The construction of good extensible Korobov rules

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 treat classical lattice rules as well as polynomial lattice rules.

• Type: Journal
• Year: 2007
• Where: COMPUTING
• Authors: Josef Dick, Friedrich Pillichshammer, Benjamin J. Waterhouse
• Keywords: Classical Lattice Rules, COMPUTING 2007, Extensible Lattice Rules, Lattice Rules