A multidimensional real dynamical analysis of a novel class of iterative approach for approximating the solutions of nonlinear systems of algebraic equations is presented in this chapter. We investigate the behaviour of the multidimensional rational operator associated with the iterative approach, acting on a system of quadratic polynomials of separate and mixed variables, respectively, using well-known discrete dynamic multivariate tools. Some stability results for the proposed class are shown. These findings enable us to identify and avoid family members with poor stability features and chaotic behaviour. To confirm the theoretical and dynamical results, certain numerical tests are presented.
Author (S) Details
Raudys R. Capdevila
Instituto de Matematica Multidisciplinar, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain and Dpto de Educacion en Linea, Universidad San Francisco de Quito, Ecuador.
Alicia Cordero
Instituto de Matematica Multidisciplinar, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain.
Juan R. Torregrosa
Instituto de Matematica Multidisciplinar, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain.
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