Science in China Series A: Mathematics

, Volume 50, Issue 11, pp 1651–1660

On the Hermite interpolation

Article

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 interpolation cycle index numerical differentiation explicit representation remainder 

MSC(2000)

65D25, 65D05 

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Copyright information

© Science in China Press 2007

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina

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