A sum of squares approximation of nonnegative polynomials

Abstract

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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• S.o.s. approximation of polynomials nonnegative on a real algebraic set