用Hermte插值多项式构造五次、三次样条函数

在文［１］中我们给出了一种Ｈｅｒｍｉｔｅ插值多项式的构造方法，其中的系数Ｈｑ（ｔｊ）是以元素为已知的行列式表示的．本文对结点是两个和三个的情形讨论行列式Ｈｑ（ｔｊ）的展开式，并且可以类似地得到更一般的情形．作为应用的例子，我们利用Ｈｑ（ｔｊ）的展开式和有关约束条件导出五次样条函数的表达式，三次样条函数则可以看作五次样条函数的特例，并得到和［３］完全一样的结果．

The Construction of quintic and Cubic splines is Given by Hermite Interpolotion Polynomials

A construct method of Hermite interpolation polynomials is given in the paper[1]. In it,the coeffieiant Hg (tj) is described by the determinant that its elements are known. In this paper, the authorhas discussed the expansions of Hg (tj) determinant in the status of two and three connection points. and hasobtained the more general form similarly. As an applied example. the author uses the expansions of Hg (tj)to infer the expressions of quintic splines under some constraint conditions. The cubic splines can be used asan special example of quintic splines, and it can be finished with a same conclusion of [3] entirely.