定义于单叶双曲面上的多元切触插值问题研究
Research on Multivariate Contact Interpolation Defined on Hyperboloid of One Sheet

多元插值问题一直是计算数学专业研究领域的一个重要的研究方向，与生产实践相结合更是成为主流趋势。本文针对在建筑学领域中常用的单叶双曲面来研究其上的多元函数切触插值问题。首先给出了定义于单叶双曲面上的多元切触插值定义以及其上正则性问题的提法，对插值条件组的拓扑结构进行了较为深入的研究，得到了定义于单叶双曲面上的切触插值正则条件组的判定定理及两种构造方法，最后给出了定理证明，并以实验算例验证了算法的有效性。
The multivariate interpolation problem has been an important research direction in the research field of computational mathematics, and the combination with production practice has become a mainstream trend. In this paper, we study the multivariate tangent interpolation problem on hyperboloid of one sheet, which is commonly used in the field of architecture. Firstly, the definition of multivariate contact interpolation on hyperboloid of one sheet and the formulation of the regularity problem are given, the topology of the interpolation condition group is studied in depth, and the decision theorem of the contact interpolation condition group on hyperboloid of one sheet and the two constructive methods are obtained, and finally, the theorem proof is given, and the validity of the algorithm is verified by the experimental example.