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 Erdős–Turán inequality.

Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus

BRANDOLINI, Luca;GIGANTE, Giacomo;
2016-01-01

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 Erdős–Turán inequality.
journal article - articolo
2016
Brandolini, Luca; Colzani, Leonardo; Gigante, Giacomo; Travaglini, Giancarlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/56140
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