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A Universal Algorithm for Multivariate Integration

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Abstract

We present an algorithm for multivariate integration over cubes that is unbiased and has optimal order of convergence (in the randomized sense as well as in the worst-case setting) for all Sobolev spaces \({H^{r,\mathrm{mix}}([0,1]^d)}\) and \({H^s([0,1]^d)}\) for \(s>d/2\).

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Authors and Affiliations

  1. Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany

    David Krieg & Erich Novak

Authors
  1. David Krieg
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  2. Erich Novak
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Correspondence to David Krieg.

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Communicated by Andrew Stuart.

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Krieg, D., Novak, E. A Universal Algorithm for Multivariate Integration. Found Comput Math 17, 895–916 (2017). https://doi.org/10.1007/s10208-016-9307-y

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  • DOI: https://doi.org/10.1007/s10208-016-9307-y

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