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 this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [−1, 1] still diverges every where in the interval except at zero and the end-points.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bernstein, S., Quelques Remarques Surl’interpolation, Math. Ann., 79(1918), 1–12.
Natanson, I. P., Constructive Function Theory, Vol. III, Frederick Ungar, New York, 1965.
Byrne, G., Mills, T. M. and Smith, S. J., On Lagrange Interpolation with Equidistant Nodes, Bull. Austral Math. Soc., 42(1990), 81–89.
Brutman, L. and Passow, E., On the Divergence of Lagrange Interpolation to |x|, J. Approx. Theory, 81(1995), 127–135.
Revers, M., The Divergence of Lagrange Interpolation for |x|a at Equidistant nodes, J. Approx. Theory, 103(2000), 269–280.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhikang, L., Mao, X. The divergence of Lagrange interpolation in equidistant nodes. Anal. Theory Appl. 19, 160–165 (2003). https://doi.org/10.1007/BF02835241
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02835241