On the Boolean complexity of real root refinement
Résumé
We assume that a real square-free polynomial A has a degree d, a maximum coefficient bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we quantify this assumption). Then, we combine the {\em Double Exponential Sieve} algorithm (also called the {\em Bisection of the Exponents}), the bisection, and Newton iteration to decrease the width of this inclusion interval by a factor of t=2−L. The algorithm has Boolean complexity ˜OB(d2τ+dL). Our algorithms support the same complexity bound for the refinement of r roots, for any r≤d.
Domaines
Calcul formel [cs.SC]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...