Improving the applicability of the secant method to solve nonlinear systems of equations

  1. Amat, S. 1
  2. Hernández-Verón, M.A. 2
  3. Rubio, M.J. 2
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Any de publicació: 2014

Volum: 247

Pàgines: 741-752

Tipus: Article

DOI: 10.1016/J.AMC.2014.09.066 SCOPUS: 2-s2.0-84908102429 WoS: WOS:000344474800064 GOOGLE SCHOLAR

Altres publicacions en: Applied Mathematics and Computation

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Resum

A modification of the secant method for the approximation of nonlinear system of equations is considered to improve the applicability of the secant method. This modification changes the resolution of a linear system in each step, necessary to apply the secant method, for several matrix multiplications. In this way, the numerical stability of the secant method can be improved. In addition, in this paper, we prove that the modification considered keeps two important properties of the secant method, such as: does not use derivatives in its algorithm and has R-order of convergence at least 1+5/2.