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Optimal recovery on the classes of functions with bounded mixed derivative

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China

    Gen Sun Fang

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Li Qin Duan

  3. Institute of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, P. R. China

    Li Qin Duan

Authors
  1. Gen Sun Fang
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  2. Li Qin Duan
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Correspondence to Gen Sun Fang.

Additional information

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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Fang, G.S., Duan, L.Q. Optimal recovery on the classes of functions with bounded mixed derivative. Acta. Math. Sin.-English Ser. 25, 279–286 (2009). https://doi.org/10.1007/s10114-008-7005-7

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  • DOI: https://doi.org/10.1007/s10114-008-7005-7

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