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Open AccessArticle

New Improvement of the Domain of Parameters for Newton’s Method

1
Escuela Superior de Ingeniería y Tecnología, UNIR, 26006 Logroño, Spain
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Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
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Escuela de Ciencias Físicas y Matemáticas, Universidad de las Americas, Quito 170517, Ecuador
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Departamento de Matemáticas y Computación, Universidad de la Rioja, 26004 Logroño, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 103; https://doi.org/10.3390/math8010103
Received: 26 November 2019 / Revised: 30 December 2019 / Accepted: 4 January 2020 / Published: 8 January 2020
(This article belongs to the Special Issue Computational Methods in Analysis and Applications 2020)
There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability of the methods. The new idea involves the construction of a tighter set than the ones used before also containing the iterates leading to at least as tight Lipschitz parameters and consequently a finer local as well as a semi-local convergence analysis. We used Newton’s method to demonstrate our technique. However, our technique can be used to extend the applicability of other methods too in an analogous manner. In particular, the new information related to the location of the solution improves the one in previous studies. This work also includes numerical examples that validate the proven results. View Full-Text
Keywords: domain; Newton’s method; improvement domain; Newton’s method; improvement
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MDPI and ACS Style

Amorós, C.; Argyros, I.K.; González, D.; Magreñán, Á.A.; Regmi, S.; Sarría, Í. New Improvement of the Domain of Parameters for Newton’s Method. Mathematics 2020, 8, 103.

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