构造切触有理插值的一种方法

切触有理插值是Hermite插值的一种推广,已有的构造切触有理插值方法都与连分式相联系,因此其算法可行性是有条件的,且计算量较大,讨论无条件的构造切触有理插值的方法具有实际应用价值。利用凸组合方法可方便地构造出数量值切触有理插值函数或向量值和矩阵值函数,其构造过程公式化,便于在计算机上实现,且计算量较小,具有广阔的应用前景。

A way of constructing osculatory rational interpolation

Osculatory rational interpolation is a generalization of Hermite interpolation.As the existing methods of constructing osculatory rational interpolation are all related to continued fractions,the feasibility of their algorithms is conditional and they need a large amount of calculation.In this paper,the method of convex combination is used to construct the osculatory rational interpolating function.The presented method can also be used to construct conveniently the vector-valued osculatory rational interpolating function or the matrix-valued osculatory rational interpolating function.The course of constructing is formulary and convenient to realize on the computer,and it needs a small amount of calculation,so the presented method has a bright application future.