Science in China Series A: Mathematics

, Volume 50, Issue 11, pp 1651–1660

On the Hermite interpolation

Authors

    • Department of MathematicsZhejiang University
Article

DOI: 10.1007/s11425-007-0116-2

Cite this article as:
Wang, X. SCI CHINA SER A (2007) 50: 1651. doi:10.1007/s11425-007-0116-2

Abstract

Explicit representations for the Hermite interpolation and their derivatives of any order are provided. Furthermore, suppose that the interpolated function f has continuous derivatives of sufficiently high order on some sufficiently small neighborhood of a given point x and any group of nodes are also given on the neighborhood. If the derivatives of any order of the Hermite interpolation polynomial of f at the point x are applied to approximating the corresponding derivatives of the function f(x), the asymptotic representations for the remainder are presented.

Keywords

Hermite interpolationcycle indexnumerical differentiationexplicit representationremainder

MSC(2000)

65D25, 65D05

Copyright information

© Science in China Press 2007