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Efficient lattice assessment for LCG and GLP parameter searches |
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| Authors: | Karl Entacher Thomas Schell Andreas Uhl. |
| Affiliation: | School of Telecommunications Engineering, University of Applied Sciences and Technologies, Schillerstr.~30, A-5020 Salzburg, Austria ; Department of Scientific Computing, Salzburg University, Hellbrunnerstr.~34, A-5020 Salzburg, Austria Andreas Uhl ; Department of Scientific Computing, Salzburg University, Hellbrunnerstr.~34, A-5020 Salzburg, Austria |
| Abstract: | In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi-Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically demonstrate the speed-up and the quality loss obtained by the LLL reduction, and we present important applications for parameter selections. |
| Keywords: | Monte Carlo and quasi--Monte Carlo methods lattice rules good lattice points random number generation lattice basis reduction LLL algorithm Fincke-Pohst algorithm spectral test |
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