In this paper, we propose a new Schulz-type method to find the pseudoinverse (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 × n and n × (n + 10), n=100,200,300,400, ten random matrices were chosen to make these comparisons. So, overall 800 problems were solved.
