Efficient lattice assessment for LCG and GLP parameter searches

作     者：Entacher, K Schell, T Uhl, A 

作者机构：Univ Appl Sci & Technol Sch Telecommun Engn A-5020 Salzburg Austria Salzburg Univ Dept Comp Sci A-5020 Salzburg Austria 

出 版 物：《MATHEMATICS OF COMPUTATION》 (计算数学)

年 卷 期：2002年第71卷第239期

页      面：1231-1242页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：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 

摘      要：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.