平面代数曲线上的二元Birkhoff插值问题研究

Research on Binary Birkhoff Interpolation Problem on Plane Algebraic Curves

摘要: 主要研究了二元Birkhoff插值泛函组适定性问题。给出平面代数曲线上的二元Birkhoff插值适定结点组的定义并证明了相关性质定理，在过去已得到的构造适定二元切触插值泛函组的基础上给出了构造二元Birkhoff插值适定泛函组的一种新的构造方法——添加曲线交点法。该方法是通过迭加过程来实现的。因此便于在计算机上实现其构造过程。最后给出了具体实验算例。

Abstract: We mainly studied the problem of fitness of binary Birkhoff interpolation functional groups. We defined the fitness node group of binary Birkhoff interpolation on planar algebraic curves and proved the relevant property theorems. Based on the construction of fitness binary tangent interpolation functional groups that have been obtained in the past, we proposed a new construction method for constructing fitness binary Birkhoff interpolation functional groups—the method of adding curve intersection points. This method is implemented through the superposition process, making it easy to implement its construction process on computers. Finally, specific experimental examples were provided.