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Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A.

Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols. (English) Zbl 1302.65086

J. Math. Anal. Appl. 422, No. 2, 1308-1334 (2015).
Summary: The paper presents higher-order asymptotic formulas for the eigenvalues of large Hermitian Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line. The formulas are established not only for the extreme eigenvalues, but also for the inner eigenvalues. The results extend and make more precise existing results, which so far pertain to banded matrices or to matrices with infinitely differentiable symbols. Also given is a fixed-point equation for the eigenvalues which may be solved numerically by an iteration method.

Cited in 4 Reviews
Cited in 30 Documents

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15B05 Toeplitz, Cauchy, and related matrices
15B57 Hermitian, skew-Hermitian, and related matrices

Keywords:

Toeplitz matrix; eigenvalue; asymptotic expansion; spectral asymptotics; extreme eigenvalue; inner eigenvalue; banded matrices; fixed-point iteration; iteration method
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References:

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