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Listar por autor "Torregrosa, Juan Ramón"

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    • A new efficient parametric family of iterative methods for solving nonlinear systems 

      Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Difference Equations and Applications, 18/09/2019)
      A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...

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

      Cordero, Alicia; Feng, Licheng; Magreñán, Á. Alberto ; 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 ...

    • Anomalies in the convergence of Traub-type methods with memory 

      Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Blackwell Publishing Ltd, 2020)
      The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the speed ...

    • Anomalies in the convergence of Traub‐type methods with memory 

      Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Computational and Mathematical Methods, 06/08/2019)
      The stability analysis of a new family of iterative methods with memory isintroduced. This family, designed from Traub's method, allows to add memorythrough the introduction of an accelerating parameter. Hence, the speed ...

    • CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems 

      Chicharro, Francisco Israel ; Cordero, Alicia; Martínez, Tobias H. ; 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 ...

    • Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications 

      Chicharro, Francisco Israel ; 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 ; 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 ; Cordero, Alicia; Garrido, Neus ; 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 ...

    • Iterative schemes for finding all roots simultaneously of nonlinear equations 

      Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón; Triguero-Navarro, Paula (Applied Mathematics Letters, 2022)
      In this paper, we propose a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations. By applying this procedure ...

    • Mean-based iterative methods for solving nonlinear chemistry problems 

      Chicharro, Francisco Israel ; Cordero, Alicia; Martínez, Tobias H. ; 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 ...

    • Memory in the iterative processes for nonlinear problems 

      Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón; Triguero-Navarro, Paula (Mathematical Methods in the Applied Sciences, 2023)
      In this paper, we study different ways for introducing memory to a parametric family of optimal two-step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained by ...

    • On the choice of the best members of the Kim family and the improvement of its convergence 

      Chicharro, Francisco Israel ; 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 ...

    • On the convergence of a damped Newton-like method with modified right hand side vector 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto ; 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 ; 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 ; 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 effect of the multidimensional weight functions on the stability of iterative processes 

      Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus ; Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 15/05/2022)
      In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family ...

    • On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory 

      Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus ; 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. ...

    • Preface of the "iterative Procedures for Solving Nonlinear Problems" 

      Cordero, Alicia; Magreñán, Á. Alberto ; Torregrosa, Juan Ramón (AIP Conference Proceedings, 2018)
      Ponencia de la conferencia "International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017; The MET HotelThessaloniki; Greece; 25 September 2017 through 30 September 2017"

    • Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane 

      Magreñán, Á. Alberto ; 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 ...

    • Reverse teaching as a methodological strategy for mathematics learning in higher education 

      Orcos, Lara ; Cordero, Alicia; Jordán, Cristina; Magreñán, Á. Alberto; Sanabria, E.; Torregrosa, Juan Ramón (Nova Science Publishers, Inc., 2020)
      The aim of this study is to assess the opinions of the first year students of the subject Discrete Mathematics of the degree of Big Data, at the Universitat Politècnica de Valencia (UPV) that have used flip methodology as ...