Eigenvalues of non-Hermitian banded Toeplitz matrices approaching simple points of the limiting set

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详细

For large non-Hermitian banded Toeplitz matrices, it is well known that their eigenvalues cluster along a limiting set, which is formed by a finite union of closed analytic arcs. We consider general non-Hermitian banded Toeplitz matrices and extend the simple-loop method to obtain individual asymptotic expansions for eigenvalues approaching simple and non-degenerate points of the limiting set as the matrix order increases to infinity. We also develop an algorithm to effectively compute these expansions.

作者简介

M. Bogoya

Universidad del Valle

Email: johan.bogoya@correounivalle.edu.co
Cali, Colombia

S. Grudsky

CINVESTAV-IPN; Southern Federal University, Regional Mathematical Center

Email: grudsky@math.cinvestav.mx
CDMX, Mexico; Rostov-on-Don, Russia

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