Perturbation Formulas and Bounds for the Group Inverse
N. Castro-González, M.F. Martínez-Serrano, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2010
Let A = I−T, where T is any stochastic matrix and let E be a perturbation matrix such that T−E is a stochastic matrix. The group inverse of A is denoted by A♯. The purpose of this paper is to give an explicit representation for (A+E)♯, under conditions rank(A) = rank(A+E) = rank(A(A+E)A), and upper bounds for the relative error ||(A+E)♯−A♯||/||A♯||. In a numerical example, we compare our bound with the bound obtained by Xu, Song, and Wei [SIAM J. Matrix Anal. Appl.,31(2010), 1507–1520].