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Stochastic Approximation of Functions and Applications

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Monte Carlo and Quasi-Monte Carlo Methods 2010

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 23))

Abstract

We survey recent results on the approximation of functions from Sobolev spaces by stochastic linear algorithms based on function values. The error is measured in various Sobolev norms, including positive and negative degree of smoothness. We also prove some new, related results concerning integration over Lipschitz domains, integration with variable weights, and study tractability of generalized versions of indefinite integration and discrepancy.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Kaiserslautern, D-67653, Kaiserslautern, Germany

    Stefan Heinrich

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  1. Stefan Heinrich
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Correspondence to Stefan Heinrich .

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Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Heinrich, S. (2012). Stochastic Approximation of Functions and Applications. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_5

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