A Guass–Newton-like method for inverse eigenvalue problems

Abstract

In this paper, we propose a Guass–Newton-like method for finding least-square solutions to inverse eigenvalue problems. We show that the proposed method converges under some mild conditions. In particular, if the method converges to the exact solution, the convergence rate is at least quadratic in the root sense. Numerical examples are given to justify the theoretical result.

Keywords:

• inverse eigenvalue problem
• the Guass–Newton method
• least-square solutions
• iterative methods
• inverse power method

2010 AMS Subject Classifications :

• 65F18
• 65F10
• 15A18

Acknowledgements

The authors are very grateful to the two anonymous referees for their valuable comments which have considerably improved this paper. The authors also thank Prof. Xiao-Qing Jin for helpful discussions on this problem. This research is supported by the grant MYRG086(Y1-L2)-FST12-VSW from the University of Macau.