The perturbation of the Drazin inverse

Abstract

In this paper, we present the explicit expressions of the perturbation of the Drazin inverse under different conditions. Also, we give the upper bounds of ‖(A+E)^D−A ^D‖ _P /‖A ^D‖ _P for these cases.

Keywords:

• Drazin inverse
• block matrix
• perturbation
• P-norm
• numerical analysis

2010 AMS Subject Classifications :

• 15A09
• 15A18
• 15A24

Acknowledgements

This work was supported by the National Natural Science Foundation of China (11061005), the Ministry of Education Science and Technology Key Project under Grant 210164 and Grants (HCIC201103) of Guangxi Key Laborarory of Hybrid Computational and IC Design Analysis Open Fund.