A Discrepancy-Based Analysis of Figures of Merit for Lattice Rules
Classical figures of merit for choosing quasi-Monte Carlo methods for integration over thes-dimensional unit cube are the L p star discrepancy of the corresponding set of quadrature points and, when considering periodic integrands, Pα— usually withα an even positive integer. Hickernell (1998) introduced a generalised notion of discrepancy of which both these figures of merit are special cases. In this paper Hickernell’s decomposition of generalised discrepancy into lower-dimensional components is used to characterise differences between reported results achieved by rules selected according to these figures of merit. A further extension with application to rank-1 lattice rules and their k s copies is also described.
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