Lattice rules for nonperiodic smooth integrands

The aim of this paper is to show that one can achieve convergence rates of N−α+δ for α > 1/2 (and for δ > 0 arbitrarily small) for nonperiodic α-smooth cosine series using lattice rules without random shifting. The smoothness of the functions can be measured by the decay rate of the cosine coefficients. For a specific choice of the parameters the cosine… CONTINUE READING