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Computing real zeros of a polynomial by branch and bound and branch and reduce algorithms

Le Thi Hoai An (Laboratoire d'Informatique Théorique et Appliquée (LITA) Université de Lorraine, Metz, France)
Ouanes Mohand (Département de Mathématiques, Faculté des Sciences, Université de Tizi-Ouzou, Algérie)
Zidna Ahmed (Laboratoire d'Informatique Théorique et Appliquée (LITA) Université de Lorraine, Metz, France)

In this paper we propose two algorithms based on branch and bound method and reduced interval techniques to compute all real zeros of a polynomial. Quadratic bounding functions are proposed which are better than the well known linear underestimator. Experimental result shows the efficiency of the two algorithms when facing ill-conditioned polynomials.

Keywords: Global optimization quadratic upper function quadratic lower function root-finding Bound and Reduce Branch and Bound w-subdivision