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The information-based complexity of approximation problem by adaptive Monte Carlo methods

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Abstract

In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW r p,α (\( \mathbb{T}^d \)), 1 < p < ∞, in the norm of L q (\( \mathbb{T}^d \)), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    GenSun Fang & LiQin Duan

Authors
  1. GenSun Fang
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  2. LiQin Duan
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Corresponding author

Correspondence to GenSun Fang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10671019) and the Research Fund for the Doctoral Program of Higher Education (Grant No. 20050027007)

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Fang, G., Duan, L. The information-based complexity of approximation problem by adaptive Monte Carlo methods. Sci. China Ser. A-Math. 51, 1679–1689 (2008). https://doi.org/10.1007/s11425-008-0008-0

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  • DOI: https://doi.org/10.1007/s11425-008-0008-0

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