The multivariate bisection algorithm

• Manuel López Galván ^[1]
  1. [1] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 1, 2019, págs. 79-98
• Idioma: inglés
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• Resumen

  • 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.