Communication Dans Un Congrès Année : 2013

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=2L. The algorithm has Boolean complexity ˜OB(d2τ+dL). Our algorithms support the same complexity bound for the refinement of r roots, for any rd.
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Dates et versions

hal-00816214 , version 1 (20-04-2013)
hal-00816214 , version 2 (21-04-2013)
hal-00816214 , version 3 (25-04-2013)

Identifiants

Citer

Victor Y. Pan, Elias Tsigaridas. On the Boolean complexity of real root refinement. ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, United States. ⟨10.1145/2465506.2465938⟩. ⟨hal-00816214v3⟩
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