International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 8, Pages 497-507
doi:10.1155/S0161171202013169

A note on computing the generalized inverse A T,S (2) of a matrix A

Xiezhang Li1 and Yimin Wei2

1Department of Mathematics and Computer Science, Georgia Southern University, Statesboro 30460, GA, USA
2Department of Mathematics, Fudan University, Shanghai 200433, China

Received 10 May 2001; Revised 1 February 2002

Copyright © 2002 Xiezhang Li and Yimin Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results.