On the Divergence of Lagrange Interpolation to |x| Original Research Article

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 show that the case of equally spaced nodes is not an exceptional one in this sense. Namely, we prove that the divergence everywhere in 0 < |x| < 1 of the Lagrange interpolation to |x| takes place for a broad family of nodes, including in particular the Newman nodes, which are known to be very efficient for rational interpolation.