Abstract
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.
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Acknowledgements
This research was supported by Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Plan Propio de Investigación, Desarrollo e Innovación [2015–2017]. Research group: Modelación matemática aplicada a la ingeniería (MOMAIN), by the the grant SENECA 19374/PI/14 and by Ministerio de Ciencia y Tecnología MTM2014-52016-C2-\(\{01\}\)-P.
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This is one of several papers published together in Journal of Mathematical Chemistry on the “Special Issue: CMMSE”.
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Magreñán, Á.A., Argyros, I.K. & Sicilia, J.A. New improved convergence analysis for Newton-like methods with applications. J Math Chem 55, 1505–1520 (2017). https://doi.org/10.1007/s10910-016-0727-3
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DOI: https://doi.org/10.1007/s10910-016-0727-3
Keywords
- Newton-type method
- Banach space
- Majorizing sequence
- Restricted domains
- Local convergence
- Semilocal convergence