二元分次插值适定性问题研究  

Research on Posedness of Binary Graded Interpolation

作　　者：范晓倩[1] 刘莹[1] 崔利宏 

机构地区：[1]辽宁师范大学,辽宁大连

出　　处：《应用数学进展》2016年第4期657-661,共5页Advances in Applied Mathematics

基　　金：辽宁省大学生实践基地建设项目基金资助。

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。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.

关 键 词：适定结点组 二元分次插值 代数曲线 

分 类 号：O1[理学—数学]