Execute Elementary Row and Column Operations on the Partitioned Matrix to Compute M-P Inverse A†

Abstract

We first study the complexity of the algorithm presented in Guo and Huang (2010). After that, a new explicit formula for computational of the Moore-Penrose inverse $A^{\mathrm{†}}$ of a singular or rectangular matrix $A$. This new approach is based on a modified Gauss-Jordan elimination process. The complexity of the new method is analyzed and presented and is found to be less computationally demanding than the one presented in Guo and Huang (2010). In the end, an illustrative example is demonstrated to explain the corresponding improvements of the algorithm.