Abstract: The methods of constructing bivariate osculatory rational interpolation function are mostly based on the continued fraction. But feasibility of the algorithm is conditional, the computation is large, and the degree of it is high. It constructs the bivariate osculatory rational interpolation function and extends it to vector-valued case, by means of the method of piecewise combination. It not only solves the existence problem of osculatory rational interpolation function, but also reduces the degree of rational function. Compared to other methods, the course of constructing function is formulary, the degree of rational interpolation function is lower, the feasibility of algorithm is unconditional, and the algorithm needs less computation and facilitates the practical application.

Key words: bivariate osculatory rational interpolation, piecewise combination, interpolation formula, bivariate Hermite interpolation

摘要： 二元切触有理插值函数的构造方法大都是基于连分式进行的，其算法可行性是有条件的，且计算量较大，有理函数的次数较高。利用分段组合方法，构造出一种二元切触有理插值函数并将其推广到向量值切触有理插值情形，既解决了切触有理插值函数的存在性问题，又降低了切触有理插值函数的次数。相比于其他方法，其构造过程公式化，算法的可行性是无条件的，有理插值函数次数较低，且计算量较小，便于实际应用。

关键词: 二元切触有理插值, 分段组合, 插值公式, 二元埃米特插值