四面体框架上的Lagrange插值

Lagrange interpolation on tetrahedron frame

在以往研究二元函数Lagrange插值的基础上,对四面体框架上的三元Lagrange插值结点组可解性问题进行了研究.给出了构造四面体框架上三元Lagrange插值可解结点组的迭加构造方法以及利用可解结点构造三元多项式空间上的插值多项式的方法,搞清了四面体框架上的Lagrange插值可解结点组的某些基本理论和拓扑结构.所得构造方法都是以迭加方式来实现的,这对于编译计算机算法程序,进而在计算机上自动完成插值可解结点组的构造并得到插值格式创造了十分便利的条件.最后给出了实例验证算法的有效性.

Based on the results for bivariate function Lagrange interpolation,the solvability problems for trivariate function interpolation are studied.The quadric surfaces complete intersection and the solvability of Lagrange interpolation nodes on the set of some basic concept are proposed.The quadric interpolation nodes on the set of some basic theory and topology are researched.The structure of quadratic algebraic surface and the space algebra curve interpolation node set to add quadric surface method are given.These methods are based on the superposition method constructed,so it is very convenient to compile the program of computer algorithm and solve automatically interpolation on the structure of the node set.A numerical example is given to verify the validity of the algorithm.