SeMA Journal

, Volume 74, Issue 1, pp 57–73 | Cite as

A multidimensional generalization of some classes of iterative methods

  • Miquel Grau-Sánchez
  • Miquel Noguera
  • José M. Gutiérrez
Article
First Online:
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Accepted:

Abstract

In this paper we extend to the multidimensional case some iterative methods that are known in their scalar version. All the schemes considered here are two-step methods with fourth-order local convergence, where the first step is Newton’s method. We analyze the efficiency of these new four algorithms and compare them in terms of the elapsed time needed for their computational implementation. We illustrate our results with some numerical examples and an application to the resolution of the systems arising from a Hammerstein’s integral equation.

Keywords

Divided difference Order of convergence Nonlinear equations  Iterative methods Efficiency 

Mathematics Subject Classification

65H10 47H99 
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Copyright information

© Sociedad Española de Matemática Aplicada 2016

Authors and Affiliations

  • Miquel Grau-Sánchez
    • 1
  • Miquel Noguera
    • 1
  • José M. Gutiérrez
    • 2
  1. 1.Department of Applied Mathematics IITechnical University of CataloniaBarcelonaSpain
  2. 2.Department of Mathematics and Computer SciencesUniversity of La RiojaLogroñoSpain

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