Relaxing the convergence conditions for Newton-like methods
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Local as well as semilocal convergence theorems for Newton-like methods have been given by us and other authors — 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 Classification65H10 65G99 47H17 49M15
Key words and phrasesNewton-like method Banach space Lipschitz condition center Lipschitz condition Newton-Kantorovich theorem radius of convergence Fréchet-derivative
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