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Approximation of Functions Using Digital Nets

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • 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)

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.

Suggested Citation

  • Josef Dick & Peter Kritzer & Prances Y. Kuo, 2008. "Approximation of Functions Using Digital Nets," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 275-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_16
    DOI: 10.1007/978-3-540-74496-2_16
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