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arXiv · 1710.00573

Tractability properties of the weighted star discrepancy of regular grids

Friedrich Pillichshammer
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Abstract

In this paper we study tractability properties of the weighted star discrepancy with general coefficients of centered regular grids with different mesh-sizes. We give exact characterizations of the weight sequences $(\gamma_j)_{j \ge 1}$ such that the regular grid with different mesh-sizes achieves weak, uniform weak, quasi polynomial, polynomial or strong polynomial tractability for the $\boldsymbol{\gamma}$-weighted star discrepancy. For example, a necessary and sufficient condition such that the regular grid with different mesh-sizes achieves weak tractability for the $\boldsymbol{\gamma}$-weighted star discrepancy is $\lim_{j \rightarrow \infty}j \gamma_j=0$.

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Friedrich Pillichshammer. 2017-10-02. Tractability properties of the weighted star discrepancy of regular grids. https://arxiv.org/abs/1710.00573

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