The weighted diaphony
Journal
COMPTES RENDUS-ACADEMIE BULGARE DES SCIENCES
Date Issued
2006
Author(s)
Dimitrievska Ristovska, Vesna
Grozdanov, Vassil
Abstract
In the present paper the authors introduce a new quantitative measure for uniform distribution of sequences in [0, 1)s , the so-called “weighted diaphony.” The definition of the weighted diaphony is based on using the trigonometric functional system.
At a special choice of the parameters α and γ on which the weighted diaphony depends, the “classical” diaphony introduced by Zinterhof is obtained. It is shown that the computing complexity of the weighted diaphony of an arbitrary net composed of N points in [0, 1)s is O(S.N2
). Relationship between the worst-case error of the quasi-Monte Carlo integration in a class of weighted Hilbert space and the weighted diaphony is obtained.
At a special choice of the parameters α and γ on which the weighted diaphony depends, the “classical” diaphony introduced by Zinterhof is obtained. It is shown that the computing complexity of the weighted diaphony of an arbitrary net composed of N points in [0, 1)s is O(S.N2
). Relationship between the worst-case error of the quasi-Monte Carlo integration in a class of weighted Hilbert space and the weighted diaphony is obtained.
Subjects
File(s)![Thumbnail Image]()
Loading...
Name
6_02-05.pdf
Size
159.85 KB
Format
Adobe PDF
Checksum
(MD5):43611079d3f3facfa16a6183307de8f9