Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols

被引：34

作者：

Bogoya, J. M. ^{[1
]}

Boettcher, A. ^{[2
]}

Grudsky, S. M. ^{[3
]}

Maximenko, E. A. ^{[4
]}

机构：

[1] Pontificia Univ Javeriana, Dept Matemat, Bogota 01110, DC, Colombia

[2] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[3] CINVESTAV, Dept Matemat, Ciudad De Mexico 07360, Mexico

[4] Inst Politecn Nacl, Escuela Super Fis & Matemat, Mexico City 07730, DF, Mexico

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 422卷 / 02期

关键词：

Toeplitz matrix; Eigenvalue; Asymptotic expansion; Spectral asymptotics; DETERMINANTS; ASYMPTOTICS;

D O I：

10.1016/j.jmaa.2014.09.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1308 / 1334

页数：27

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