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Bivariate polynomial and continued fraction interpolation over ortho-triples

机译：三元组的二元多项式和连续分数插值

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摘要

By means of the barycentric coordinates expression of the interpolating polynomial over each ortho-triple, some properties are obtained. Moreover, the explicit coefficients in terms of B-net for one ortho-triple, and two ortho-triples are worked out, respectively. Thus the computation of multiple integrals can be converted into the sum of the coefficients in terms of the B-net over triangular domain much effectively and conveniently. Based on a new symmetrical algorithm of partial inverse differences, a novel continued fractions interpolation scheme is presented over arbitrary ortho-triples in R2, which is a bivariate osculatory interpolation formula with one-order partial derivatives at all corner points in the ortho-triples. Furthermore, its characterization theorem is presented by three-term recurrence relations. The new scheme is advantageous over the polynomial one with some numerical examples.
机译：通过每个正交三元组上的插值多项​​式的重心坐标表达式，可以获得一些特性。此外，分别计算出一个正交三和两个正交三的B-net显式系数。因此，可以更有效且方便地将多个积分的计算转换为基于三角域上的B-网的系数之和。基于一种新的偏逆对称对称算法，提出了一种新颖的连续分数插值方案，该方案在R2中的任意正交三元组上，它是在正交三元组的所有角点处具有一阶偏导数的双变量接触插值公式。此外，其表征定理由三项递推关系表示。新方案比带有一些数值示例的多项式方案更具优势。

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