定义于锥面上的多元切触插值问题研究

Research on Multivariate Contact Interpolation Defined on Cone

摘要: 以定义于平面代数曲线上的切触插值研究结果为基础，对定义于锥面上的切触插值问题进行了研究。给出了定义于锥面上的切触插值问题提法和插值的正则条件组，并对插值(条件)泛函组的拓扑结构进行了较为深入的研究，得到了定义于锥面上的切触插值正则(条件)泛函组的判定定理以及迭加方式构造方法，最后给出了实验算例验证了算法的有效性。

Abstract: Based on the research results of tangent interpolation defined on planar algebraic curves, the problem of tangent interpolation defined on a cone was studied. The formulation of the tangent interpolation problem defined on a cone and the regularization condition set for interpolation was given. The topological structure of the interpolation (condition) functional set was thoroughly studied, and the decision theorem and superposition method for the tangent interpolation regu-larization (condition) functional set defined on a cone were obtained. Finally, experimental exam-ples were provided to verify the effectiveness of the algorithm.