Szegő quantiles, constructor of piecewise linear examples

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

Please, construct a piecewise linear function g.  Select the number of pieces:

Choose the intermediate points (they must strictly increase) and the values of g at the intermediate points:

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: