The construction of good extensible Korobov rules
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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.
AMS Subject Classifications11K45 65C05 65D30
KeywordsQuasi-Monte Carlo methods Lattice rules Korobov rules
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