关于二元解析插值的收敛性

关于二元解析插值的收敛性 On the Convergence of Analytic Interpolation of Two Variables 汤国明 TANG Guoming 1 first-author 刘华 LIU Hua 1 天津职业技术师范大学理学院 天津职业技术师范大学理学院 School of Science,Tianjin University of Technology and Education School of Science,Tianjin University of Technology and Education 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 be large enough for the convergence of interpolation of arbitrarily chosen nodes. 解析插值 多元全纯函数 插值收敛 analytic interpolation multivariate holomorphic function convergence of interpolation 10.14188/j.1671-8836.2011.02.013 O174.42 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） 2011-02-01 2021-04-01 2 57