摘要
通过研究多元cardinal样条函数插值的逼近性质 ,给出了各向异性Sobolev光滑函数类Wr∞(Rd)在L∞(Rd)尺度下最佳逼近的弱渐近估计 .这个结果表明 ,多元cardinal样条函数空间是各向异性Sobolev光滑类Wr∞(Rd)在L∞(Rd)尺度下关于无穷维Kolmogorov宽度的弱渐近极子空间 ,也表明多元cardinal样条函数插值是实现线性宽度的最优算子 .
The weakly asymptotic estimate for the best approximation of the anisotropic Sobolev W r ∞(R d) by means of the spaces of the multivariate cardinal splines in the metric L ∞(R d) is given by studying the approximation properties of the mulitivariate cardinal spline interpolation, the result shows that the spaces of multivariate cardinal splines are weakly asymptoticly optimal for the infinite dimensional Kolmogorov widths of the anisotropic Sobolev classes W r ∞(R d) in the metric L ∞(R d), and shows also that the multivariate spline interpolation opeators are weakly asymptoticly optimal for the infinite dimensional linear widths of the same Sobolev classes in the same metric.
出处
《北京师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2000年第5期607-611,共5页
Journal of Beijing Normal University(Natural Science)
基金
TheProjectSupportedbyScientificResearchFoundationforReturnedOverseasChinesesScholarsoftheStateEducationMinistryofChina
