Title: Lattice rules for nonperiodic smooth integrands Authors: Nuyens, DirkDick, JosefPillichshammer, Friedrich # Issue Date: Feb-2012 Conference: International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC2012) edition:10 location:Sydney, Australia date:13-17 February 2012 Abstract: We show that lattice rules can achieve convergence rates of $O(N^{-\alpha+\delta})$, for arbitrary small $\delta > 0$, for nonperiodic smooth functions and without random shifting. For this we consider a reproducing kernel Hilbert space of cosine series where the smoothness is measured as the decay rate of the cosine coefficients. This function space is in between the standard Korobov and Sobolev spaces. Publication status: published KU Leuven publication type: IMa Appears in Collections: Numerical Analysis and Applied Mathematics Section