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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Approximation of Functions Using Digital Nets
verfasst von : Josef Dick, Peter Kritzer, Prances Y. Kuo
Erschienen in: Monte Carlo and Quasi-Monte Carlo Methods 2006
Verlag: Springer Berlin Heidelberg
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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.