The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS

  • Argyros, Ioannis K. (Cameron University, Department of Mathematics Sciences) ;
  • Hilout, Said (Poitiers University, Laboratoire de Mathematiques et Applications)
  • Received : 2010.05.08
  • Accepted : 2010.11.21
  • Published : 2010.11.30
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Abstract

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

Keywords

References

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