A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
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.
Wei, Yimin, Xiezhang Li, Fanbin Bu.
"A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces."
SIAM Journal on Matrix Analysis and Applications, 27 (1): 72-81.
doi: 10.1137/S0895479804439948 source: https://epubs.siam.org/doi/10.1137/S0895479804439948