Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
classification
🧮 math.NT
math.NA
keywords
low-discrepancysequencessmoothapproximateapproximationconvexcurvaturedepends
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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.
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