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.File allegato/i alla scheda:
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Brandolini, Gigante - Low-discrepancy sequences for piecewise smooth functions.pdf
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