Optimal recovery of isotropic classes of rth differentiable multivariate functions |
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| Authors: | Bo Ling Yongping Liu |
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| Institution: | 1. School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi, 710026, China
2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education of China, Beijing, 100875, China
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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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