W2^m空间中样条插值算子与最佳逼近算子的一致性  

THE UNIFORMITY OF SPLINE INTERPOLATING OPERATORS AND THE BEST OPERATORS OF INTERPOLATING APPROXIMATION IN W_2~m SPACES

作　　者：张新建[1] 黄建华[1] 

机构地区：[1]国防科技大学应用数学系,长沙410073

出　　处：《计算数学》2001年第4期385-392,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助课题。

摘　　要：This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W_2~m spaces, The explicit constructive method for the reproducing kernel in W_2~m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W_2~m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W_2~m space, and error estimation of spline operator of approximation are obtained.

关 键 词：数值分析 再生核 样条插值算子 最佳插值逼近算子 线性 微分算子样条 GREEN函数 

分 类 号：O241.5[理学—计算数学]