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BIT Numerical Mathematics

, Volume 54, Issue 2, pp 485–500 | Cite as

Optimal recovery of isotropic classes of rth differentiable multivariate functions

  • Bo Ling
  • Yongping Liu
Article

Abstract

Estimates are given for the optimal recovery of functions in d variables, which are known to have (r−1)st absolutely continuous and rth bounded derivatives in any direction over, either a bounded convex d-dimensional body G, or which are periodic over a d dimensional lattice. The information is the values of the function and all its derivatives of order less than r at n points. We obtain some asymptotic estimates for this problem, and some exact results for several special cases which contain the results of Babenko, Borodachov, and Skorokhodov.

Keywords

Optimal recovery Approximation of function Differentiable function Sphere covering problem 

Mathematics Subject Classification (2010)

41A25 41A44 41A63 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex SystemsMinistry of Education of ChinaBeijingChina

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