Computation of weighted Moore–Penrose inverse through Gauss–Jordan elimination on bordered matrices

Abstract

In this paper, two new algorithms for computing the Weighted Moore–Penrose inverse AM,N† of a general matrix A for weights M and N which are based on elementary row and column operations on two appropriate block partitioned matrices are introduced and investigated. The computational complexity of the introduced two algorithms is analyzed in detail. These two algorithms proposed in this paper are always faster than those in Sheng and Chen (2013) and Ji (2014), respectively, by comparing their computational complexities. In the end, an example is presented to demonstrate the two new algorithms.