In this paper, we study a countable family of uniformly distributed sequences of partitions, called LS-sequences of partitions, and we give a precise estimate of their discrepancy. Among these sequences, we identify a countable class having low discrepancy (which means of order \frac1N1N). We describe an explicit algorithm that associates to each of these sequences a uniformly distributed sequence of points (we call LS-sequences of points). The main result of this paper says that the discrepancy of the sequences of points associated by our algorithm to the LS-sequences of partitions is of order α N log N, if α N is the discrepancy of the corresponding sequence of partitions. We obtain therefore, in particular, a countable family of low-discrepancy sequences of points.
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|Titolo:||Discrepancy of LS sequences of partitions and points|
|Data di pubblicazione:||2012|
|Citazione:||Discrepancy of LS sequences of partitions and points / Carbone, Ingrid. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 191:4(2012), pp. 819-844.|
|Appare nelle tipologie:||1.1 Articolo in rivista|