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, LEONARDOSecondo
;TRAVAGLINI, GIANCARLOUltimo
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.
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