Let $$f(y,z)=\frac{9\,025 y^2}{16\,384}-\frac{95 y z}{64}-\frac{3\,967\,295y}{6\,291\,456}+z^2+\frac{41\,761z}{49\,152}+\frac{1\,515\,513}{8\,388\,608}$$ be a polynomial. Suppose that we have shown that $f(y,z)\ge0$ for all $y,z\in\mathbb{R}$. Is it possible to write $f(y,z)$ as a sum of squares?
Any reference, suggestion, idea, or comment is welcome. Thank you!
Have a look at "An algorithm for sums of squares of real polynomials", Powers, Wörmann, in "Journal of Pure and Applied Algebra" (1998).
There's also a free Matlab toolbox, SOSTOOLS, providing a function findsos(). Have a look at the toolbox user's guide on page 33.