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The exact order of generalized diaphony and multidimensional numerical integration
Published online by Cambridge University Press: 09 April 2009
Abstract
For a point set in the multidimensional unit torus we introduce an Lk-measure of uniformity of distribution, which for k=2 reduces to diaphony (and thus in this case essentially coincides with Weyl L2-discrepancy). For k ∈ [1, 2] we establish a sharp asymptotic for this new measure as the number of points of the set tends to infinity. Upper and lower-bound estimates are given also for k >2.
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- Copyright © Australian Mathematical Society 1999
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