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Secure pseudorandom bit generators and point sets with low star-discrepancy

Abstract: The star-discrepancy is a quantitative measure for the irregularity of distribution of a point set in the unit cube that is intimately linked to the integration error of quasi-Monte Carlo algorithms. These popular integration rules are nowadays also applied to very high-dimensional integration problems. Hence multi-dimensional point sets of reasonable size with low discrepancy are badly needed. A seminal result from Heinrich, Novak, Wasilkowski and Wo?niakowski shows the existence of a positive number such that for every dimension there exists an -element point set in [0,1)d with star-discrepancy of at most . This is a pure existence result and explicit constructions of such point sets would be very desirable. The proofs are based on random samples of -element point sets which are difficult to realize for practical applications. In this paper we propose to use secure pseudorandom bit generators for the generation of point sets with star-discrepancy of order. This proposal is supported theoretically and by means of numerical experiments.

 Autoría: Gómez A.I., Gómez-Pérez D., Pillichshammer F.,

 Fuente: Journal of Computational and Applied Mathematics, 2021, 396, 113601

Editorial: Elsevier

 Año de publicación: 2021

Nº de páginas: 8

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.cam.2021.113601

ISSN: 0377-0427,1879-1778

Url de la publicación: https://doi.org/10.1016/j.cam.2021.113601