Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism
High Energy Physics - Phenomenology
2009-10-28 v2 High Energy Physics - Lattice
Abstract
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.
Cite
@article{arxiv.hep-ph/9601270,
title = {Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism},
author = {Jiri Hoogland and Ronald Kleiss},
journal= {arXiv preprint arXiv:hep-ph/9601270},
year = {2009}
}
Comments
23 pages, uses axodraw.sty, available at ftp://nikhefh.nikhef.nl/pub/form/axodraw Fixed some typos, tidied up section 3.2