Multiplicative perturbation bounds of the group inverse and oblique projection

Abstract

In this paper, the multiplicative perturbation bounds of the group inverse and related oblique projection under general unitarily invariant norm are presented by using the decompositions of B # − A # and BB # − AA # .

Additive perturbations and multiplicative perturbations for the core inverse of bounded linear operator in Hilbert space

“…Lately, there has been an increase of interest in multiplicative perturbation analysis. For example, Cai et.al, in [7], have studied the Moore-Penrose inverse ofà = D * 1 AD 2 , where D 1 ∈ C m×m and D 2 ∈ C n×n are nonsingular matrices and obtained the upper bound of à † − A † ; N.Castro-González, et.al, in [5,6], have discussed the Moore-Penrose inverse of a matrix of the formà = (I + E)A(I + F) ∈ C m×n , where (I + E) ∈ C m×m and (I + F) ∈ C n×n are nonsingular matrices and improved the related results in [7]; L.Meng and B.Zheng have studied multiplicative perturbation of group inverse in [16], ect. Please see [4,23,28] for more details of multiplicative perturbation theory.…”