On real factors of real interval polynomials

Hiroshi Sekigawa
2007 Proceedings of the 2007 international symposium on Symbolic and algebraic computation - ISSAC '07  
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.
more » ... 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.
doi:10.1145/1277548.1277593 dblp:conf/issac/Sekigawa07 fatcat:gjszym57obgg3cmwakagnywavm