二元有理插值公式

Formula of bivariate rational interpolation

降低有理插值函数的次数和解决有理函数的存在性是函数逼近的一个重要问题。文章利用牛顿插值的承袭性性质和分段组合方法,构造出一种二元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。

Reducing the degree of rational interpolation function and solving the existence of rational function are important problems in function approximation. To solve the two problems, we constructed a bivariate rational interpolation algorithm and extended it to vector-valued rational interpolation by means of heredity of Newton interpolation and the method of piecewise combination. Compared to other algorithms, the algorithm is unconditional, and the degree of rational function is lower. Besides, the algorithm has inherited nature and less computation, and is convenient for practical application.