Sum of squares (SOS) decompositions for nonnegative polynomials are usually computed
numerically, using convex optimization solvers. Although the underlying floating point …

We present a hybrid symbolic-numeric algorithm for certifying a polynomial or rational
function with rational coefficients to be non-negative for all real values of the variables by …

We describe methods for proving bounds on infinite-time averages in differential dynamical
systems. The methods rely on the construction of nonnegative polynomials with certain …

If a real polynomial f can be written as a sum of squares of real polynomials, then clearly f is
nonnegative on Rn, and an explicit expression of f as a sum of squares is a certificate of …

We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower
bound certificates for several well-known factorization problems in hybrid symbolic-numeric …

We construct families of explicit (homogeneous) polynomials f over Q that are sums of
squares of polynomials over R, but not over Q. Whether or not such examples exist was an …

The endlessly fascinating relationship between positivity and sums of squares, as well as
the posing and later solution of Hilbert's 17th problem, were things I learned about in …

We show that all the coefficients of the polynomial tr ((A+ tB)^ m) ∈ R t are nonnegative
whenever m≤ 13 is a nonnegative integer and A and B are positive semidefinite matrices of …

We consider the problem of computing exact sums of squares (SOS) decompositions for
certain classes of non-negative multivariate polynomials, relying on semidefinite …

Let P={h_1,\dots,h_s\}⊂ZY_1,\dots,Y_k, D≧\deg(h_i) for 1≦i≦s, σ bounding the bit length
of the coefficients of the h_i's, and let Φ be a quantifier-free P-formula defining a convex …