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

摘要

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