Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation

Abstract

This paper is devoted to the perturbation analysis for the generalized Sylvester equation and the generalized Lyapunov equation. The explicit expressions and upper bounds of normwise, mixed and componentwise condition numbers for these equations are presented. The results are illustrated by numerical examples.

Keywords:

• perturbation analysis
• condition number
• linear asymptotic bound
• generalized Sylvester equation
• generalized Lyapunov equation

2000 AMS Subject Classifications :

• 15A24
• 65F35
• 65F99

Acknowledgements

The authors would like to thank the anonymous referees for their helpful suggestions, which greatly improved the paper. The work is supported by the National Natural Science Foundation of China under grant 10801048 and the Natural Science Foundation of Hunan Province under grant 09JJ6014.