Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
Number Theory
2015-03-24 v1 Numerical Analysis
Abstract
We produce explicit low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a convex domain with positive curvature in R^2. The proof depends on simultaneous diophantine approximation and a general version of the Erdos-Turan inequality.
Cite
@article{arxiv.1503.06655,
title = {Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus},
author = {Luca Brandolini and Leonardo Colzani and Giacomo Gigante and Giancarlo Travaglini},
journal= {arXiv preprint arXiv:1503.06655},
year = {2015}
}
Comments
14 pages, 2 figures