An Expression of the Drazin Inverse of a Perturbed Matrix

Authors

• Xiezhang Li, Georgia Southern UniversityFollow
• Yimin Wei, Fudan UniversityFollow

Document Type

Article

Publication Date

5-25-2004

Publication Title

Applied Mathematics and Computation

DOI

10.1016/S0096-3003(03)00622-2

ISSN

0096-3003

Abstract

Given a square matrix A and its perturbation matrix E, a new expression for the Drazin inverse B^D of B=A+E is derived if AA^DB²=(AA^DB)² or B²AA^D=(BAA^D)². Based on the new expression, a bound of the relative error of B^D is developed. Some known results in the literature on the Drazin inverse and the perturbation bound are included by this new formula as special cases. A numerical example is given to compare the upper bounds.

Recommended Citation

Li, Xiezhang, Yimin Wei. 2004. "An Expression of the Drazin Inverse of a Perturbed Matrix." Applied Mathematics and Computation, 153 (1): 187-198. doi: 10.1016/S0096-3003(03)00622-2
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/572

Copyright

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