On real factors of real interval polynomials

• Autores: Hiroshi Sekigawa
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 7, 2009, págs. 908-922
• Idioma: inglés
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• Resumen

  • For a real multivariate interval polynomial and a real multivariate polynomial f, we provide a rigorous method for deciding whether there is a polynomial p in such that f is a factor of p. When is univariate, there is a well-known criterion for whether there exists a polynomial p in 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 l8-norm such that f is a factor of q.