• Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Axioms, 06/05/2019)
      In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing ...
    • Highly efficient family of iterative methods for solving nonlinear models 

      Behl, Ramandeep; Sarría, Iñigo (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 ...
    • Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics 

      Chand, Prem Bahadur; Chicharro, Francisco Israel (1); Jain, Pankaj; Sethi, Kriti (Mediterranean Journal of Mathematics, 16/04/2019)
      In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon ...
    • Stability and applicability of iterative methods with memory 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 15/03/2019)
      Based on the third-order Traub’s method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...
    • Stability study of eighth-order iterative methods for solving nonlinear equations 

      Cordero, Alicia; Magreñán, Á. Alberto (1); Quemada, Carlos; Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2016)
      In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ...
    • 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 ...