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ON THE ASYMPTOTICS OF EIGENVALUES OF SEMIDIAGONAL TOEPLITZ MATRICES
- Authors: Voronin I.V.1
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Affiliations:
- Moscow Institute of Physics and Technology (National Research University)
- Issue: Vol 64, No 6 (2024)
- Pages: 914-921
- Section: General numerical methods
- URL: https://ogarev-online.ru/0044-4669/article/view/273759
- DOI: https://doi.org/10.31857/S0044466924060029
- EDN: https://elibrary.ru/XZPJFN
- ID: 273759
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Abstract
Asymptotic formulas are constructed that allow a uniform estimate of the remainder term for Toeplitz matrices of size 𝑛 for 𝑛 → ∞ in the case when their symbol 𝑎(𝑡) has the form 𝑎(𝑡) = (𝑡 − 2𝑎0 + 𝑡-1)3. This result is a generalization of the result of Stukopin et al. (2021), in which similar asymptotic formulas were obtained for a diagonal Toeplitz matrix with a symbol of a similar form when 𝑎0 = 1. The obtained formulas have high computational efficiency and generalize the results of the classical works of Parterre and Widom on the asymptotics of extreme eigenvalues.
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About the authors
I. V. Voronin
Moscow Institute of Physics and Technology (National Research University)
Email: Voronin.I@phystech.edu
Dolgoprudnyi, Moscow oblast, 141700 Russia
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