Dynamics and Fractal Dimension of Steffensen-Type Methods
AbstractIn this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based on the box-counting algorithm, several iterative derivative-free methods of different convergence orders are compared. View Full-Text
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Chicharro, F.I.; Cordero, A.; Torregrosa, J.R. Dynamics and Fractal Dimension of Steffensen-Type Methods. Algorithms 2015, 8, 271-279.
Chicharro FI, Cordero A, Torregrosa JR. Dynamics and Fractal Dimension of Steffensen-Type Methods. Algorithms. 2015; 8(2):271-279.Chicago/Turabian Style
Chicharro, Francisco I.; Cordero, Alicia; Torregrosa, Juan R. 2015. "Dynamics and Fractal Dimension of Steffensen-Type Methods." Algorithms 8, no. 2: 271-279.