On a Moser–Steffensen Type Method for Nonlinear Systems of Equations

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

    Cartagena, España

    ROR https://ror.org/02k5kx966

    Geographic location of the organization Universidad Politécnica de Cartagena
  2. 2 Universitat Politècnica de Catalunya
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    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

    Geographic location of the organization Universitat Politècnica de Catalunya
  3. 3 Universidad de La Rioja
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    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

    Geographic location of the organization Universidad de La Rioja
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Journal:
Mediterranean Journal of Mathematics

ISSN: 1660-5446

Year of publication: 2016

Volume: 13

Issue: 6

Pages: 4109-4128

Type: Article

DOI: 10.1007/S00009-016-0735-3 SCOPUS: 2-s2.0-84970997359 WoS: WOS:000387090000021 GOOGLE SCHOLAR HANDLE: https://hdl.handle.net/10317/10795

More publications in: Mediterranean Journal of Mathematics

Repositorio Digital de la Universidad Politécnica de Cartagena (UPCT): lock_openOpen access Handle

Abstract

This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence, and finally, we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence. © 2016, Springer International Publishing.