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: