各向光滑性不同的多元函数类的最优恢复和宽度  

Optimal Recovery and Widths of an Anisotropic Sobolev Class of Multivariate Functions

作　　者：罗俊波[1] 孙永生[2] 

机构地区：[1]辽宁大学数学系 [2]北京师范大学数学系

出　　处：《数学进展》1998年第1期69-77,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金;国家教委博士点基金

摘　　要：本文讨论向异性类的Ｓｏｂｏｌｅｖ类ＷｒＨα在Ｃｋ空间内的最优恢复和宽度．对标准信息类（取样）得到了非线性余宽度、线性余宽度、网格宽度以及其他几种宽度的弱渐近精确估计。In this paper the optimal recovery and width for the anisotropic Sobolev class W rH α in the space C k are considered. Under the condition that the class of information operators is standard(samplings), we obtain the weakly asymptotically exact estimation for the non-linear co-width, the linear co-width, the net width as well as some other widths, all of which are of the same order of magnitude.

关 键 词：最优恢复 余宽度 宽度 多元函数 各向光滑性 

分 类 号：O174.1[理学—数学]