二元双n次多项式插值问题研究  

Researches on binary double n degree polynomial interpolation

作　　者：崔利宏[1] 聂碧宏 李雪 CUI Lihong;NIE Bihong;LI Xue(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）》2021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(41971388)。

摘　　要：以构造二元插值正则结点组的方法为研究基础,对二元双n次代数多项式插值正则性问题进行了详尽的研究和探讨.搞清了二元双n次插值正则结点组的基本拓扑结构和几何特征,并给出了构造二元双n次插值多项式空间及沿二元双n次代数曲线插值正则结点组的迭加构造法,最后通过两个实验算例对所得研究结果进行了验证.Based on the method of constructing binary interpolation regular node group,we researched the interpolation regularity problem of binary double n degree algebraic polynomials.In this paper,we have basically understood the basic topological structure and geometric features of the binary double n degree interpolation regular node group.Then we employed a superposition method to construct binary double n degree interpolation polynomial space and a set of interpolated regular nodes along binary double n degree algebraic curve.Finally,the results are verified by two experimental examples.

关 键 词：二元双n次代数多项式 二元双n次Lagrange插值 正则结点组 

分 类 号：O174.41[理学—数学]