Sensitivity analysis for the SR decomposition

Abstract

The explicit expressions for the condition numbers and the first-order perturbation bounds for both factors R and S of the SR decomposition are presented by using the operator. The new first-order bounds are sharper than those previous results given by Bhatia and Chang. Besides, we also give the rigorous perturbation bounds for these two factors. The first-order terms of the rigorous bounds are the same as the first-order perturbation bounds given by Bhatia.

Keywords:

• sensitivity
• condition number
• first-order perturbation bound
• rigorous perturbation bound
• SR decomposition

AMS Subject Classifications:

• 15A23
• 65F35

Acknowledgements

The authors would like to thank the reviewer and the editor for their helpful suggestions.

Notes

This work is supported in part by National Natural Science Foundations of China [grant number 10971075], [grant number 11271144], Guangdong Provincial Natural Science Foundations [grant number 09150631000021], [grant number s2012010009985] and Research Fund for the Doctoral Program of Higher Education of China [grant number 20104407110001].