An acceleration of the continuous Newton's method

  1. Gutiérrez, J.M. 1
  2. Hernández-Verón, M.Á. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Any de publicació: 2018

Tipus: Article

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DOI: 10.1016/J.CAM.2018.03.013 SCOPUS: 2-s2.0-85047364601 GOOGLE SCHOLAR

Altres publicacions en: Journal of Computational and Applied Mathematics

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Resum

In this work, we study some numerical properties of the continuous Newton's method, the continuous version of the classical Newton's method for solving nonlinear equations p(z)=0. In fact, continuous Newton's method is an initial value problem whose solutions flow to a root of the equation. We show the influence of the multiplicity of the roots of the considered equation in the Jacobian matrix related to the problem. In addition, we study some modifications of the continuous Newton's method that allow us to increase the velocity of the convergence of the solutions towards the roots of p(z)=0. © 2018 Elsevier B.V.