Year: 2024
Type: article
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.
Author: I. V. Voronin
Institution: Moscow Institute of Physics and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4405611077