关于三元分次插值适定性的研究

Research on Posedness of Ternary Graded Interpolation

摘要: 多元函数插值是一个经典而又复杂的问题，本文在以往二元分次插值研究的基础上，进一步对的三元分次插值问题进行探究。首先给出了三元分次空间的定义，进而在欧式空间中对三元插值结点组的适定性进行了探索。将递归构造原理具体到三元空间，通过添加斜平面法来证明构造新的插值适定结点组。然后，通过添加平面和二次代数曲面研究了构造三元分次多项式插值的适定结点问题，并使用MATLAB软件对实际应用的例题计算结果进行了展示。

Abstract: Multifunction interpolation is a classic but complex issue. Based on the previous binary graded interpolation research, we study the ternary graded interpolation further. Firstly, we give the definition of ternary graded space, then we explore the well-posedness of the ternary interpolation node group in the European space. We generalize the recursive structure principle to ternary space, and then construct new properly posed node group by adding bevel plane. Lastly, we research the problem of structuring the nodes group of ternary graded interpolation by adding plane and quadric surface, and show the calculation results of the practical examples by using MATLAB.