Optimal Recovery on the Classes of Functions with Bounded Mixed Derivative  

作　　者：Gen Sun FANG Li Qin DUAN 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China [2]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China [3]Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第2期279-286,共8页数学学报（英文版）

基　　金：supported by the Natural Science Foundation of China (Grant No.10671019);Research Fund for the Doctoral Program of Higher Education (Grant No.20050027007)

摘　　要：Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.

关 键 词：optimal recovery standard information class of functions with bounded mixed derivative 

分 类 号：O174[理学—数学]