多元插值格式的计算机实现

Acquired by Computer on the Schemes of Multivariate Interpolation

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。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 prod- uct design, research and production. This paper first introduces the basic concepts of multivariate interpola- tion, and then studies the existence and uniqueness of multivariate interpolation function, that is, how to cho- ose 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 and curve superposition method. The application of construction method is given in this paper. We use MATLAB software to realize binary linear interpolation, binary quadric and bi- nary cubic interpolation and find that interpolation effect is also getting better and better along with the in- crease in the degree of interpolation polynomial