二元插值的几何特征与插值结点平面构形

journal6 ›› 2008, Vol. 29 ›› Issue (1): 18-21.

二元插值的几何特征与插值结点平面构形

（辽宁师范大学数学学院, 辽宁大连 116029）

出版日期:2008-01-25 发布日期:2012-05-26
作者简介:崔利宏(1964-)，男，黑龙江绥滨人，辽宁师范大学数学学院教授，博士生，主要从事多元逼近与计算机辅助几何设计研究.

Geometric Characterization for Bivariate Interpolation and Plane Configurations of Interpolation Nodes

(School of Mathematics,Liaoning Normal University,Dalian 116029,Liaoning China)

Online:2008-01-25 Published:2012-05-26

摘要/Abstract

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.

关键词： 二元插值, 插值结点组的几何特征, GCn集合亏量

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.

Key words: bivariate interpolation, interpolation nodes；geometric characterization；GCｎ set, defect

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]. journal6, 2008, 29(1): 18-21.

CUI Li-Hong, FENG Da-Yu. Geometric Characterization for Bivariate Interpolation and Plane Configurations of Interpolation Nodes[J]. journal6, 2008, 29(1): 18-21.