Algorithms for implementation of general limit representations of generalized inverses (Q2770159)

Three algorithms for the computation of generalized inverses which are contained in the limit expressions \(\lim_{z \mapsto 0}V(DT + zI)^{-1}U\) and \(\lim_{z \mapsto 0}V(DT + zI)^{-1}z^e\) are described. The first algorithm is a generalization of the embedding methods described e.g. by \textit{R. Kalaba} and \textit{N. Rasakhoo} [J. Optimization Theory Appl. 48, 427-435 (1986; Zbl 0563.65025)], \textit{G. Wang} [J. Comput. Math. 8, No. 4, 353-362 (1990; Zbl 0716.65039)], and \textit{G. Wang} and \textit{Y. Wei} [Numer. Math. J. Chin. Univ. 4, No. 1, 25-30 (1995; Zbl 0847.65025)]. The second algorithm makes use of several sets of orthogonal vectors. This algorithm is an extension of a method proposed by R. Kalaba and N. Rasakhoo [loc. cit.]. The third algorithm is a generalization of the Leverrier-Faddeev algorithm.