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The Newtonian Operator and Global Convergence Balls for Newton’s Method

Author

Listed:
  • José A. Ezquerro

    (Department of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, Spain)

  • Miguel A. Hernández-Verón

    (Department of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, Spain)

Abstract

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

Suggested Citation

  • José A. Ezquerro & Miguel A. Hernández-Verón, 2020. "The Newtonian Operator and Global Convergence Balls for Newton’s Method," Mathematics, MDPI, vol. 8(7), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1074-:d:379399
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    References listed on IDEAS

    as
    1. José Antonio Ezquerro & Miguel Ángel Hernández-Verón, 2019. "How to Obtain Global Convergence Domains via Newton’s Method for Nonlinear Integral Equations," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
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