The complexity of function approximation on Sobolev spaces with bounded mixed derivative by linear Monte Carlo methods

  • Authors:

  • Gensun Fang;Liqin Duan

  • Affiliations:

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

  • Venue:
  • Journal of Complexity
  • Year:
  • 2008

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Abstract

We study the information-based complexity of the approximation problem on the multivariate Sobolev space with bounded mixed derivative MW"p","@a^r in the norm of L"q by linear Monte Carlo methods. Applying the Maiorov's discretization technique and some properties of pseudo-s-scale, we determine the exact orders of this problem for 1