旋转抛物面上的Lagrange插值问题研究

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 La-grange interpolation nodes of ternary functions is studied in this paper.The basic concept of La-grange 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 be defined in the solution node group the Lagrange interpolation has been defined in the structure on rotating parabo-loid solvable node group added cone surface method.These methods are constructed by using super-position method,w hich creates a very convenient condition for compiling a computer program,and then automatically completing the construction of an interpolated node group and obtainint the inter-polation scheme on the computer.Finally,an example is given to illustrate the effectiveness of the proposed algorithm.