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
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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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