The Divergence of Lagrange Interpolation for |x|α at Equidistant Nodes Original Research Article

In 1918 S. N. Bernstein published the surprising result 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 (0<α⩽1) on equidistant nodes in [−1, 1] diverges everywhere in the interval except at zero and the end-points.