Discrepancy-based error estimates for Quasi-Monte Carlo II. Results in one dimension

✍ Scribed by Jiri K. Hoogland; Ronald Kleiss

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 410 KB
• Volume: 98
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(96)00083-5

✦ Synopsis

The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of their nonuniformity. Point sets with a discrepancy that is low with respect to the expected value for truly random point sets, are generally thought to be desirable. A low value of the discrepancy implies a negative correlation between the points, which may be usefully employed to improve the error estimate of a numerical integral based on the point set. We apply the formalism developed in a previous publication to compute this correlation for one-dimensional point sets, using a few different definitions of discrepancy.