三角网格上的对称型混合有理插值

Symmetric type blending rational interpolation on the triangular grid

将对称型连分式与逐次降价的一元多项式结合起来,通过定义偏差商和混合反差商,建立递推算法,构造三角网格上的有理插值函数,满足所给的有理插值问题的条件,并给出了插值定理、特征定理及其证明.最后给出的数值例子,验证了算法的有效性.

By defining the partial difference quotient and blending inverse difference quotient,the recursive algorithm was built, combined the symmetric type interpolating continued fractions with successive depressed polynomial, a rational interpolation function on the triangular grid was structured and the given interpolating conditions was satisfied, the interpolating theorem and characteristic theorem was illustructed and a numerical example was presented to illustrate the efficiency of this algorithm in the end.