• Corpus ID: 117871897

Low rank approximation of polynomials

  title={Low rank approximation of polynomials},
  author={Alexander Schrijver},
  journal={arXiv: Combinatorics},
  • A. Schrijver
  • Published 15 November 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… 

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