关于二元解析插值的收敛性  

On the Convergence of Analytic Interpolation of Two Variables

作　　者：汤国明[1] 刘华[1] 

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《武汉大学学报（理学版）》2011年第2期119-122,共4页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助(10601036);天津市自然科学基金资助项目(07JCYBJC13600)

摘　　要：对于一个二元解析函数,讨论了它在一个矩形区域上的二元多项式的Lagrange插值,证明了为使任意选取节点的插值收敛,被插值函数必须解能析延拓到一个足够大的区域.In this paper, the multivariate polynomial interpolation is discussed for functions of two variables. For a holomorphic function of two variables, we discussed its Lagrange interpolation by the polynomial with two variables in the domain which is a rectangle. It was proved that the function interpolated must have an analytic continuity to a domain which could he large enough for the convergence of interpola- tion of arbitrarily chosen nodes.

关 键 词：解析插值 多元全纯函数 插值收敛 

分 类 号：O174.56[理学—数学]