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Batalshchikov, A. A.; Grudsky, S. M.; Malisheva, I. S.; Mihalkovich, S. S.; Ramírez de Arellano, E.; Stukopin, V. A.

Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbols. (English) Zbl 1420.15019

Linear Algebra Appl. 580, 292-335 (2019).
Summary: This paper is devoted to the asymptotic behavior of all eigenvalues of the increasing finite principal sections of an infinite symmetric (in general non-Hermitian) Toeplitz matrix. The symbol of the infinite matrix is supposed to be moderately smooth and to trace out a simple loop in the complex plane. The main result describes the asymptotic structure of all eigenvalues. The asymptotic expansions constructed are uniform with respect to the location of the eigenvalues in the bulk of the spectrum.

Cited in 4 Documents

MSC:

15B05 Toeplitz, Cauchy, and related matrices
15A18 Eigenvalues, singular values, and eigenvectors
41A25 Rate of convergence, degree of approximation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

Toeplitz matrices; eigenvalues; asymptotic expansions
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References:

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