An Improved Convergent Iterative Method for Finding the Moore- Penrose Inverse

The goal of this paper is to suggest and establish an efficient iterative method based on matrix by matrix multiplications for finding the approximate inverse of nonsingular square matrices. We then analytically extend this proposed method so as to compute the Moore-Penrose generalized inverse of a non-square matrix. A theoretical analysis has been employed to compare the computational efficiency of the presented scheme with the other existing methods in the literature to show that it is economic. Numerical experiments are also executed to manifest its superiority.