Tractability of multivariate integration for weighted Korobov classes
The authors study the worst case error of multivariate integration in weighted Korobkov classes of periodic functions of \(d\)~coordinates. These classes are defined in terms of weights which moderate the behavior of functions with respect to successive coordinates. Two classes of quadrature rules are studied, i.e., the quasi Monte Carlo rules which use \(n\) function values and in which all quadrature weights are \(1/n\) and rules for which all quadrature weights are non-negative. The tractability and strong tractability results are achieved under the relatively small class of lattice rules. The authors also check how the randomized error of the (classical) Monte Carlo algorithm depends on~\(d\) for weighted Korobkov classes.
scientific article; zbMATH DE number 1736576
scientific article