Abstract
In this paper, we introduce construction algorithms for Korobov rules for numerical integration which work well for a given set of dimensions simultaneously. The existence of such rules was recently shown by Niederreiter. Here we provide a feasible construction algorithm and an upper bound on the worst-case error in certain reproducing kernel Hilbert spaces for such quadrature rules. The proof is based on a sieve principle recently used by the authors to construct extensible lattice rules. We only treat classical lattice rules. The same ideas apply for polynomial lattice rules.
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The second author is supported by the Austrian Research Foundation (FWF), Project S9609 that is part of the Austrian National Research Network ``Analytic Combinatorics and Probabilistic Number Theory''.
The support of the Australian Research Council under its Center of Excellence Program is greatfully acknowledged.
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Dick, J., Pillichshammer, F. & Waterhouse, B.J. The construction of good extensible Korobov rules. Computing 79, 79–91 (2007). https://doi.org/10.1007/s00607-006-0216-9
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DOI: https://doi.org/10.1007/s00607-006-0216-9