Title: On higher order of convergence using lattice sequences
Authors: Nuyens, Dirk
Hickernell, Fred J.
Kritzer, Peter
Kuo, Frances Y. #
Issue Date: Feb-2009
Conference: 3rd Workshop on High-Dimensional Approximation (HDA09) edition:3 location:University of New South Wales, Sydney, Australia date:16-20 February 2009
Abstract: We study the worst case integration error of combinations of quadrature rules in a reproducing kernel Hilbert space. We show that the error, with respect to the total number N of function evaluations used, cannot decrease faster than O(N^{-1}) in the case where several quasi-Monte Carlo rules are combined to a compound quasi-Monte Carlo rule. However, if the errors of the quadrature rules constituting the compound rule have an order of convergence O(N^{-a}) for a > 1 then, by introducing weights, this order of convergence can be shown to be recovered for the compound rule. We apply our results to the case of lattice sequences.
Publication status: published
KU Leuven publication type: IMa
Appears in Collections:Numerical Analysis and Applied Mathematics Section
# (joint) last author

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