定义于抛物柱面上的多元切触插值问题研究

Research on Multivariate Contact Interpolation Defined on Parabolic Cylinder

摘要: 以沿平面代数曲线的切触插值研究结果为基础，对沿具体流形抛物柱面的切触插值问题做出了研究。首先对定义于抛物柱面上的多元切触插值正则条件组给出定义并对其拓扑结构进行了较为详尽的研究，得到沿抛物柱面切触插值正则条件组的判定定理以及迭加方式构造插值正则条件组的方法，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 contact interpolation along planar algebraic curves, the problem of contact interpolation along a specific manifold parabolic cylinder is studied. Firstly, the multivariate contact interpolation regularization condition set defined on the parabolic cylinder is defined and its topology is studied in detail. The decision theorem of the contact interpolation regularization condition set along the parabolic cylinder and the method of constructing the interpolation regu-larization condition set by superposition is obtained. Finally, an experimental example is given to verify the effectiveness of the algorithm.