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 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 .