An algorithm for decomposing a non-negative polynomial as a sum of squares of rational functions

This paper presents an algorithm for computing a decomposition of a non‐negative real polynomial as a sum of squares of rational functions. Rational functions in our algorithm have the denominators that are powers of the sum of squares of coordinate functions. Numerical experiments are performed for several well‐known polynomials such as Motzkin polynomials, Choi‐Lam polynomials and Robinson polynomials.