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ON THE ASYMPTOTICS OF EIGENVALUES OF SEMIDIAGONAL TOEPLITZ MATRICES
- Authors: Voronin I.V.1
-
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://rjonco.com/0044-4669/article/view/665059
- DOI: https://doi.org/10.31857/S0044466924060029
- EDN: https://elibrary.ru/XZPJFN
- ID: 665059
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Abstract
Asymptotic formulas are constructed that allow a uniform estimate of the remainder term for Toeplitz matrices of size
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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
References
- Stukopin V., Grudsky S., Voronin I., Barrera M. Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form // arXive. 2021. Nov. 2111.07196.
- Savage L. J., Grenander U., Szego G. Toeplitz forms and their Applications // J. Am. Statistic. Associat. 1958. V. 53. N 283. P. 763.
- Schmidt P., Spitzer F. The Toeplitz matrices of an arbitrary Laurent polynomial // Math. Scandinavica. 1960. V. 8. P. 15.
- Widom H. Eigenvalue distribution of nonselfadjoint Toeplitz matrices and the asymptotics of Toeplitz determinants in the case of nonvanishing index // Oper. Theory Adv. Appl. 1990. V. 48.
- Bottcher A., Grudsky S. M. Spectral properties of banded Toeplitz matrices // Soc. Industrial and Appl. Math. 2005.
- Bottcher A., Silbermann B. Introduction to large truncated Toeplitz matrices. Springer New York, 1999.
- Deift P., It’s A., Krasovsky I. Toeplitz Matrices and Toeplitz determinants under the impetus of the ising model: some history and some recent results // Comm. on Pure and Appl. Math. 2013. V. 66, N 9. P. 1360–1438.
- Deift P., It’s A., Krasovsky I. Eigenvalues of Toeplitz matrices in the bulk of the spectrum // Bull. Inst. Math. Acad. Sin. 2012. V. 7. P. 437–461.
- Kadano L. P. Spin-spin correlations in the two-dimensional ising model // Il Nuovo Cimento B Ser. 10. 1966. V. 44. N 2. P. 276–305.
- McCoy B., Wu T. The Two-Dimensional Ising Model, 1973.
- Batalshchikov A. A., Grudsky S. M., Stukopin V. A. Asymptotics of eigenvalues of symmetric Toeplitz band matrices // Linear Algebra and its Applications. 2015. V. 469. P. 464–486. https://www.sciencedirect.com/science/article/pii/S0024379514007691
- Szego G. Ein Grenzwertsatz uber die Toeplitzschen Determinanten einer reellen positiven Funktion // Math. Annalen. 1915. V. 76. N 4. P. 490–503.
- Eloua M. On a relationship between Chebyshev polynomials and Toeplitz determinants // Appl. Math. Comput. 2014. V. 229. P. 27–33.
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