Robust semi-local convergence analysis for inexact Newton method

  1. Argyros, I.K. 1
  2. Hilout, S. 24
  3. Magreñán, Á.A. 3
  1. 1 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

  2. 2 University of Poitiers
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    University of Poitiers

    Poitiers, Francia

    ROR https://ror.org/04xhy8q59

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  4. 4 University of Quebec at Montreal
    info

    University of Quebec at Montreal

    Montreal, Canadá

    ROR https://ror.org/002rjbv21

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Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2014

Volumen: 227

Páginas: 741-754

Tipo: Artículo

DOI: 10.1016/J.AMC.2013.11.076 SCOPUS: 2-s2.0-84890155139 WoS: WOS:000331496400066 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

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Resumen

We present a more flexible semi-local convergence analysis for inexact Newton with relative residual error tolerance than in earlier studies. A combination of a majorant function and a center-majorant function is used in the convergence analysis. The center-majorant function is used instead of the majorant function to obtain more precise estimates. The advantages of the new approach are under the same computational cost: weaker convergence criteria; more precise error estimates on the distances involved and an at least as precise information on the location of the solution. Special cases and applications are also provided in the study. © 2013 Elsevier Inc. All rights reserved.