沿非代数曲面的多元拉格朗日插值问题研究  

Research on multivariate lagrange interpolation along non-algebraic surfaces

作　　者：崔利宏[1] 张敬 宋文健 CUI Lihong;ZHANG Jing;SONG Wenjian(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）》2023年第2期145-150,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(41971388)。

摘　　要：为解决给定非代数曲面多元插值结点组构造问题.以基本代数理论与以往沿代数曲面插值理论为基础,给出沿非代数曲面插值适定结点组定义并研究其性质与构造方法,解决了G0连续非代数曲面插值适定结点组的存在性问题,得到了在严格非代数曲面上构造沿该曲面插值适定结点组的构造方法.举出具体算例来验证本文所得方法是可行有效性的.To solve the multivariate interpolation node construction problem after a given non-algebraic surface.Based on the basic algebraic theory and the theory of interpolation along algebraic surfaces,the definition of suitable node groups for interpolation along non-algebraic surfaces is given and their properties and construction methods are studied.The problem of the existence of the interpolation-adapted node group along non-algebraic surfaces on G 0 continuous non-algebraic surfaces is solved,and a method for constructing the interpolation-adapted node group along non-algebraic rotation surfaces on strictly non-algebraic surfaces is given.Specific interpolation examples are given to show that the resulting interpolation node set construction method is feasible and effective.

关 键 词：插值论 多元函数插值法 非代数曲面 插值适定结点组 

分 类 号：O174.42[理学—数学]