On an interpolation polynomial of S. N. Bernstein type (Q1912698)

The main object of the paper is the modification of the construction of a sequence of interpolation nodes (zeros of Chebyshev polynomials) and of the corresponding prescription of values due to S. N. Bernstein (1932) in such a way that for any continuous function \(f: [-1,1 ]\to \mathbb{R}\) the order of convergence of the corresponding interpolation polynomials \(P_n (f)\), \(n=1, 2, \dots\), is the order of best approximation.