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arXiv · 1610.02852

Truncation Dimension for Function Approximation

Peter Kritzer·Friedrich Pillichshammer·G. W. Wasilkowski
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Abstract

We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number ${\rm dim^{trnc}}(\varepsilon)$ of variables. Here $\varepsilon$ is the error demand and we refer to ${\rm dim^{trnc}}(\varepsilon)$ as the $\varepsilon$-truncation dimension. We show that for sufficiently fast decaying product weights and modest error demand (up to about $\varepsilon \approx 10^{-5}$) the truncation dimension is surprisingly very small.

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Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski. 2016-10-10. Truncation Dimension for Function Approximation. https://arxiv.org/abs/1610.02852

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