定义于双曲抛物面上的多元Lagrange插值问题

Multivariate Lagrange Interpolation Defined on Hyperbolic Paraboloid

摘要: 对计算数学领域的重要内容多元Lagrange插值的问题做出了研究。首先对定义于双曲抛物面上的多元Lagrange插值下定义并对定义进行了简单的分析，随后，提出了迭加构造方法且对双曲抛物面上的结点组能否构成插值唯一可解结点组给出了判定定理，对多元函数插值的意义进行了一些简单的分析，最终通过三次分别选取不同的被插值函数与不同的双曲抛物面的方程对所得方法展开进一步的验证。

Abstract: Multivariate Lagrange interpolation, an important content in the field of computational mathematics, is studied. Firstly, the multivariate Lagrange interpolation defined on hyperbolic paraboloid is defined and the definition is simply analyzed. Then, the superposition construction method is proposed and the judgment theorem is given for whether the node group on hyperbolic paraboloid can form the unique solvable node group of interpolation. The significance of multivariate function interpolation is simply analyzed. Finally, the method is further verified by selecting different interpolated functions and hyperbolic paraboloid equations three times respectively.