A Note on the Perturbation Bound of the Drazin Inverse
Applied Mathematics and Computation
A perturbation bound for the Drazin inverse AD with Ind(A+E)=1 has recently been developed. However, those upper bounds are not satisfied since it is not tight enough. In this paper, a sharper upper bounds for ||(A+E)#−AD|| with weaker conditions is derived. That new bound is also a generalization of a new general upper bound of the group inverse. We also derive a new expression of the Drazin inverse (A+E)D with Ind(A+E)>1 and the corresponding upper bound of ||(A+E)D−AD|| in a special case. Numerical examples are given to illustrate the sharpness of the new bounds.
Li, Xiezhang, Yimin Wei.
"A Note on the Perturbation Bound of the Drazin Inverse."
Applied Mathematics and Computation, 140 (2-3): 329-340.
doi: 10.1016/S0096-3003(02)00230-8 source: https://www.sciencedirect.com/science/article/pii/S0096300302002308?via%3Dihub