A two-dimensional bisection method using the Poincaré-Miranda Theorem
Manuel López Galván · arXiv (Cornell University) · 2017
In this paper we develop a root-finding algorithm in order to solve non-linear systems of two equations using the Poincare-Miranda theorem. This theorem is the natural extension of the Bolzano's theorem for the multidimensional case and it looks for sign conditions throughout the border domain in order to guarantee the existence of a root. In this work we propose a two-dimensional bisection method following the terms of this theorem. Given a system to solve and given a starting rectangle verifying the border conditions, we perform refinement of the rectangle following the sign conditions and taking the center we generate root's approximation for the system.