中文摘要：

讨论了一般多点多重Hermite插值问题,利用局部自由因子获得了完全展开的多点多重Newton型插值公式,给出了增加一个自由度时的插值递推公式及有重差商表的构造原理.并提出了计算Newton型插值公式的多种快速算法.

英文摘要：

This paper discusses the general multiple hermite interpolation problem. A complete expansion of Newton-form with multiple and multiple points is proceeded using locally free factor, and an interpolation recursion formula and the construction theorem of multiple divided difference table are given if a degree of freedom is added. Many fast algorthims are provided to compute the Newton-form interpolation formula.