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Listar por tema "dynamics"

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    • A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative 

      Argyros, Ioannis K; Magreñán, Á. Alberto (Numerical Algorithms, 01/2016)
      We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...

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

      Behl, Ramandeep; Amat, Sergio; Magreñán, Á. Alberto ; 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 ; Orcos, Lara (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 ...

    • CMMSE: Family of fourth-order optimal classes for solving multiple-root nonlinear equations 

      Chicharro, Francisco Israel; Garrido, Neus; Jerezano, Julissa H.; Pérez-Palau, Daniel (Journal of Mathematical Chemistry, 2023)
      We present a new iterative procedure for solving nonlinear equations with multiple roots with high efficiency. Starting from the arithmetic mean of Newton’s and Chebysev’s methods, we generate a two-step scheme using weight ...

    • Convergence and dynamics of a higher order family of iterative methods 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we study the convergence as well as the dynamics of some high convergence order family of iterative methods.

    • Convergence and Dynamics of a Higher-Order Method 

      Moysi, Alejandro; Argyros, Ioannis K; Regmi, Samundra; González, Daniel; Magreñán, Á. Alberto; Sicilia, Juan Antonio (Symmetry, 03/2020)
      Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves ...

    • Convergence and the dynamics of Chebyshev-Halley type methods 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present a weak convergence analysis and the dynamics of Chebyshev–Halley type methods.

    • Effect in the spectra of eigenvalues and dynamics of RNNs trained with excitatory-inhibitory constraint 

      Jarne, Cecilia; Caruso, M. (Cognitive Neurodynamics, 2023)
      In order to comprehend and enhance models that describes various brain regions it is important to study the dynamics of trained recurrent neural networks. Including Dale's law in such models usually presents several ...

    • Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation 

      Argyros, Ioannis K; Magreñán, Á. Alberto ; Orcos, Lara (Journal of Mathematical Chemistry, 08/2016)
      We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...

    • Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions 

      Amat, Sergio ; Argyros, Ioannis K; Busquier, Sonia; Magreñán, Á. Alberto (Numerical Algorithms, 02/2017)
      We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...

    • Local Convergence and the Dynamics of a Two-Step Newton-Like Method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 05/2016)
      We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.

    • Problem-based learning proposal for teaching dynamical systems 

      Chicharro, Francisco Israel ; Garrido, Neus (Nova Science Publishers, Inc., 2020)
      Dynamic systems, in general, and discrete dynamic systems based on iterative methods, in particular, have several features that can be exploited: they can be performed by computation and there are graphical tools ready to ...

    • Second derivative free sixth order continuation method for solving nonlinear equations with applications 

      Maroju, P; Magreñán, Á. Alberto ; Motsa, S S; Sarría, Íñigo (Journal of Mathematical Chemistry, 08/2018)
      In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least ...

    • Study of a high order family: Local convergence and dynamics 

      Amorós, Cristina ; Argyros, Ioannis K; González-Crespo, Rubén ; Magreñán, Á. Alberto; Orcos, Lara ; Sarría, Íñigo (Mathematics, 01/03/2019)
      The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...

    • Study of local convergence and dynamics of a king-like two-step method with applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Moysi, Alejandro; Sarría, Íñigo ; Sicilia, Juan Antonio (Mathematics, 01/07/2020)
      In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...