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arXiv · 2308.03154

On optimization of cubature formulae for Sobolev classes of functions defined on star domains

Oleg Kovalenko
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Abstract

We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm of their distributional gradient; thus we generalize the known solution of this optimization problem in the case, when the domain of definition of the functions is convex.

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Oleg Kovalenko. 2023-08-06. On optimization of cubature formulae for Sobolev classes of functions defined on star domains. https://doi.org/10.30970/ms.61.1.84-96

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