On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions

On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions

We study the problem of local convergence of the accelerated Newton method for the solution of nonlinear functional equations under generalized Lipschitz conditions for the first- and second-order Fréchet derivatives. We show that the accelerated method is characterized by the quadratic order of con...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016, Vol.212 (1), p.16-26
1. Verfasser: Shakhno, S. М.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We study the problem of local convergence of the accelerated Newton method for the solution of nonlinear functional equations under generalized Lipschitz conditions for the first- and second-order Fréchet derivatives. We show that the accelerated method is characterized by the quadratic order of convergence and compare it with the classical Newton method.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-015-2645-5