多元函数插值格式的构造方法

Methods of Construction on the Schemes of Multivariate Interpolation

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.本文首先介绍了多元插值的基本概念,进而研究了多元插值函数的存在唯一性问题,也就是如何选择结点组才能使多元插值多项式函数惟一存在问题,同时本文给出了多元插值结点组的一些构造方法,如:直线法叠加法、弧线叠加法.本文将这两种构造方法应用到具体的示例中,最后应用本文给出的构造方法,我们用MATLAB软件来分别实现了二元一次、二元二次和二元三次插值,并将它们进行了对比,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 is one of the hot research problems of computational mathematics,which derives its widespread application in the list,the multiple functions of finite element method,industrial product design,research and production. This paper first introduces the basic concepts of multivariate interpolation,and then studied the existence and uniqueness of multivariate interpolation function,that is how to choose the set of nodes to make the existence and uniqueness of multivariate interpolation polynomial function at the same time, this paper gives some construction methods on set of nodes for multivariate interpolation,such as： linear superposition method,curve superposition method. The application of construction method is given in this paper, we use MATLAB software to realize Linear interpolation,two times three times interpolation and found that along with the increase in the degree of interpolation polynomial interpolation effect is also getting better and better.