方形网格上的Stieltijes型混合有理插值

摘要

文章基于Stieltijes型分叉连分式有理插值，结合Thiele型连分式及Newton多项式，构造了一种方形网格上的二元混合有理插值函数，通过定义偏差商、偏逆差商和混合逆差商建立递推算法。构造的这种有理插值函数满足有理插值P1题中所给的插值条件，并给出了插值的特征定理及其证明，进行了误差分析，最后给出的数值例子，验证了所给算法的有效性。%In this paper, bivariate blending rational interpolation function was constructed based on stieltijes＇ branched continued fraction, Thiele rational interpolation and Newton polynomial. By defining the partial difference, the partial inverse difference and blending inverse difference building the recursive algorithm. The bivariate rational function which interpolates the given support points, and interpolating characteristic theorem and its proof is given, also error analysis.. Numerical examples are given to show the effectiveness of the result.