Corpus ID: 117871897

# Low rank approximation of polynomials

@article{Schrijver2012LowRA,
title={Low rank approximation of polynomials},
author={A. Schrijver},
journal={arXiv: Combinatorics},
year={2012}
}
• A. Schrijver
• Published 2012
• Mathematics
• arXiv: Combinatorics
• Let $k\leq n$. Each polynomial $p\in\oR[x_1,...,x_n]$ can be uniquely written as $p=\sum_{\mu}\mu p_{\mu}$, where $\mu$ ranges over the set $M$ of all monomials in $\oR[x_1,...,x_k]$ and where $p_{\mu}\in\oR[x_{k+1},...,x_n]$. If $p$ is $d$-homogeneous and $\varepsilon>0$, we say that $p$ is {\em $\varepsilon$-concentrated on the first $k$ variables} if \sum_{\mu\in M\atop\deg(\mu) 0$there exists$k_{d,\varepsilon}$such that for each$n$and each$d$-homogeneous$p\in\oR[x_1,...,x_n]\$ there… CONTINUE READING
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