Two-step Ulm–Chebyshev-like Cayley transform method for inverse eigenvalue problems

Abstract

In this paper, based on the two-step Ulm–Chebyshev iterative procedure and the Cayley transform, we propose a two-step Ulm–Chebyshev-like Cayley transform method for inverse eigenvalue problems. Under some mild assumptions, our results show that the two-step Ulm–Chebyshev-like Cayley transform method is cubically convergent. Numerical implementations demonstrate the effectiveness of the new method.

Keywords:

• Inverse eigenvalue problems
• Ulm–Chebyshev-like Cayley transform method
• cubically convergent

2010 AMS subject classifications:

• 65F18
• 65F15
• 15A18

Acknowledgments

The author would like to thank the anonymous referees for their valuable comments and suggestions on our early version.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of this author was partially supported by the Special Project Grant of Nanyang Normal University (ZX2014078).