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Discrepancy-based error estimates for Quasi-Monte Carlo I. General formalism

✍ Scribed by Jiri K. Hoogland; Ronald Kleiss

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 852 KB
Volume: 98
Category: Article
ISSN: 0010-4655
DOI: 10.1016/0010-4655(96)00084-7

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✦ Synopsis

We show how information on the uniformity properties of a point set employed in numerical multi-dimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non)uniformity for point sets, and derive explicit expressions for the various entities that enter in such an improved error estimate.

📜 SIMILAR VOLUMES

Discrepancy-based error estimates for Qu

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

✍ Jiri K. Hoogland; Ronald Kleiss 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 410 KB

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 v