Approximation of Functions Using Digital Nets

Josef Dick (), Peter Kritzer () and Prances Y. Kuo ()
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Josef Dick: University of New South Wales, School of Mathematics and Statistics
Peter Kritzer: Universität Salzburg, Fachbereich Mathematik
Prances Y. Kuo: University of New South Wales, School of Mathematics and Statistics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 275-297 from Springer

Abstract: Summary In analogy to a recent paper by Kuo, Sloan, and Woźniakowski, which studied lattice rule algorithms for approximation in weighted Korobov spaces, we consider the approximation problem in a weighted Hilbert space of Walsh series. Our approximation uses a truncated Walsh series with Walsh coefficients approximated by numerical integration using digital nets. We show that digital nets (or more precisely, polynomial lattices) tailored specially for the approximation problem lead to better error bounds. The error bounds can be independent of the dimension s, or depend only polynomially on s, under certain conditions on the weights defining the function space.

Keywords: Approximation Problem; Lattice Rule; Walsh Function; Polynomial Lattice; Multivariate Integration (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_16

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DOI: 10.1007/978-3-540-74496-2_16

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