多元分次插值适定性问题研究  

Researches on posedness of multivariate graded interpolation

作　　者：崔利宏[1] 范晓倩[1] 刘莹[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2016年第4期433-437,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61502217);辽宁省大学生实践基地建设项目(辽教[2015]399号)

摘　　要：主要研究了多元函数插值与逼近问题中的二元分次插值适定性问题.以已有的构造二元分次插值适定结点组的"添加横直线和竖直线方法"为基础,对二元分次插值适定性问题进行了进一步的研究和探讨,基本搞清了二元分次插值适定结点组的几何拓扑结构和基本特征,给出了构造这类插值适定结点组的"添加斜直线方法",该方法将目前已有的研究结果推广到了最一般的情形.由于所得构造方法都是以叠加方式来实现的,这对于编译计算机算法程序,进而在计算机上自动实现二元分次插值适定结点组的构造过程并最终得到所需要的插值格式创造了十分便利的条件.最后给出算例对所得研究结果进行了验证.In this paper,the posedness problems of the multivariate function interpolation and approximation on the bivariate graded interpolation are investigated.We discuss further the literature bivariate graded interpolation by giving the appropriate set of nodes Add horizontal and straight vertical line method,which is based on dualistic graded interpolation posedness,and find out the basic geometry and topology of the basic characteristics of the Properly Posed Set of Nodes on the bivariate graded interpolation.We give the structure on Properly Posed Set of Nodes for bivariate graded interpolation Add oblique straight line method,which is the most general case.Since the construction is in superposition method,which is to compile program algorithm,and then automatically process bivariate graded interpolation Properly Posed Set of Nodes and ultimately give the desired format.These make the interpolation very convenient.Finally,examples of the obtained results were verified.

关 键 词：二元插值 二元分次插值 适定结点组 代数曲线 叠加构造方法 

分 类 号：O174.41[理学—数学]