An efficient method to compute the Moore–Penrose inverse

Abstract

AbstractA 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 always converge with fourth-order. 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. For each of sizes{n\times n}and{n\times(n+10)},{n=200,400,600,800,1000,1200}, ten random matrices were chosen to make these comparisons.