New regions including eigenvalues of Toeplitz matrices

Abstract

Two new eigenvalue inclusion regions for matrices with a constant main diagonal are given. We then apply these results to Toeplitz matrices, and obtain two regions including all eigenvalues of Toeplitz matrices. Furthermore, it is proved that the new regions are tighter than those in [Melman A. Ovals of Cassini for Toeplitz matrices, Linear and Multilinear Algebra. 2012;60:189–199].

Keywords:

• eigenvalue
• Toeplitz
• Geršgorin
• Brauer

AMS Subject Classifications:

• 15A18
• 15B05

Acknowledgments

The authors are grateful to the referees for their useful and constructive suggestions. This work was supported by National Natural Science Foundations of China (10961027, 71161020, 71162005), IRTSTYN and 2012CG017.