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Sbornik: Mathematics, 2017, Volume 208, Issue 11, Pages 1578–1601
DOI: https://doi.org/10.1070/SM8865 (Mi sm8865) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

A. Böttchera, J. M. Bogoyab, S. M. Grudskyc, E. A. Maximenkod

a Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany
b Pontificia Universidad Javeriana, Bogotá, Colombia
c Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Ciudad de México, Mexico
d Instituto Politécnico Nacional, Escuela Superior de Física y Matemáticas, Ciudad de México, Mexico
English version PDF (604 kB) Citations (17)
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DOI: https://doi.org/10.1070/SM8865
Abstract: Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009–2010. A survey of this new field is presented here.
Bibliography: 55 titles.
Keywords: Toeplitz matrices, eigenvalues, eigenvectors, asymptotic expansion.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología 238630
IPN-SIP - Secretaría de Investigación y Posgrado, Instituto Politécnico Nacional 20170660
S. M. Grudsky's research was carried out with the support of Proyecto CONACYT (grant no. 238630). E. A. Maximenko's research was carried out with the support of Proyecto IPN-SIP (grant no. 20170660).
Received: 19.11.2016 and 06.02.2017
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 11, Pages 4–28
DOI: https://doi.org/10.4213/sm8865
Bibliographic databases:
Document Type: Article
UDC: 512.643.5
MSC: Primary 15A18, 15B05; Secondary 47B35
Language: English
Original paper language: Russian
Citation: A. Böttcher, J. M. Bogoya, S. M. Grudsky, E. A. Maximenko, “Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices”, Mat. Sb., 208:11 (2017), 4–28; Sb. Math., 208:11 (2017), 1578–1601
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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