三角网格上的对称型向量值混合连分式插值

Symmetrical Vector-valued Blending Continued Fractions Interpolation on Triangular Mesh

基于向量Samlson逆的意义下,给出了三角网格上向量有理插值问题,本文将对称型向量连分式与逐次降阶的一元向量值多项式结合起来,通过定义偏差商和混合反差商,建立递推算法,构造了三角网格上的向量有理插值函数,满足所给的向量有理插值问题的条件,并给出了插值定理及它的证明,最后给出的数值例子,验证了算法的有效性。

Based on generalized vector of Samlson inverse, and some issues concerning rational interpolation, this paper combines symmetrical vector valued continued fractions with decreasing mono-vector valued polynomials, establishes recursive algorithm through defined partial inverted difference and blending inverse difference, constructs vector valued rational interpolation functions satisfying all the conditions of vector valued rational interpolation, and offers interpolation theorem, characteristics theorem and the demonstration. Finally, numerical examples are provided to prove the validity of the algorithm.