Local convergence theorems for Newton methods |
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Authors: | Ioannis K Argyros |
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Institution: | 1. Department of Mathematics, Cameron University, 73505, Lawton, IK
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Abstract: | Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods.
The first uses conditions on the first Fréchet-derivative whereas the second theorem employs hypotheses on themth (m ≥ 2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear
convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on
the mth Fréchet-derivative our radius of convergence can sometimes be larger than the corresponding one in 10]. This allows
a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger
than the one in 10]. |
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Keywords: | |
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