Abstract
The goal of this study is threefold. In order to calculate the weighted Moore–Penrose inverse, we first derive a new matrix iteration for computing the inverse of non-singular square matrices. We then analytically extend the obtained results so as to compute the Moore–Penrose generalized inverse of a non-square matrix. Subsequently, these results will again be theoretically extended to find the weighted Moore–Penrose inverse. The computational efficiency of the presented scheme is rigourously studied and compared with the existing matrix iterations to show that it is economic. Some applications are given as well.