A sum of squares approximation of nonnegative polynomials

Details A sum of squares approximation of nonnegative polynomials A sum of squares approximation of nonnegative polynomials

2004-12-20

arxiv.org/abs/math/0412398v1

Mathematics

Algebraic Geometry

Scientific paper

We show that every real nonnegative polynomial $f$ can be approximated as
closely as desired by a sequence of polynomials $\{f_\epsilon\}$ that are sums
of squares. Each $f_\epsilon$ has a simple et explicit form in terms of $f$ and
$\epsilon$. A special representation is also obtained for convex polynomials,
nonnegative on a convex semi-algebraic set.

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