定义于圆锥体上的Hermite插值研究

Hermite Interpolation Defined on a Cone

摘要: 本文主要是对定义于圆锥体上的Hermite插值问题进行研究，所讨论的内容基于多元逼近的范畴，在二元Hermite插值公式的基础上，给出了三元Hermite插值公式。作者根据直角三角形通过旋转得到的圆锥体，从直角三角形上的二元Hermite插值联想到圆锥体上的三元Hermite插值。根据代数集和理想的相关知识，得到了添加平面法构造插值适定结点组的方法，从而找到了圆锥体上的插值适定结点组。并以圆锥体上的Hermite插值为例，给出了插值公式和计算方法，通过具体的算例和Matlab软件给出插值效果图，可以看出此算法的优势。

Abstract: This paper mainly studies the Hermite interpolation problem defined on the cone. The content dis-cussed is based on the category of multivariate approximation. Based on the Two-dimensional Her-mite interpolation formula, the ternary Hermite interpolation formula is given. The author associ-ates the binary Hermite interpolation on the right triangle with the ternary Hermite interpolation on the cone according to the cone obtained by rotating the right triangle. According to the relevant knowledge of algebraic set and ideal, the method of adding plane method to construct the interpo-lation well-posed node group is obtained, and the interpolation well-posed node group on the cone is found. Taking Hermite interpolation on the cone as an example, the interpolation formula and calculation method are given. The advantages of this algorithm can be seen through the specific example and the interpolation effect diagram given by Matlab software.