K. Castillo, C.M. da Fonseca, J. Petronilho (2024) On Chebyshev polynomials and the inertia of certain matrices, Applied Mathematics and Computation, Vol. 467, pp. 128-497, 10.1016/j.amc.2023.128497
Abstract. It was first conjecture and latter proved that the inertia of a certain antipodal tridiagonal pattern that depends on a real parameter \epsilon attains a certain ordered triple for all sufficiently small \epsilon>0. In this note, we show how to compute upper bounds on \epsilon using Chebyshev polynomials.