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Mathematics of Computation

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Local convergence of difference Newton-like methods


Author: T. J. Ypma
Journal: Math. Comp. 41 (1983), 527-536
MSC: Primary 65H10
DOI: https://doi.org/10.1090/S0025-5718-1983-0717700-4
MathSciNet review: 717700
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Abstract: Using affine invariant terms, we give a local convergence analysis of difference Newton-like methods for solving the nonlinear equation $ F(x) = 0$. The convergence conditions are weaker than those standardly required for methods of this class. The technique and results are valid for all currently known difference Newton-like methods which require evaluation of all components of F at the same point. Radius of convergence and rate of convergence results for particular difference Newton-like methods may easily be derived from the results reported here.


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DOI: https://doi.org/10.1090/S0025-5718-1983-0717700-4
Article copyright: © Copyright 1983 American Mathematical Society