一般Hermite插值公式的金字塔算法

Pyramid algorithm of general Hermite interpolation

为了克服求解一般Hermite插值公式的复杂计算,利用Neville公式构造算法金字塔,推导在节点x0,x1,…,xn上带有一阶导数信息的插值公式,并给出了基函数及组合系数,进而,综合Neville和Aitken思想,得到函数下标的可交换性,该性质大大减少了计算复杂度,并由此推广得到带有任意阶导数信息的一般Hermite插值公式的金字塔算法,将该算法应用于数值算例中。给定了4个节点上的插值信息,分段计算并画图,在端点处进行拼接,图形表明在内节点处拼接曲线仍保持一定光滑性。结果表明:该算法直观简便,可操作性强,极大的克服了传统代数方法求解的复杂性。

To overcome the complex calculations of solving the general Hermite interpolation. Hermite interpolation formula with first-order derivative was deduced by Neville pyramid algorithm, and the basis function and combination coefficient were obtained. Furthermore, in combination with the thought of Neville and Aitken, we could get the interchangeability about the subscript of function. This nature makes the calculating more easy. And thus we could promote that to get the pyramid algorithm of general Hermite interpolation with any order derivative, and this algorithm could be used in the numerical example. The numerical exam- ple presented the information of four points, we divided it into two sections and calculated respectively and drew it. The two sec tions will be pieced together at both ends. Picture shows that the node. The algorithm is simple and intuitive, easy to operate, and ods. two sections still maintain certain smoothness on the common greatly overcome the complexity of traditional algebraic meth-ods.