Abstract
We consider the class of functions on a convex body in [Formula: see text], which are uniformly bounded by some second-order differential operator in any direction, and the class of periodic functions with respect to a full-rank lattice [Formula: see text], which have the same restriction in any direction. We study the optimal recovery problems of these classes and obtain the estimate of the optimal algorithm that recovers functions with their values and gradient values at [Formula: see text] nodes, respectively.
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