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Subject: weighted diaphony, diaphony, worst-case error

Year: 2006

Type: Article

Title: The weighted diaphony

Author: Dimitrievska Ristovska, Vesna
Author: 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.

Publisher:

Relation: COMPTES RENDUS-ACADEMIE BULGARE DES SCIENCES

Identifier: oai:repository.ukim.mk:20.500.12188/20062
Identifier: http://hdl.handle.net/20.500.12188/20062

Title	Date	Views
The weighted diaphony	2006	21