马鞍面上的多元Birkhoff插值问题研究
Study on Multivariate Birkhoff Interpolation of Saddle Surfaces
摘要: 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。
Abstract: 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.
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