An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices
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
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.
Toeplitz matrix, rational function, generalized eigenvalues, (vector) potential theory
IdentifiersURN: urn:nbn:se:kth:diva-93348DOI: 10.1137/090778468ISI: 000279347600018OAI: oai:DiVA.org:kth-93348DiVA: diva2:515711
QC 201206272012-04-142012-04-142012-06-27Bibliographically approved