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On the Hermite interpolation

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Xing-hua Wang

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  1. Xing-hua Wang
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Correspondence to Xing-hua Wang.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471128)

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Wang, Xh. On the Hermite interpolation. SCI CHINA SER A 50, 1651–1660 (2007). https://doi.org/10.1007/s11425-007-0116-2

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  • DOI: https://doi.org/10.1007/s11425-007-0116-2

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