Thick restarting the weighted harmonic Arnoldi algorithm for large interior eigenproblems

Abstract

We propose a thick-restarted weighted harmonic Arnoldi algorithm for computing interior eigenpairs of large sparse matrices. Moreover, we consider how to determine the weighting matrix efficiently in practice. Some properties of the new algorithm are discussed. Numerical experiments demonstrate the numerical behaviour of our new algorithm.

Keywords:

• interior eigenproblems
• Arnoldi process
• weighted Arnoldi process
• Krylov subspace
• thick restarting

2000 AMS Subject Classifications :

• 65F15
• 65F10

Acknowledgements

We express our special thanks to Prof. Choi-Hong Lai and the two reviewers for their valuable suggestions that make us greatly improve the presentation of this paper. Hong-xiu Zhong is supported by the Postgraduate Science Topical Foundation of Xuzhou Normal University under grant 08YLB023. Gang Wu is partially supported by the National Natural Science Foundation of China under grant 10901132, the Natural Science Foundation for Colleges and Universities in Jiangsu Province under grant 08KJB110012, the Qing-Lan Project of Jiangsu Province under grant QL200612, and the Natural Science Foundation of Xuzhou Normal University under grant 08XLY01. \reversemarginpar