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Journal of Mathematical Chemistry

, Volume 55, Issue 7, pp 1505–1520 | Cite as

New improved convergence analysis for Newton-like methods with applications

  • Á. Alberto Magreñán
  • Ioannis K. Argyros
  • Juan Antonio Sicilia
Original Paper

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.

Keywords

Newton-type method Banach space Majorizing sequence Restricted domains Local convergence Semilocal convergence 

Mathematics Subject Classification

65H10 65G99 65B05 65N30 47J25 47J05 

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Á. Alberto Magreñán
    • 1
  • Ioannis K. Argyros
    • 2
  • Juan Antonio Sicilia
    • 1
  1. 1.Universidad Internacional de La Rioja (UNIR)LogroñoSpain
  2. 2.Department of Mathematics Sciences LawtonCameron UniversityLawtonUSA

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