再生核空间中样条插值算子与最佳插值逼近算子的一致性  

THE UNIFORMITY OF SPLINE INTERPOLATING OPERATORS AND THE BEST OPERATORS OF INTERPOLATING APPROXIMATION IN REPRODUCING KERNEL SPACES

作　　者：邓彩霞[1] 邓中兴 

机构地区：[1]哈尔滨科技大学数学系,哈尔滨150080

出　　处：《高等学校计算数学学报》1995年第2期119-128,共10页Numerical Mathematics A Journal of Chinese Universities

摘　　要：<正> 对于微分算子样条,为了保证一致收敛性,通常要求较高的光滑性条件。对多项式样条来说,至少要求二阶导数连续才能保证一致收敛性。本文在再生核空间H_0~1中把微分算子样条与再生核联系起来了,证明了这种微分算子样条与H_0~1中的最佳插值逼近算子的一致性。To guarantee uniform convergence, higher smooth conditions are genereally required for splines of differential operators, and at least, differential condition of the second order, for polynomial splines. This paper has combined splines of differential operators with reproducing kernel functions in H10 space of reproducing kernel and has shown the uniformity between these splines of differential operators and operators of the best interpolating approximation in H10, from which the uniform convergence of absolutely smooth functions is obtained for a type of differential operator of the second order in H10. A useful computational method is given in application for the approximation solution of linear differential equations of the second order with the boundary value problems of kind one.

关 键 词：再生核空间 样条插值算子 插值 逼近 算子 

分 类 号：O241.5[理学—计算数学]