A two-steps algorithm for approximating real roots of a polynomial in Bernstein basis

Authors:
Ahmed Zidna;Dominique Michel
Affiliations:
Laboratoire d'Informatique Théorique et Appliquée, Université Paul Verlaine, Ile du Saulcy, F-57045 METZ, France;Laboratoire d'Informatique Théorique et Appliquée, Université Paul Verlaine, Ile du Saulcy, F-57045 METZ, France
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

The surface/curve intersection problem, through the resultants process results in a high degree (n=100) polynomial equation on [0,1] in the Bernstein basis. The knowledge of multiplicities of the roots is critical for the topological coherence of the results. In this aim, we propose an original two-steps algorithm based on successive differentiations which separates any root (even multiple) and guarantees that the assumptions of Newton global convergence theorem are satisfied. The complexity is @q(n^4) but the algorithm can easily be parallelized. Experimental results show its efficiency when facing ill-conditioned polynomials.