Eigenvalues of tridiagonal Hermitian Toeplitz matrices

This demo is a part of a joint work by J. M. Bogoya , A. Böttcher, S. Grudsky, E. A. Maximenko.

Here we consider Toeplitz matrices generated by the symbol   g(x) = a + b cos(x) + c sin(x).

The associated quantile function is  Q(p) = a − (b2 + c2)1/2 cos(π p).

Please, choose the values of the coefficients:

  

  

  


Graph of the generating function g: Graph of the quantile function Q:

Show the eigenvalues λn,1,…λn,n of the Toeplitz matrix of order n: