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 ℝ2. The proof depends on simultaneous diophantine approximation and a general version of the Erdos-Turán inequality.

Brandolini, L., Colzani, L., Gigante, G., Travaglini, G. (2016). Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus. JOURNAL OF COMPLEXITY, 33, 1-13 [10.1016/j.jco.2015.09.003].

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

COLZANI, LEONARDO
Secondo
;
TRAVAGLINI, GIANCARLO
Ultimo
2016

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 ℝ2. The proof depends on simultaneous diophantine approximation and a general version of the Erdos-Turán inequality.
Articolo in rivista - Articolo scientifico
Diophantine approximation; Discrepancy; Erdos-Turán inequality; Koksma-Hlawka inequality; Piecewise smooth functions;
Low-discrepancy sequences, Erdős–Turán inequality
English
1
13
13
Brandolini, L., Colzani, L., Gigante, G., Travaglini, G. (2016). Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus. JOURNAL OF COMPLEXITY, 33, 1-13 [10.1016/j.jco.2015.09.003].
Brandolini, L; Colzani, L; Gigante, G; Travaglini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/102014
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