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An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices
Katholieke Univ Leuven, Belgium.ORCID iD: 0000-0002-7598-4521
2009 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 31, no 4, 1894-1914 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 31, no 4, 1894-1914 p.
Keyword [en]
Toeplitz matrix, rational function, generalized eigenvalues, (vector) potential theory
National Category
URN: urn:nbn:se:kth:diva-93348DOI: 10.1137/090778468ISI: 000279347600018OAI: diva2:515711
QC 20120627Available from: 2012-04-14 Created: 2012-04-14 Last updated: 2012-06-27Bibliographically approved

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Duits, Maurice
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