A note on the perturbation bound of the Drazin inverse

摘要

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.