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Optimal recovery of isotropic classes of rth differentiable multivariate functions

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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.

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Notes

  1. In [8] K(W;X) is called the error on W of the coding method using the information on nodes X.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi, 710026, China

    Bo Ling

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

    Yongping Liu

Authors
  1. Bo Ling
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  2. Yongping Liu
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Correspondence to Yongping Liu.

Additional information

Communicated by Michael Vogelius.

Supported partly by National Natural Science Foundation of China (Project No. 11071019), partly by The research Fund for the Doctoral Program of Higher Education and partly by Beijing Natural Science Foundation (Project 1102011).

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Ling, B., Liu, Y. Optimal recovery of isotropic classes of rth differentiable multivariate functions. Bit Numer Math 54, 485–500 (2014). https://doi.org/10.1007/s10543-013-0453-1

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  • DOI: https://doi.org/10.1007/s10543-013-0453-1

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