摘要
给定结点系为{x_k=x_(k,n)=2kπ/n,k=0,1,…,n-1},定义线性插值算子为:(U_nf)(x)=sum from j=0 to n-1 f(x_j)K_n(x-x_j),(n=1,2,3,…),这里K_n(x)=1/n{1+2 sum from k=1 to n-1 p(i(n-k))/[p(ik)+p(i(n-k))]cosk^x},f∈C_(2x)。本文讨论算子U_n的逼近问题,得到关于逼近阶的结果。
Given a system of nodal point{x_k=x_(k,n)=2Kπ/n,k=0,1,…,n-1},define linear interpolation operators U_n b_y (U_nf)(X)=sum from j=0 to n-1 f(X_1)K_n(X-X_j) (n=1,2,…)Where K_n(X)=1/n{1+2 sum from K=1 to n-1 P(i(n-k)/P(iK)+P(i(n-K))coskx}and f is a 2π-Periodic continuons function. In this paper the anthors strdy the approximation probllms of the operators U_n andobtain results concerning the approximation order.
关键词
插值算子
逼近阶
连续模
interpolation operator
approximation order
modulus of continuity
