On combined component-by-component constructions of lattice point sets

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On combined component-by-component constructions of lattice point sets

The standard method for constructing generating vectors for good lattice point sets is the componentby-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have recurring components, which can lead to the problem of having projections with all lattice points lying on the main diagonal. In this paper we combine method...

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In a series of recent articles, such as, e.g., [5, 9, 16, 22], point sets mixed from integration node sets in different sorts of quasi-Monte Carlo rules have been studied. In particular, a finite version, based on Hammersley and lattice point sets, was introduced in [16], where the existence of such hybrid point sets with low star discrepancy was shown. However, up to now it has remained an ope...

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Component-By-Component Construction of Good Intermediate-Rank Lattice Rules

It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a n...

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ژورنال

عنوان ژورنال: Journal of Complexity

سال: 2017

ISSN: 0885-064X

DOI: 10.1016/j.jco.2016.04.001