中文摘要：

针对目前高阶导数切触有理插值方法计算复杂度较高的问题,利用多项式插值基函数和多项式插值误差的性质,给出一种不仅满足各点插值阶数不相同且插值阶数最高为2的切触有理插值算法,并将其推广到向量值切触有理插值中.解决了切触有理插值函数的存在性及算法复杂性问题,并通过数值实例证明了算法的有效性.

英文摘要：

In view of the higher computational complexity of the osculatory rational interpolation method of higher derivative mostly based on the idea of generalized vandermonde matrix, by means of basis function of polynomial interpolation and error nature of polynomial interpolation, we proposed an osculatory rational interpolation algorithm that not only satisfies different interpolation order but also makes the toppest of interpolation order equal 2, and it also meets the vector-valued osculatory rational interpolation. It solves the problem of the existence of osculatory rational interpolation function and complexity of algorithm. In the end, we illustrated the effectiveness of the algorithm with a numerical example.