In the present paper we consider the approximation of \x\ a on [-1,1] by interpolating polynomials and we establish upper bounds for the approximation error. It turns out that these bounds, apart from the constants, are of the best possible order. We compare our results with estimates for the best approximation, established by Bernstein.

A well-known result due to S.N. Bernstein is that the sequence of Lagrange interpolation polynomials for \x\ at equally spaced nodes in [-1,1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x| at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

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In this paper we present a generalized quantitative version of a result due to D. L. Berman concerning the exact convergence rate at zero of Lagrange interpolation polynomials to x j j a based on equally spaced nodes in À1Y 1 . The estimates obtained turn out to be best possible.