• Highly efficient family of iterative methods for solving nonlinear models 

      Behl, Ramandeep; Sarría, Íñigo (1); González-Crespo, Rubén (1); Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 15/01/2019)
      In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case ...
    • Measures of the Basins of Attracting n-Cycles for the Relaxed Newton's Method 

      Gutierrez, J. M; Hernandez, L. J.; Magreñán, Á. Alberto (1); Rivas, M. T. (Advances in iterative methods for nonlinear equations, 2016)
      The relaxed Newton's method modifies the classical Newton's method with a parameter h in such a way that when it is applied to a polynomial with multiple roots and we take as parameter one of these multiplicities, it is ...
    • On the choice of the best members of the Kim family and the improvement of its convergence 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Mathematical Methods in the Applied Sciences, 30/09/2020)
      The best members of the Kim family, in terms of stability, are obtained by using complex dynamics. From this elements, parametric iterative methods with memory are designed. A dynamical analysis of the methods with memory ...
    • Third-degree anomalies of Traub's method 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)
      Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...