Mostrando ítems 1-15 de 15

    • A new fourth-order family for solving nonlinear problems and its dynamics 

      Cordero, Alicia; Feng, Licheng; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2015)
      In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
    • CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Martínez, Tobias H. (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2020)
      The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods ...
    • 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 ...
    • Impact on Stability by the Use of Memory in Traub-Type Schemes 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus (1); Torregrosa, Juan Ramón (Mathematics, 02/2020)
      In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub's method, they have been designed using linear ...
    • Mean-based iterative methods for solving nonlinear chemistry problems (November, 10.1007/S10910-019-01085-2, 2019) 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Martínez, Tobias H. (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2020)
      The original version of this article unfortunately contained an error in title. Unintentionally, the special issue title was presented in addition to the article’s title. The correct title of the article should read as ...
    • On the convergence of a damped Newton-like method with modified right hand side vector 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Applied Mathematics and Computation, 09/2015)
      We present a convergence analysis for a damped Newton like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special ...
    • On the convergence of a Damped Secant method with modified right-hand side vector 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Applied Mathematics and Computation, 02/2015)
      We present a convergence analysis for a Damped Secant method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case ...
    • On the convergence of a higher order family of methods and its dynamics 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)
      In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
    • On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus (1); Torregrosa, Juan Ramón (Applied Mathematics Letters, 06/2020)
      Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second order. ...
    • Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane 

      Magreñán, Á. Alberto (1); Cordero, Alicia; Gutiérrez, José M; Torregrosa, Juan Ramón (Mathematics and Computers in Simulation, 11/2014)
      The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used ...
    • Stability analysis of a parametric family of iterative methods for solving nonlinear models 

      Cordero, Alicia; Gutiérrez, José M; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Applied Mathematics and Computation, 07/2016)
      A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods ...
    • 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 ...
    • Study of a Biparametric Family of Iterative Methods 

      Campos, B; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón; Vindel, P (Abstract and Applied Analysis, 2014)
      The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the -iterative methods and the well-known Chebyshev-Halley family. We find 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 ...