Ball convergence of the Newton–Gauss method in Banach space

Ball convergence of the Newton–Gauss method in Banach space We study the local convergence of a fifth-order Newton–Gauss method in order to approximate a locally-unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the fifth derivative or even higher, although only the first derivatives are used in the method. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies can not apply. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

Ball convergence of the Newton–Gauss method in Banach space

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Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0091-z
Publisher site
See Article on Publisher Site

Abstract

We study the local convergence of a fifth-order Newton–Gauss method in order to approximate a locally-unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the fifth derivative or even higher, although only the first derivatives are used in the method. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies can not apply.

Journal

SeMA JournalSpringer Journals

Published: Sep 23, 2016

References

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