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arXiv · 1705.04567

Optimal Monte Carlo Methods for $L^2$-Approximation

David Krieg
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Abstract

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ 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 $n$ pieces of arbitrary linear information, including function values.

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David Krieg. 2018-03-15. Optimal Monte Carlo Methods for $L^2$-Approximation. https://arxiv.org/abs/1705.04567

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