Revista de la
Unión Matemática Argentina
The multivariate bisection algorithm
Manuel López Galván
Volume 60, no. 1 (2019), pp. 79–98

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The aim of this paper is to study the bisection method in $\mathbb{R}^n$. 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.