On optimization of cubature formulae for Sobolev classes of functions defined on star domains
arXiv:2308.03154 · doi:10.30970/ms.61.1.84-96
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 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.