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Extended local convergence for some inexact methods with applications

Abstract

We present local convergence results for inexact iterative procedures of high convergence order in a normed space in order to approximate a locally unique solution. The hypotheses involve only Lipschitz conditions on the first Fréchet-derivative of the operator involved. Earlier results involve Lipschitz-type hypotheses on higher than the first Fréchet-derivative. The applicability of these methods is extended this way and under less computational cost. Special cases and applications are provided to show that these new results can apply to solve these equations.

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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 3 [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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Correspondence to Juan Antonio Sicilia.

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Argyros, I.K., Legaz, M.J., Magreñán, Á.A. et al. Extended local convergence for some inexact methods with applications. J Math Chem 57, 1508–1523 (2019). https://doi.org/10.1007/s10910-019-01004-5

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Keywords

  • Normed space
  • Local convergence
  • Inexact Newton-like methods
  • Fréchet derivative

Mathematics Subject Classification

  • 65D10
  • 65D99