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The multivariate bisection algorithm
Volume 60, no. 1
(2019),
pp. 79–98
https://doi.org/10.33044/revuma.v60n1a06
Abstract
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.
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Published by the Unión Matemática Argentina |
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