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

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

1996-01-15

arxiv.org/abs/hep-ph/9601270v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages, uses axodraw.sty, available at ftp://nikhefh.nikhef.nl/pub/form/axodraw Fixed some typos, tidied up section 3.2

Scientific paper

10.1016/0010-4655(96)00084-7

We show how information on the uniformity properties of a point set employed in numerical multidimensional 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. The use of Feynman diagrams provides a transparent and straightforward way to compute this improved error estimate.

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