A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces
Yimin Wei, Xiezhang Li, Fanbin Bu · SIAM Journal on Matrix Analysis and Applications · 2005
A constructive perturbation bound of the Drazin inverse of a square matrix is derived using a technique proposed by G. Stewart and based on perturbation theory for invariant subspaces. This is an improvement of the result published by the authors Wei and Li [Numer. Linear Algebra Appl., 10 (2003), pp. 563--575]. It is a totally new approach to developing perturbation bounds for the Drazin inverse of a matrix. A numerical example which indicates the sharpness of the perturbation bound is presented.