Science in China Series A: Mathematics

, Volume 50, Issue 11, pp 1651–1660

On the Hermite interpolation



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.


Hermite interpolation cycle index numerical differentiation explicit representation remainder 


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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