# On the Hermite interpolation

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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

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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.