Relaxing the convergence conditions for Newton-like methods



Local as well as semilocal convergence theorems for Newton-like methods have been given by us and other authors [1]—[8] using various Lipschitz type conditions on the operators involved. Here we relax these conditions by introducing weaker center-Lipschitz type conditions. This way we can cover a wider range of problems than before in the semilocal case, where as in the local case a larger convergence radius can be obtained in some cases.

AMS Mathematics Subject Classification

65H10 65G99 47H17 49M15 

Key words and phrases

Newton-like method Banach space Lipschitz condition center Lipschitz condition Newton-Kantorovich theorem radius of convergence Fréchet-derivative 


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Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCameron UniversityLawtonUSA

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