A Note on the Perturbation Bound of the Drazin Inverse

Document Type

Article

Publication Date

8-10-2003

Publication Title

Applied Mathematics and Computation

DOI

10.1016/S0096-3003(02)00230-8

ISSN

0096-3003

Abstract

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.

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