered as a fast method. For each of sizes , n=100,200,300,400, ten random matrices were chosen to make these comparisons. So, overall 800 problems were solved.