定义于马鞍面上的多元Lagrange插值
Multivariate Lagrange Interpolation Defined on Saddle Surface
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理论和拓扑结构，得到了构造定义于马鞍面上的Lagrange插值可解结点组的添加圆锥曲面法。这些方法都是以迭加方式构造完成的，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。
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 algorithm 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.
参考文献
|
[1]
|
De Boor, C. and Ron, A. (1990) On Multivariate Polynomial Interpolation. Constructive Approximation, 6, 287-302.
[Google Scholar] [CrossRef]
|
|
[2]
|
Liang, X.Z., Wang, R.H., Cui, L.H., et al. (2006) Some Researches on Trivariate Lagrange Interpolation. Journal of Computational and Applied Mathematics, 195, 192-205.
[Google Scholar] [CrossRef]
|
|
[3]
|
梁学章, 张明, 张慧杰, 等. 关于球面上的Lagrange插值[J]. 高等学校计算数学学报, 2011(33): 169-177.
|
|
[4]
|
Castell, W.Z., Fernandez, N.L. and Xu, Y. (2007) Polynomial In-terpolation on the Unit Sphere II. Advances in Computational Mathematics, 26, 155-171
[Google Scholar] [CrossRef]
|
|
[5]
|
梁学章. 关于多元函数的插值与逼近[J]. 高等学校计算数学学报, 1979(1): 123-124.
|
|
[6]
|
梁学章. 二元插值的适定结点组与迭加插值法[J]. 吉林大学自然科学学报, 1979(1): 27-32.
|
|
[7]
|
梁学章, 张洁琳, 崔利宏. 多元Lagrange插值与Cayley-Bacharach定理[J]. 高等数学计算数学学报, 2005(27): 276-281.
|