Abstract:
Asymptotic formulas are derived that admit a uniform estimate of the remainder for Toeplitz matrices of size $n$ as $n\to\infty$ in the case when their symbol $a(t)$ has the form $a(t)=(t-2a_0+t^{-1})^3$. This result is a generalization of the result of Stukopin et al. (2021), who obtained similar asymptotic formulas for a seven-diagonal Toeplitz matrix with a similar symbol in the case $a_0=1$. The resulting formulas are of high computational efficiency and generalize the classical results of Parter and Widom on asymptotics of extreme eigenvalues.
