超球面上多元Lagrange插值问题研究
Research on Multivariate Lagrange Interpolation Problems on Hyperspheres

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.