Backward errors of periodic invariant subspaces for regular periodic matrix pairs

Abstract

In this paper, the backward error of periodic invariant subspaces for regular periodic pairs is defined and its explicit expression is derived. In particular, we also present the expression of the backward error of generalized invariant subspaces for the regular matrix pair. The results are illustrated by two numerical examples.

Keywords:

• backward error
• periodic invariant subspace
• Frobenius norm

AMS Subject Classifications:

• 65F15
• 65F99

Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestions.

Notes

1 This work is supported by NSF of Guangdong province [grant number S20130100112530], [grant number S2012010009985]; NNSF of China [grant number 0971075], [grant number 11271144]; Research Fund for the Doctoral Program of Higher Education of China [grant number 20104407110001] and Project of Department of Education of Guangdong Province.