关于二元解析插值的收敛性

On the Convergence of Analytic Interpolation of Two Variables

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.