A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function

DOI：10.3770/j.issn:1000-341X.2011.04.004

 作者 单位 郑林 上海大学数学系, 上海 200444 朱功勤 合肥工业大学 数学系, 安徽 合肥 230009

目前矩形网格上的向量值有理插值函数的构造方法,都是基于分叉连分式建立的(见[1]). 为了得到次数较低,逼近效果较好的向量值有理插值函数,本文利用选取非负整参数$d_{1}(0\leq d_{1}\leq m)$和$d_{2}(0\leq d_{2}\leq n)$, 将矩形网格分片,对每一片建立二元多项式向量插值,再进行适当组合,给出一种新的构造向量值有理插值函数的方法. 与已有方法相比,具有简便易行,次数较低.

At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters $d_{1}~(0\leq d_{1}\leq m)$ and $d_{2}~(0\leq d_{2}\leq n)$, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.