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Chapitre D'ouvrage Année : 2014

Discrepancy bounds for low-dimensional point sets

Résumé

The class of $(t,m,s)$-nets and $(t,s)$-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of $(t,m,s)$-nets and $(t,s)$-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, as they are interesting mathematical objects from a theoretical point of view, and simultaneously serve as examples that make it easier to understand the structural properties of $(t,m,s)$-nets and $(t,s)$-sequences in arbitrary dimension. For these reasons, a considerable number of papers have been written on the properties of low-dimensional nets and sequences.

Dates et versions

hal-01109423 , version 1 (26-01-2015)

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Citer

Henri Faure, Peter Kritzer. Discrepancy bounds for low-dimensional point sets. Applied Algebra and Number Theory, 4 (58-90), Cambridge University Press, 2014, 9781107074002. ⟨10.1017/CBO9781139696456.005⟩. ⟨hal-01109423⟩
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