摘要
多元插值是目前计算数学领域的一个热门研究问题,这源于它在多元函数列表、有限元法、工业产品外形设计等实际科研生产中的广泛应用.首先给出了三元分次插值的基本概念,进而研究了多元分次插值函数的存在唯一性问题,构造出六面体上的插值基函数,得到了构造三元分次插值适定结点组的构造方法.最后应用本文给出的构造方法,使用MATLAB软件来分别计算三元函数在六面体上的三元一次、三元二次插值多项式,并将计算所得结果进行了对比,发现随着插值多项式次数的增加插值效果也越来越好.
Multivariate interpolation problem is one of the important contents which is a hot research currently.This paper firstly proposed what is multivariate interpolation problem. On one dimensional space,there must be the interpolation polynomial,but on（ n） space,interpolation polynomial may not necessarily exist,so in this paper,the existence and uniqueness of multivariate interpolation function problem was studied,that is to say what kind of node configuration to make the multivariate interpolation polynomial existent and unique. Then put the well-posed node set of methods applied to concrete function,and use computer to realize one dimensional interpolation and bivariate interpolation of trivariate polynomials. Finally we compared their results,and found that with the increase of number of polynomial interpolation,the interpolation effect is getting better and better.
出处
《吉林师范大学学报（自然科学版）》
2016年第2期45-49,共5页
Journal of Jilin Normal University:Natural Science Edition
基金
国家自然科学基金项目(41171137)
关键词
适定结点组
多元多项式
分次插值
多元插值
well-posed node set
the multivariate polynomial
graded interpolation
the multivariate interpolation
