Takashi Goda

Optimality of Quasi-Monte Carlo Methods and Suboptimality of the Sparse-Grid Gauss–Hermite Rule in Gaussian Sobolev Spaces

Abstract. Optimality of several quasi-Monte Carlo methods and suboptimality of the sparse-grid quadrature based on the univariate Gauss–Hermite rule are proved in the Sobolev spaces of mixed dominating smoothness of order [Formula: see text], where the optimality is in the sense...