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The Newton Method for Operators with Hölder Continuous First Derivative

Author

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  • M. A. Hernández

    (University of La Rioja)

Abstract

We analyze the convergence of the Newton method when the first Fréchet derivative of the operator involved is Hölder continuous. We calculate also the R-order of convergence and provide some a priori error bounds. Based on this study, we give some results on the existence and uniqueness of the solution for a nonlinear Hammerstein integral equation of the second kind.

Suggested Citation

  • M. A. Hernández, 2001. "The Newton Method for Operators with Hölder Continuous First Derivative," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 631-648, June.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:3:d:10.1023_a:1017571906739
    DOI: 10.1023/A:1017571906739
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    Cited by:

    1. Y. Zhang & H. Sun & D. T. Zhu, 2016. "The Local Convergence Analysis of Inexact Quasi-Gauss–Newton Method Under the Hölder Condition," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 958-970, March.

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