中文摘要：

二元切触有理插值是有理插值的一个重要内容．而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题．二元切触有理插值算法的可行性大都是有条件的，且计算复杂度较大，有理函数的次数较高．利用二元Hermite（埃米特）插值基函数的方法和二元多项式插值误差性质，构造出了一种二元切触有理插值算法并将其推广到向量值情形．较之其它算法，有理插值函数的次数和计算量较低．最后通过数值实例说明该算法的可行性是无条件的，且计算量低．

英文摘要：

The bivariate osculatory rational interpolation is an important element of rational interpolation, and reducing the degrees of the osculatory rational interpolation functions and solving their existence make an important problem. The bivariate osculatory rational interpolation algorithms mostly have conditional feasibility and massive computational complexity with high function degrees. A bivariate osculatory rational interpolation algorithm was obtained on rectangular grids and extended to vector-valued cases, with the method of bivariate Hermite interpolation basis function in view of the error characteristics of bivariate polynomial interpolation. The numerical examples illustrate that, compared to other methods, the feasibility of the presented algorithm is unconditional, the degrees of the related rational functious are lower, and the algorithm has less computational complexity.