Published 2010
| Published
Journal Article
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An Equilibrium Problem for the Limiting Eigenvalue Distribution of Rational Toeplitz Matrices
- Creators
- Delvaux, Steven
- Duits, Maurice
Abstract
We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a particular component of the unique solution to a vector equilibrium problem. Moreover, we show that the other components describe the limiting behavior of certain generalized eigenvalues. In this way, we generalize recent results by Kuijlaars and one of the authors [SIAM J. Matrix Anal. Appl., 30 (2008), pp. 173–196] that were concerned with banded Toeplitz matrices.
Additional Information
© 2010 Society for Industrial and Applied Mathematics. Received by the editors November 30, 2009; accepted for publication (in revised form) by H. J. Woerdeman February 19, 2010; published electronically April 21, 2010. The authors thank professor Arno Kuijlaars for stimulating discussions.Attached Files
Published - Delvaux2010p10796Siam_J_Matrix_Anal_A.pdf
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Additional details
- Eprint ID
- 19107
- Resolver ID
- CaltechAUTHORS:20100719-112202959
- Created
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2010-07-19Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field