Abstract

GOMEZ, Luis Antonio; REYES, Edilberto José  and  CORREA, Carlos Rodrigo. AN ALGORITHM FOR NUMERICAL SOLUTION OF NONLINEAR EQUATIONS SYSTEMS USING A STRATEGY OF GLOBAL OPTIMIZATION BASED ON INTERVAL ANALYSIS. Rev.EIA.Esc.Ing.Antioq [online]. 2012, n.18, pp.77-89. ISSN 1794-1237.

In this paper an algorithm for the numerical solution of nonlinear equations systems is presented. For this purpose the system of equations becomes a function of real value which will be minimized, in the global sense, in a given initial domain (a box in ⁿ) using analysis of intervals. The designed algorithm has the ability to determine the existence or not of solutions to the system of equations in a given box. The solutions of the system of equations, if they exist inside the given box, are expressed by means of enclosures by sub-boxes whose size is smaller than the established accuracy. There is not restriction about the relationship between the number of equations and the number of unknowns of the system. It is also carried out an analysis of the convergence of the algorithm, and the results of their application are shown for some test problems.

Keywords : systems of nonlinear equations; global optimization; minimization; interval analysis; box in ⁿ.

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