An error analysis for a certain class of iterative methods |
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Authors: | Ioannis K Argyros |
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Institution: | 1. Department of Mathematics, Cameron University, 73505, Lawton, OK, USA
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Abstract: | We provide local convergence results in affine form for in-exact Newton-like as well as quasi-Newton iterative methods in
a Banach space setting. We use hypotheses on the second or on the first andmth Fréchet-derivative (m ≥ 2 an integer) of the operator involved. Our results allow a wider choice of starting points since our radius of convergence
can be larger than the corresponding one given in earlier results using hypotheses on the first-Fréchet-derivative only. A
numerical example is provided to illustrate this fact. Our results apply when the method is, for example, a difference Newton-like
or update-Newton method. Furthermore, our results have direct applications to the solution of autonomous differential equations. |
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Keywords: | |
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