基于降维的多维插值数值算法

在科学研究和工程技术中,常遇到数据插值问题,多维插值作为比一维插值更一般的形式,其典型代表是二维插值。对于二维插值问题,文章用基于降维思想的分析方法推导出二元函数F(X,Y)的插值多项式,并对插值误差作了分析,得到插值多项式的余项,用来对计算结果进行误差估计。最后给出了多维插值在工程上的一个算例。

In scientific research and project technology, some interpolation questions are often encountered. Multi-dimensional interpolation, whose typical representative is two-dimensional interpolation, is considered more general than one-dimensional interpolation. Regarding the two- dimensional interpolation question, this paper, with the analysis method based on the thought falling dimension, deduces the interpolation multinomial of binary function f（x,y）, analyzes the interpolation error of the interpolation error, and obtains the remainder of the interpolation multinomial to estimate the computed result. Finally, the paper presents an example of the multi-dimensional in project.