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On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods. (English) Zbl 1193.65078
Summary: A novel method of locating all real roots of systems of nonlinear equations is presented. The root finding problem is transformed to an optimization problem, enabling the application of global optimization methods. Among many methods that exist in the global optimization literature, multistart and minfinder are applied because of their ability to locate not only the global minimum but also all local minima of the objective function. This procedure enables to locate all the possible roots of the system.
Various test cases are examined in order to validate the proposed procedure. This methodology does not make use of a priori knowledge of the number of the existing roots in the same manner as the corresponding global optimization methodology which does not make use of a priori knowledge of the existed number of local minima. The application of the new methodology results in finding all the roots in all test cases. The proposed methodology is general enough to be applied in any root finding problem.

MSC:
 65H10 Numerical computation of solutions to systems of equations 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming
Software:
MinFinder; GENLS; COPRIN; STRSCNE
Full Text:
References:
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