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.
Brandolini, L., Colzani, L., Gigante, G., Travaglini, G. (2018). Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus. In J. Dick, F. Kuo, H. Woźniakowski (a cura di), Contemporary Computational Mathematics – A Celebration of the 80th Birthday of Ian Sloan (pp. 135-152). Springer [10.1007/978-3-319-72456-0_8].
Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus
Colzani, L;Travaglini, G
2018
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.
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