切触有理插值函数存在性的判别方法

A criterion for the existence of the osculatory rational interpolating functions

利用Hermite-Newton插值多项式给出了一种代数方法,可直接计算切触有理插值函数的分母在节点处的值,进而得到判别切触有理插值函数存在性的一个充分必要条件;在判别出相应的切触有理插值函数存在时,给出它的具体表达式;文章的最后给出了两个数值例子,具体阐述了上述方法的有效性。

In this paper,a kind of algebra method is presented by means of Hermite-Newton polynomial interpolants,then a new criterion for the existence of the osculatory rational interpolating functions is given, and the expression of the corresponding rational interpolating function when it exists is presented. At the end of this paper, two numerical examples are given to illustrate the proposed criterion.