Details:
Title  Subdivision methods for solving polynomial equations  Author(s)  Bernard Mourrain, J.P. Pavone  Type  Article in Journal  Abstract  This paper presents a new algorithm for solving a system of polynomials, in a domain of R n . It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke and Patrikalakis [Sherbrooke, E.C., Patrikalakis, N.M., 1993. Computation of the solutions of nonlinear polynomial systems. Comput. Aided Geom. Design 10 (5), 379–405]. It uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte’s rule. We analyse the behavior of the method, from a theoretical point of view, shows that for simple roots, it has a local quadratic convergence speed and gives new bounds for the complexity of approximating real roots in a box of R n . The improvement of our approach, compared with classical subdivision methods, is illustrated on geometric modeling applications such as computing intersection points of implicit curves, selfintersection points of rational curves, and on the classical parallel robot benchmark problem.  Keywords  Resolution, Real solution, Symbolicnumeric computation, Polynomial equation, Subdivision, Bernstein basis, Descartes rule, Complexity  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001168 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  3  Pages  292  306  Year  2009  Note  Polynomial System Solving in honor of Daniel Lazard  Edition  0  Translation 
No  Refereed 
No 
