Newton-like Methods with At least Quadratic Order of Convergence for the Computation of Fixed Points
نویسنده
چکیده
The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Newton-like method of at least Q-order 3 which uses this information. Here we provide a finer local convergence analysis for the same method under weaker hypotheses which do not necessarily imply the contraction property of the mapping. A numerical example is provided to show that our results compare favorably with the ones in [9]. The semilocal convergence of the method not considered in [9] is also examined. AMS (MOS) Subject Classification Codes: 65G99, 65H10, 47H17, 49M15
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