• An efficient optimal family of sixteenth order methods for nonlinear models 

      Behl, Ramandeep; Amat, Sergio; Magreñán, Á. Alberto (1); Motsa, S S (Journal of Computational and Applied Mathematics, 2018)
      The principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ Newton’s method to further develop new interesting optimal ...
    • An Overview on Steffensen-Type Methods 

      Amat, Sergio; Busquier, Sonia; Magreñán, Á. Alberto (1); Orcos, Lara (1) (Advances in iterative methods for nonlinear equations, 2016)
      In this chapter we present an extensive overview of Steffensen-type methods. We first present the real study of the methods and then we present the complex dynamics related this type of methods applied to different ...
    • Complexity of an Homotopy Method at the Neighbourhood of a Zero 

      Yakoubsohn, J. C.; Gutierrez, J. M.; Magreñán, Á. Alberto (1) (Advances in iterative methods for nonlinear equations, 2016)
      This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered ...
    • Extending the Applicability of Stirling's Method 

      Amorós, Cristina (1); Argyros, Ioannis K; Magreñán, Á. Alberto; Regmi, Samundra; González-Crespo, Rubén (1); Sicilia, Juan Antonio (1) (Mathematics, 01/2020)
      Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require ...
    • Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (MDPIMathematics, 05/12/2019)
      A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to nonlinear ...
    • 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, 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 ...