On real factors of real interval polynomials

Abstract

For a real multivariate interval polynomial P and a real multivariate polynomial f, we provide a rigorous method for deciding whether there exists a polynomial p in P such that p is divisible by f. When P is univariate, there is a well-known criterion for whether there exists a polynomial p(χ)in P such that p(α)=0 for a given real number α. Since p(α)=0 if and only if p(χ) is divisible by χ--α, our result is a generalization of the criterion to multivariate polynomials and higher degree factors.