定义于马鞍面上的多元Lagrange插值.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1045-1049 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69126 Multivariate Lagrange Interpolation Defined on Saddle Surface Nan Zhao, Fu Liu, 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 Lagrange interpolation of binary functions, we study the regularity of La- grange interpolation nodes of ternary functions and propose the basic concepts of Lagrange inter- polation regular nodes defined on saddle. By interpolating some basic theories and topological structures of regular node groups, an additive conic surface method of constructing Lagrange inter- polation solvable nodes defined on the saddle surface is obtained. These methods are all constructed in a superposed manner, which creates a very convenient condition for compiling a computer algo- rithm program, and then automatically completing the construction of an interpolated node group and obtaining the interpolation format on the computer. Finally, an example is given to illustrate the effectiveness of the proposed algorithm. Keywords Saddle Surface, Multivariate Lagrange Interpolation, Regular Set of Nodes, Superposition Interpolation Method 定义于马鞍面上的多元Lagrange插值 赵 楠，刘 孚，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插值结点组的正则性问题进行了研究， 提出了定义于马鞍面上的Lagrange插值正则结点组的基本概念，研究了这类插值正则结点组的某些基本 文章引用: 赵楠, 刘孚, 崔利宏. 定义于马鞍面上的多元Lagrange 插值[J]. 应用数学进展, 2017, 6(9): 1045-1049. DOI: 10.12677/aam.2017.69126 赵楠 等 理论和