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Title: Lattice rules for nonperiodic smooth integrands
Authors: Nuyens, Dirk
Dick, Josef
Pillichshammer, 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
# (joint) last author

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