Computation of {2,4} and {2,3}-inverses based on rank-one updates

Abstract

Two finite recurrent procedures for computing and -inverses of a matrix are presented. Each of introduced methods exploits certain matrix product which includes the Moore–Penrose inverse of a symmetric matrix and a generalization of the Sherman-Morrison formula to the case of the Moore–Penrose inverse of a symmetrically rank one modified matrix. The computational complexity of the methods is analysed. In the essence, presented representations investigate dual methods with respect to these introduced in [Stanimirović PS, Katsikis VN, Pappas D, Computing {2,4} and {2,3}-inverses by using the Sherman-Morrison formula, Appl. Math. Comput. 2016;273:584–603].