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Approximation of Functions Using Digital Nets

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Monte Carlo and Quasi-Monte Carlo Methods 2006

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.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    Josef Dick & Prances Y. Kuo

  2. Fachbereich Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020, Salzburg, Austria

    Peter Kritzer

Authors
  1. Josef Dick
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  2. Peter Kritzer
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  3. Prances Y. Kuo
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ulm University, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Alexander Keller

  2. Department of Computer Science, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Stefan Heinrich

  3. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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Dick, J., Kritzer, P., Kuo, P. (2008). Approximation of Functions Using Digital Nets. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_16

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