Algorithm stabilization techniques and their application to 
symbolic computation of generalized inverses

Author : Hiroyuki Minakuchi, Hiroshi Kai, Kiyoshi Shirayanagi and 
         Matu-Tarow Noda

Abstract: 

We give an algorithm to compute the Moore-Penrose generalized inverse of a
matrix, which permits the use of limited precision computation in a convergent
fashion, based on Greville's algorithm.  This does not mean that Greville's
algorithm may be directly computed with limited precision computation in a
convergent fashion, but rather the algorithm is amenable to the stabilization
techniques proposed by Shirayanagi and Sweedler, and we apply these
stabilization techniques to the algorithm.  Computations were done on a
computer algebra system Risa/Asir.