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