空间代数曲线上的三元Birkhoff插值问题研究

The Research on the Three-Dimensional Birkhoff Interpolation Problem for Space Algebraic Curves

文章以二元Birkhoff插值研究结果为基础,对三元Birkhoff插值泛函组的适定性问题进行了研究。并提出了空间代数曲线上和代数曲面上的Birkhoff插值适定泛函组的基本概念,研究了空间代数曲线上和代数曲面上的Birkhoff插值适定泛函组的某些基本理论和拓扑结构,得到了构造空间代数曲线上Birkhoff插值适定泛函组的添加曲线交点法。方法是以迭加方式完成的,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。Based on the results of the two-dimensional Birkhoff interpolation, the study investigates the well-posedness of the three-dimensional Birkhoff interpolation functional systems. The fundamental concepts of well-posed Birkhoff interpolation functional systems on space algebraic curves and algebraic surfaces are proposed. The research delves into some basic theories and topological structures of well-posed Birkhoff interpolation functional systems on space algebraic curves and surfaces. The study presents the method of constructing well-posed Birkhoff interpolation functional systems on space algebraic curves through the addition of intersection points of curves. This method is performed in an iterative manner, making it feasible to implement the construction process on a computer. Finally, specific experimental examples are provided.