| 二元插值的几何特征与插值结点平面构形 |
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| 引用本文： | 崔利宏,冯大雨.二元插值的几何特征与插值结点平面构形[J].吉首大学学报(自然科学版),2008,29(1):18-21. |
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| 作者姓名： | 崔利宏 冯大雨 |
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| 作者单位： | 辽宁师范大学数学学院,辽宁,大连,116029;辽宁师范大学数学学院,辽宁,大连,116029 |
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| 摘 要： | 插值结点组的几何特征(GC)决定二元插值问题的解的存在性与唯一性.通过引入亏量的概念对满足GC5条件的集合进行讨论，得到了猜想在n=5时的几何平面构形.该构形确定的二元Lagrange公式最终表示成一次因子乘积的形式，进一步验证了该猜想的正确性.
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| 关 键 词： | 二元插值 插值结点组的几何特征 GCn集合亏量 |
| 文章编号： | 1007-2985(2008)01-0018-04 |
| 修稿时间： | 2007年11月18 |
Geometric Characterization for Bivariate Interpolation and Plane Configurations of Interpolation Nodes |
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| CUI Li-hong,FENG Da-yu.Geometric Characterization for Bivariate Interpolation and Plane Configurations of Interpolation Nodes[J].Journal of Jishou University(Natural Science Edition),2008,29(1):18-21. |
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| Authors: | CUI Li-hong FENG Da-yu |
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| Institution: | (School of Mathematics,Liaoning Normal University,Dalian 116029,Liaoning China) |
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| Abstract: | The existence and uniqueness of solution of bivariate interpolation problems are determined by the geometric characterization (GC) of a set of interpolation nodes.By means of the introduced concept defect,the sets satisfying the GC5 condition are discussed in this paper and geometric plane configurations of the conjecture are obtained when n=5.The constructed bivariate Lagrange formula can finally be expressed as a product of linear factors,through which the correctness of the conjecture is verified. |
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| Keywords: | bivariate interpolation interpolation nodes geometric characterization GCｎ set defect |
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