Gauss-Jordan elimination method for computing all types of generalized inverses related to the {1}-inverse

We derive a unified representation for all types of generalized inverses related to the {1}-inverse. Based on this representation, we propose a unified Gauss-Jordan elimination procedure for the computation of all types of generalized inverses related to the {1}-inverse. Complexity analysis indicates that when applied to compute the Moore-Penrose inverse, our method is more efficient than the existing Gauss-Jordan elimination methods in the literature for a large class of problems. Finally, numerical experiments show our method for Moore-Penrose inverse has good efficiency and accuracy, and especially for computing the Moore-Penrose inverse of m×n matrices with m