Some new properties of Chebyshev polynomials

摘要

This paper deals with the problem of the polynomial interpolation of data subject to bounded perturbations. In particular, we show that interpolation on the Chebyshev polynomial extrema minimizes the diameter of the set of the vectors of the coefficients of all possible polynomials interpolating the perturbed data. In doing so, some new properties of the Chebyshev polynomials are obtained as well. Some of the proposed results are of direct interest in system identification theory when considering the optimal input design for the identification of non linear block described dynamic systems, such as Hammerstein and Wiener models.