Resumen de The multivariate bisection algorithm

Manuel López Galván

• The aim of this paper is to study the bisection method in Rn. We propose a multivariate bisection method supported by the Poincaré–Miranda theorem in order to solve non-linear systems of equations. Given an initial cube satisfying the hypothesis of the Poincaré–Miranda theorem, the algorithm performs congruent refinements through its center by generating a root approximation. Through preconditioning we will prove the local convergence of this new root finder methodology and moreover we will perform a numerical implementation for the two dimensional case.