单纯形上多元Lagrange插值问题研究  

Research on Multivariate Lagrange Interpolation on Simplexes

作　　者：马亚茹 周鹏宇 崔利宏[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2023年第12期3594-3602,共9页Pure Mathematics

摘　　要：以四面体框架上的Lagrange插值研究为基础,进一步研究了高维空间中单纯形上的Lagrange插值。给出了构造超四面体框架上四元Lagrange插值可解结点组的迭代方法,并给出了n维空间中单纯形上的Lagrange插值算法,最后给出具体实例进行验证。Building upon the research on Lagrange interpolation in the framework of tetrahedra, this study further investigates Lagrange interpolation on simplices in high-dimensional spaces. An iterative method is proposed for constructing solvable node sets for four-element Lagrange interpolation on hyper-tetrahedra frameworks. Additionally, a Lagrange interpolation algorithm on simplices in n-dimensional space is provided. Finally, specific examples are presented to validate the proposed approach.

关 键 词：单纯形 多元Lagrange插值 可解结点组 迭加插值法 

分 类 号：O17[理学—数学]