English

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.

Keywords

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

R2 v1 2026-06-22T08:59:34.993Z