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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
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.
Received: 19.11.2016 and 06.02.2017
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
Linking options:
https://www.mathnet.ru/eng/sm8865https://doi.org/10.1070/SM8865 https://www.mathnet.ru/eng/sm/v208/i11/p4
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Abstract page: | 596 | Russian version PDF: | 134 | English version PDF: | 27 | References: | 57 | First page: | 38 |
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