On the extension of Householder's method for weighted Moore-Penrose inverse

This note discusses how to extend and use the well-known method of Householder (1964) [6] for finding weighted Moore-Penrose inverse. The discussions cover both theoretical and numerical aspects. An approach for accelerating the initial phase of convergence will be contributed. Some tests will also be employed to check the validity and superiority of the results over the Schulz method.