定义于抛物柱面上的多元Lagrange插值问题.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1039-1044 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69125 Multivariate Lagrange Interpolation Defined on Parabolic Cylinder Fu Liu, Nan Zhao, Lihong Cui Liaoning Normal University, Dalian Liaoning th st th Received: Nov. 14 , 2017; accepted: Dec. 1 , 2017; published: Dec. 8 , 2017 Abstract Based on the results of two-element function Lagrange interpolation, the only solvable problem of ternary function Lagrange interpolation node group is studied. This paper presents the basic con- cept of the Lagrange interpolation unique solvable node group, which is defined on the parabolic cy- linder surface, and studies some basic theory and topological structure of the Lagrange interpolation unique solvable node group defined on the parabolic cylinder. The method of adding conic surface for constructing the Lagrange interpolating solvable node group which is defined on the parabolic cylindrical surface is obtained. All of these methods are constructed by means of superposition, so it is very convenient for compiling computer algorithm program and then automatically completing interpolation in the computer to solve the structure of node group and get interpolation format. Fi- nally, an example is given to illustrate the effectiveness of the proposed algorithm. Keywords Parabolic Cylinder, Multivariate Lagrange Interpolation, The Only Solution Node Group, Superposition Interpolation Method 定义于抛物柱面上的多元Lagrange插值问题 刘 孚，赵 楠，崔利宏 辽宁师范大学，辽宁 大连 收稿日期：2017年11月14 日；录用日期：2017年12月1 日；发布日期：2017年12月8 日 摘 要 以二元函数Lagrange插值研究结果为基础，对三元函数Lagrange插值结点组的唯一可解问题进行了研究。 文章引用: 刘孚, 赵楠, 崔利宏. 定义于抛物柱面上的多元Lagrange 插值问题[J]