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pro vyhledávání: '"11K38, 11K31"'
Autor:
Dick, Josef, Pillichshammer, Friedrich
In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue constants of the Walsh function system that play an important role in appro
Externí odkaz:
http://arxiv.org/abs/2412.03164
Publikováno v:
B. Tuffin and P. L' Ecuyer: Monte Carlo and Quasi-Monte Carlo Methods, Serie Proceedings of the MCQMC, Springer, pp. 329--344, 2020
We study the $L_p$ discrepancy of digital NUT sequences which are an important sub-class of digital $(0,1)$-sequences in the sense of Niederreiter. The main result is a lower bound for certain sub-classes of digital NUT sequences.
Comment: 13 pa
Comment: 13 pa
Externí odkaz:
http://arxiv.org/abs/1904.01433
Autor:
Weiß, Christian
This paper adresses the question whether the $LS$-sequences constructed by Carbone yield indeed a new family of low discrepancy sequences. While it is well known that the case $S=0$ corresponds to van der Corput sequences, we prove here that the case
Externí odkaz:
http://arxiv.org/abs/1706.08949
Autor:
Hofer, Roswitha, Puchhammer, Florian
We consider the star discrepancy of two-dimensional sequences made up as a hybrid between a Kronecker sequence and a perturbed Halton sequence in base 2, where the perturbation is achieved by a digital-sequence construction in the sense of Niederreit
Externí odkaz:
http://arxiv.org/abs/1611.01288
Publikováno v:
Uniform Distribution Theory 13(1): 65-86, 2018
The star discrepancy $D_N^*(\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\mathcal{P}$ in the multi-dimensional unit cube which is intimately related to the integration error of quasi-Monte Carlo
Externí odkaz:
http://arxiv.org/abs/1605.00378
In 1935 J.G. van der Corput introduced a sequence which has excellent uniform distribution properties modulo 1. This sequence is based on a very simple digital construction scheme with respect to the binary digit expansion. Nowadays the van der Corpu
Externí odkaz:
http://arxiv.org/abs/1506.03764
The class of $(0,m,s)$-nets in base $b$ has been introduced by Niederreiter as examples of point sets in the $s$-dimensional unit cube with excellent uniform distribution properties. In particular such nets have been proved to have very low discrepan
Externí odkaz:
http://arxiv.org/abs/1506.03201
Publikováno v:
Arch. Math. (104), Nr. 5, pp. 407--418, 2015
It is well known that the $L_p$-discrepancy for $p \in [1,\infty]$ of the van der Corput sequence is of exact order of magnitude $O((\log N)/N)$. This however is for $p \in (1,\infty)$ not best possible with respect to the lower bounds according to R
Externí odkaz:
http://arxiv.org/abs/1501.02552
Publikováno v:
Unif. Distrib. Theory (10), pp. 115--133, 2015
It is well known that the two-dimensional Hammersley point set consisting of $N=2^n$ elements (also known as Roth net) does not have optimal order of $L_p$-discrepancy for $p \in (1,\infty)$ in the sense of the lower bounds according to Roth (for $p
Externí odkaz:
http://arxiv.org/abs/1410.4315
Autor:
Steiner, Wolfgang
Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined for abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is computed explicit
Externí odkaz:
http://arxiv.org/abs/0809.3994