马鞍面上的多元Birkhoff插值问题研究

Study on Multivariate Birkhoff Interpolation of Saddle Surfaces

以二元Birkhoff插值研究为基础,进一步研究了三维欧氏空间中马鞍面上的Birkhoff插值。首先给出了马鞍面上的多元Birkhoff插值相关定义,对插值条件组的拓扑结构进行了较为深入的研究,然后给出了构造多元函数插值适定泛函组的添加马鞍面法,最后给出具体实例进行验证。Based on the research of two-dimensional Birkhoff interpolation, this study further investigates Birkhoff interpolation on a saddle surface in three-dimensional Euclidean space. First, relevant definitions of multivariate Birkhoff interpolation on saddle surfaces are provided. An in-depth study of the topological structure of the interpolation condition set is conducted. Then, the method of adding saddle surface techniques to construct a suitable functional set for multi-variable function interpolation is introduced. Finally, specific examples are provided for verification.