The divergence of Lagrange interpolation for |x|α (2 < α < 4) at equidistant nodes

Abstract

It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to |x|at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x| α (2 < α < 4) on equidistant nodes in [−1, 1] diverges everywhere, except at zero and the end-points.