Optimal Monte Carlo Methods for $L^2$-Approximation
Numerical Analysis
2018-03-16 v3
Abstract
We construct Monte Carlo methods for the -approximation in Hilbert spaces of multivariate functions sampling no more than function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling pieces of arbitrary linear information, including function values.
Cite
@article{arxiv.1705.04567,
title = {Optimal Monte Carlo Methods for $L^2$-Approximation},
author = {David Krieg},
journal= {arXiv preprint arXiv:1705.04567},
year = {2018}
}