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Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions

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Abstract

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295, 2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study.

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Authors and Affiliations

  1. Department of Mathematics Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

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Argyros, I.K., Hilout, S. Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions. Numer Algor 58, 23–52 (2011). https://doi.org/10.1007/s11075-011-9446-9

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