On theL2âdiscrepancies of van der Corput sequences
نویسندگان
چکیده
منابع مشابه
Van der Corput Sequences and Linear Permutations
This extended abstract is concerned with the irregularities of distribution of onedimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter.
متن کاملRegularities of the distribution of abstract van der Corput sequences
Similarly to β-adic van der Corput sequences, abstract van der Corput sequences can be defined by abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is computed explicitly, and the bounded remainder sets of the form [0, y) are characterized.
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We prove that the upper bound for the van der Corput property of the set of perfect squares is O((logn)−1/3), giving an answer to a problem considered by Ruzsa and Montgomery. We do it by constructing non-negative valued, normed trigonometric polynomials with spectrum in the set of perfect squares not exceeding n, and a small free coefficient a0 = O((logn)−1/3).
متن کاملThe Discrepancy of Generalized Van-der-corput-halton Sequences
The purpose of this paper is to provide upper bounds for the discrepancy of generalized Van-der-Corput-Halton sequences that are built from Halton sequences and the Zeckendorf Van-der-Corput sequence.
متن کاملWeak multipliers for generalized van der Corput sequences
Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P (i) = ai (mod b) for c...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700710