二元切触有理插值公式

Formula of bivariate osculatory rational interpolation

降低切触有理插值的次数和解决切触有理插值函数的存在性是有理插值的一个重要问题。利用牛顿插值承袭性的思想和分段组合方法,构造出一种二元切触有理插值算法并推广到向量值有理插值,既解决了有理插值的存在性问题,又降低了切触有理插值函数的次数。相比于其他方法,算法的可行性是无条件的,有理插值函数次数较低,算法具有承袭性、计算量低、便于实际应用的特点。

Reducing the degree of osculatory rational interpolation function and solving the existence of osculatory rational in- terpolation function is an important problem of rational interpolation. This paper constructs a bivariate osculatory rational inter- polation algorithm and extends it to vector-valued rational interpolation, by means of nature of heredity and the method of piece- wise combination. Compared to other algorithms, this algorithm is unconditional, the degree of rational function is lower, this al- gorithm has inherited nature and has less computation, and it is easy to application.