Diaphony, discrepancy, spectral test and worst-case error

Josef Dick and Friedrich Pillichshammer

Mathematics and Computers in Simulation (MATCOM), 2005, vol. 70, issue 3, 159-171

Abstract: In this paper various measures for the uniformity of distribution of a point set in the unit cube are studied. We show how the diaphony and spectral test based on Walsh functions appear naturally as the worst-case error of integration in certain Hilbert spaces which are based on Walsh functions. Furthermore, it has been shown that this worst-case error equals to the root mean square discrepancy of an Owen scrambled point set.

Keywords: Diaphony; Spectral test; Worst case error; Quasi-Monte Carlo (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:70:y:2005:i:3:p:159-171

DOI: 10.1016/j.matcom.2005.06.004

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