Optimal recovery of isotropic classes of rth differentiable multivariate functions
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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.
KeywordsOptimal recovery Approximation of function Differentiable function Sphere covering problem
Mathematics Subject Classification (2010)41A25 41A44 41A63
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