Weighted Discrepancy and High-Dimensional Numerical Integration

Authors: Larcher G.1; Pillichshammer F.2; Scheicher K.3

Source: Bit Numerical Mathematics, Volume 43, Number 1, March 2003 , pp. 123-137(15)

Publisher: Springer

Buy & download fulltext article:

OR

Price: $47.00 plus tax (Refund Policy)

Abstract:

The concept of weighted discrepancy of sequences was introduced by Sloan and Wozacuteniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the “importance” of the projections of the integrand into account.

In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences.

Keywords: Weighted discrepancy; numerical integration; Koksma–Hlawka inequality; Faure–Niederreiter net; Sobol–Niederreiter net

Language: English

Document Type: Research article

Affiliations: 1: Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria. email: gerhard.larcher@jku.at 2: Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria. email: friedrich.pillichshammer@jku.at 3: Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria. email: klaus.scheicher@jku.at

Publication date: 2003-03-01

Related content

Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content

Text size:

A | A | A | A
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages. print icon Print this page