Optimal recovery on the classes of functions with bounded mixed derivative |
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| Authors: | Gen Sun Fang Li Qin Duan |
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| Institution: | (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 |
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| Abstract: | Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L
p
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.
Project supported by the Natural Science Foundation of China (Grant No. 10671019) and Research Fund for the Doctoral Program
of Higher Education (Grant No. 20050027007) |
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| Keywords: | optimal recovery standard information class of functions with bounded mixed derivative |
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