On real factors of real interval polynomials

For a real multivariate interval polynomial P and a real multivariate polynomial f, we provide a rigorous method for deciding whether there is a polynomial p in P such that f is a factor of p. When P is univariate, there is a well-known criterion for whether there exists a polynomial p in P such that p(a)=0 for a given real number a. Since p(a)=0 if and only if x−a is a factor of p, our result is a generalization of the criterion to multivariate polynomials and higher degree factors. Furthermore, for real multivariate polynomials p and f, we show a method for computing a nearest polynomial q to p in a weighted l∞-norm such that f is a factor of q.