Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus

Luca Brandolini (), Leonardo Colzani (), Giacomo Gigante () and Giancarlo Travaglini ()
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Luca Brandolini: Università degli Studi di Bergamo, Dipartimento di Ingegneria Gestionale, dell’Informazione e della Produzione
Leonardo Colzani: Università di Milano-Bicocca, Dipartimento di Matematica e Applicazioni
Giacomo Gigante: Università degli Studi di Bergamo, Dipartimento di Ingegneria Gestionale, dell’Informazione e della Produzione
Giancarlo Travaglini: Università di Milano-Bicocca, Dipartimento di Matematica e Applicazioni

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 135-152 from Springer

Abstract: 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 $$\mathbb {R}^{d}$$ . The proof depends on simultaneous Diophantine approximation and on appropriate estimates of the decay of the Fourier transform of characteristic functions.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_8

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DOI: 10.1007/978-3-319-72456-0_8

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