超球面上多元Lagrange插值问题研究  

Research on Multivariate Lagrange Interpolation Problems on Hyperspheres

作　　者：王心蕊 马亚茹 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11期3246-3253,共8页Pure Mathematics

摘　　要：以三元函数Lagrange插值研究结果为基础,对n元函数Lagrange插值结点组的适定性问题进行了研究。提出了超球面上的Lagrange插值适定结点组的基本概念,研究了超球面上的Lagrange插值适定结点组的某些基本理论和拓扑结构,得到了构造超球面上的Lagrange插值适定结点组的添加超平面法。这些方法都是以迭加方式完成的,因此便于在计算机上实现其构造过程。最后给出了具体实验算例。Based on the research results of three-variable Lagrange interpolation, an investigation into the suitability of node sets for n-variable Lagrange interpolation was conducted. The fundamental concept of well-suited node sets for Lagrange interpolation on hyperspheres was proposed. Certain fundamental theories and topological structures of well-suited node sets for Lagrange interpolation on hyperspheres were studied, leading to the development of the method of adding hyperplanes for constructing well-suited node sets for Lagrange interpolation on hyperspheres. These methods are accomplished in an iterative manner, making them suitable for implementation on a computer. Finally, specific experimental examples are provided.

关 键 词：多元Lagrange插值 唯一可解结点组 超球面 迭加插值法 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]