Lattice Rules for Multivariate Approximation in the Worst Case Setting

Abstract

We develop algorithms for multivariate approximation in weighted Korobov spaces of smooth periodic functions of d variables. Our emphasis is on large d . The smoothness of functions is characterized by the parameter α >1 that controls the decay of Fourier coefficients in the L 2 norm. The weight γ j of the Korobov space moderates the behaviour of functions with respect to the j th variable. Small γ j means that functions depend weakly on the j th variable.