二元分次插值适定性问题研究

Research on Posedness of Binary Graded Interpolation

摘要: 本文从研究二元多项式插值的适定性问题着手，在构造二元分次插值适定结点组的“添加横直线法”和“添加竖直线法”的基础上，对二元分次插值适定性问题进一步研究和探讨，给出了二元分次插值适定结点组的几何结构和基本特征，构造了二元分次插值适定结点组的“添加抛物线”方法，推广了已有的研究结果，最后给出算例对所得研究结果进行了验证。

Abstract: The paper studies from the posedness of bivariate polynomial interpolation. Based on the methods of “adding a horizontal line” and “adding vertical line” in constructing well-posed node group of binary interpolation, this paper further researches and discusses the posedness of binary graded interpolation, and gives geometrical structure and basic characteristics of well-posed node group of binary graded interpolation, then constructs the method that adds parabola for the well-posed node group of binary graded interpolation and generalizes the existing research results. Finally, the numerical examples are given to verify the research results.