二次曲面上Lagrange插值结点组构造问题研究  

Researches on the set of nodes for Lagrange interpolation on quadratic surfaces

作　　者：崔利宏[1] 孟敏[1] 李笑笑[1] 高小淞[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）》2015年第2期145-149,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(41171137)

摘　　要：以二元函数Lagrange插值研究结果为基础,对三元函数Lagrange插值结点组可解性问题进行了研究,提出了二次曲面充分相交和二次曲面上Lagrange插值可解结点组的基本概念,研究了二次曲面插值可解结点组的某些基本理论和拓扑结构,得到了构造二次代数曲面和二次空间代数曲线插值可解结点组的添加二次曲面法.这些方法都是以迭加方式构造完成的,这对于编译计算机算法程序,进而在计算机上自动完成插值可解结点组的构造,并得到插值格式创造了十分便利的条件.最后给出了实例验证算法的有效性.Based on the results for bivariate function Lagrange interpolation ,the solvability problem for trivariate function interpolation are studied .The quadric surfaces complete intersection and the solvability of Lagrange interpolation nodes on the set of basic concept are proposed .The quadric in‐terpolation nodes set some of the basic theory and topology are investigated ,the structure of quadrat‐ic algebraic surface and the space algebra curve interpolation node set to add quadric surface method are obtained .T hese methods are based on the superposition method constructed w hich has created a very convenient conditions ,to compile the program of computer algorithm ,and then solve automati‐cally interpolation of the structure of the node set and get the interpolation format on the computer . A numerical example is given to verify the validity of the algorithm .

关 键 词：多元Lagrange插值 二次曲面插值 可解结点组 

分 类 号：O174.41[理学—数学]