多元插值格式的计算机实现
Acquired by Computer on the Schemes of Multivariate Interpolation
DOI:10.12677/AAM.2013.24024,PDF,HTML,被引量下载: 3,095浏览: 8,425国家自然科学基金支持
作者:崔利宏,王晓婉,杨一浓：辽宁师范大学数学学院，大连；鲍 焕：大连理工大学数学学院，大连
关键词:适定结点组；多元多项式；多元插值；Well-Posed Node Set; The Multivariate Polynomial; The 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 studiesthe 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 methodandcurve superposition method. The application of construction method is given in this paper.We use MATLAB software to realize binary linear interpolation,binaryquadricandbi-nary cubic interpolation and find that interpolation effect is also getting better and betteralong with the in-crease in the degree of interpolation polynomial
文章引用：崔利宏, 王晓婉, 杨一浓, 鲍焕. 多元插值格式的计算机实现[J]. 应用数学进展, 2013, 2(4): 179-185. http://dx.doi.org/10.12677/AAM.2013.24024
为你推荐



Baidu
map