三元欧式空间分次插值适定性问题研究  

Researches on Ternary Graded Interpolation Posedness of Euclidean Space

作　　者：崔利宏[1] 刘莹[1] 范晓倩[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林师范大学学报（自然科学版）》2016年第4期75-79,共5页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然基金资助项目(61502217);辽宁省大学生实践基地建设项目(2015399)

摘　　要：以文献[1-2]中所给出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,深层次地讨论和探究了三元分次插值的适定性问题.并提出了三元分次插值适定结点组的基本定义,基本搞清了三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"添加竖平面、横平面和纵平面法".这个方法可将定义于平面区域上的二元分次插值适定结点组一般性构造方法拓展到定义于空间上的三元分次插值的情形.由于本文所得构造方法都是以迭加方式来实现的,这对于编译计算机算法程序,进而在计算机上自动实现三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.Based on the method of ＂Add horizontal and straight vertical line method,＂,BIVARIATE Graded Interpolation given the appropriate set of nodes in the literature[1][2],we researched and discussed ternary Graded Interpolation Posedness issues further. we gave ternary Graded Interpolation suitable set of nodes for the definition basic and figure out ternary Graded Interpolation geometric topology and basic characteristics suitable set of nodes,it gives structure such interpolation suitable set of nodes ＂adding a vertical plane,horizontal plane and the vertical plane normal. ＂This method binary function Graded Interpolation on general constructor given node group are extended to the case of three yuan graded interpolation. Since we construct resulting in superposition methods are ways to achieve,which is to compile a computer program algorithm,and then the computer automatically ternary Graded Interpolation suitable set of nodes for the construction process and ultimately give the desired format to create interpolated a very convenient conditions. Finally,we pronided examples to verify the obtained results.

关 键 词：三元分次插值 适定结点组 三元分次多项式 

分 类 号：O174.41[理学—数学]