Abstract
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a component-by-component construction to ensure a small weighted star discrepancy. Our aim is to significantly reduce the construction cost of such generating vectors by restricting the size of the set of polynomials from which we select the components of the vectors. To gain this reduction we exploit the fact that the weights of the spaces we consider decay very fast.
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Acknowledgements
We would like to thank Peter Kritzer and Friedrich Pillichshammer for their valuable comments and suggestions which helped to improve our paper. All three authors are supported by the Austrian Science Fund (FWF): Project F5509-N26, Project F5506-N26, Project F5505-N26, where all three projects are part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.
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Kritzinger, R., Laimer, H., Neumüller, M. (2018). A Reduced Fast Construction of Polynomial Lattice Point Sets with Low Weighted Star Discrepancy. In: Owen, A., Glynn, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2016. Springer Proceedings in Mathematics & Statistics, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-91436-7_21
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DOI: https://doi.org/10.1007/978-3-319-91436-7_21
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