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

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Department of Mathematics Sciences, Cameron University, Lawton, USA 73505;Laboratoire de Mathématiques et Applications, Poitiers University, Futuroscope Chasseneuil Cedex, France 86962
Venue:
Numerical Algorithms
Year:
2011

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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.