Bernstein's basis and real root isolation

Bernard Mourrain , Fabrice Rouillier (1) , Marie-Françoise Roy

1 SPIRAL - Systèmes Polynomiaux, Implantation, Résolution Algébrique

In this mostly expository paper we explain how the Bernstein basis, widely used in computer-aided geometric design, provides an efficient method for real root isolation, using de Casteljau’s algorithm. We discuss the link between this approach and more classical methods for real root isolation. We also present a new improved method for isolating real roots in the Bernstein basis inspired by Roullier and Zimmerman.

Domaines: Informatique [cs]

Bernard Mourrain, Fabrice Rouillier, Marie-Françoise Roy. Bernstein's basis and real root isolation. Combinatorial and Computational Geometry, 52, Cambridge University Press, pp.459-478, 2005, MSRI Publications. ⟨hal-01486849⟩