Corpus ID: 119635360

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

@article{Kunsch2017HighDimensionalFA,
title={High-Dimensional Function Approximation: Breaking the Curse with Monte Carlo Methods},
author={Robert J. Kunsch},
journal={arXiv: Numerical Analysis},
year={2017}
}
• 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… Expand
5 Citations
The difficulty of Monte Carlo approximation of multivariate monotone functions
• R. Kunsch
• Mathematics, Computer Science
• J. Approx. Theory
• 2019