• Corpus ID: 119635360

High-Dimensional Function Approximation: Breaking the Curse with Monte Carlo Methods

  title={High-Dimensional Function Approximation: Breaking the Curse with Monte Carlo Methods},
  author={Robert J. Kunsch},
  journal={arXiv: Numerical Analysis},
  • R. Kunsch
  • Published 26 April 2017
  • Mathematics
  • arXiv: Numerical Analysis
In this dissertation we study the tractability of the information-based complexity $n(\varepsilon,d)$ for $d$-variate function approximation problems. In the deterministic setting for many unweighted problems the curse of dimensionality holds, that means, for some fixed error tolerance $\varepsilon>0$ the complexity $n(\varepsilon,d)$ grows exponentially in $d$. For integration problems one can usually break the curse with the standard Monte Carlo method. For function approximation problems… 
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