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