We produce low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a smooth convex domain with positive curvature in R^d. The proof depends on simultaneous Diophantine approximation and on appropriate estimates of the decay of the Fourier transform of characteristic functions.
(2018). Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus . Retrieved from http://hdl.handle.net/10446/124749
Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus
Brandolini, Luca;Gigante, Giacomo;
2018-01-01
Abstract
We produce low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a smooth convex domain with positive curvature in R^d. The proof depends on simultaneous Diophantine approximation and on appropriate estimates of the decay of the Fourier transform of characteristic functions.File allegato/i alla scheda:
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