An Efficient Matrix Iterative Method for Computing Moore–Penrose Inverse

The aim of this article is to develop and analyze the matrix iterative method for computing the Moore–Penrose inverse of a given complex matrix. The theoretical analysis of the presented method is established, which indicates that the method achieves at least ninth order of convergence. The effectiveness of the developed method is tested via computational efficiency index, and the number of iterations required for convergence. Besides it, numerical reports are provided on a variety of problems arising from different fields of science and engineering. In particular, we study the linear system of equations originated from the statically determinate truss problems, elliptic partial differential equations, and balancing chemical equations. It is demonstrated that the performance of the presented method is significantly better than its existing counterparts.