International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 8, Pages 497-507
A note on computing the generalized inverse of a matrix
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.
The generalized inverse of a matrix is a -inverse of with the prescribed range and null space . A representation for the generalized inverse
has been recently developed with the condition
, where is a matrix with and. In this note, we remove the above condition. Three types of iterative methods for are presented if is a subset of the open right half-plane and they are extensions of existing computational procedures of , including special cases such as the weighted Moore-Penrose inverse and the Drazin inverse . Numerical examples are given to illustrate our results.