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

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Abstract

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.

About the authors

M. Bogoya

Universidad del Valle

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

S. M Grudsky

CINVESTAV-IPN; Southern Federal University, Regional Mathematical Center

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

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