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On Selection Criteria for Lattice Rules and Other Quasi-Monte Carlo Point Sets (2001)
| Content Provider | CiteSeerX |
|---|---|
| Author | L.'Ecuyer, Pierre Lemieux, Christiane |
| Abstract | We define new selection criteria for lattice rules for quasi-Monte Carlo integration. The criteria examine the projections of the lattice over subspaces of small or successive dimensions. Their computation exploits the dimension-stationarity of certain lattice rules, and of other low-discrepancy point sets sharing this property. Numerical results illustrate the usefulness of these new figures of merit. 1 Background on Monte Carlo and Quasi-Monte Carlo We want to estimate the integral of a function f over the s-dimensional unit hypercube [0; 1) s , namely = Z [0;1) s f(u)du (1) by the average value of f over the point set P n = fu 0 ; : : : ; u n\Gamma1 g ae [0; 1) s , Q n = 1 n n\Gamma1 X i=0 f(u i ): (2) 1 This work has been supported by NSERC-Canada grant No. ODGP0110050 to the second author and by scholarships from NSERC-Canada and FCAR-Qu'ebec to the first author. We thank the 2 referees, whose comments helped clarifying the presentation. Preprint submitted to ... |
| File Format | |
| Publisher Date | 2001-01-01 |
| Access Restriction | Open |
| Subject Keyword | Quasi-monte Carlo Second Author Low-discrepancy Point Set Quasi-monte Carlo Point Set Selection Criterion Certain Lattice Rule First Author Lattice Rule Monte Carlo Nserc-canada Grant Numerical Result New Selection Criterion S-dimensional Unit Hypercube Average Value New Figure Quasi-monte Carlo Integration Gamma1 Ae Successive Dimension |
| Content Type | Text |
