Execute elementary row and column operations on the partitioned matrix to compute M-P inverse \(A^!\) (Q1724477)

Summary: We first study the complexity of the algorithm presented in [\textit{W. Guo} and \textit{T. Huang}, Appl. Math. Comput. 216, No. 5, 1614--1617 (2010; Zbl 1200.65027)]. After that, a new explicit formula for computational of the Moore-Penrose inverse \(A^!\) 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 [loc. cit.]. In the end, an illustrative example is demonstrated to explain the corresponding improvements of the algorithm.