旋转抛物面上的Lagrange插值问题研究  

Multivariate Lagrange interpolation defined on paraboloid surface of revolution surface

作　　者：崔利宏[1] 惠婷婷 刘海波 CUI Lihong;HUI Tingting;LIU Haibo(School of Mathematics, Liaoning Normal University, Dalian 116029,China)

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）》2018年第1期5-9,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省大学生实践基地建设项目(辽教[2015]399号);辽宁省高校科学研究项目(L201683661)

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,提出了定义于旋转抛物面上的Lagrange插值正则结点组的基本概念,研究了定义于旋转抛物面上的Lagrange插值可解结点组的某些基本理论和拓扑结构,得到了构造定义于旋转抛物面上的Lagrange插值可解结点组的添加圆锥曲面法.这些方法都是以叠加方式构造完成的,因而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 of Lagrange interpolation of binary funcitions,the solvability of Lagrange interpolation nodes of ternary functions is studied in this paper.The basic concept of Lagrange interpolation of the regular set of nodes is proposed to define the paraboloid of revolution,some basic theory and topology of Lagrange interpolation on rotating paraboloid can solution node group the Lagrange interpolation has been defined in the structure on rotating paraboloid solvable node group added cone surface method.These methods are constructed by using superposition method,which creates a very convenient condition for compiling a computer program,and then automatically completing the construction of an interpolated node group and obtainint the interpolation scheme on the computer.Finally,an example is given to illustrate the effectiveness of the proposed algorithm.

关 键 词：旋转抛物面 多元Lagrange插值 

分 类 号：O174.41[理学—数学]