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The Newton Method for Operators with Hölder Continuous First Derivative

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computation, University of La Rioja, Logroño, Spain

    M. A. Hernández (Professor)

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  1. M. A. Hernández
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Hernández, M.A. The Newton Method for Operators with Hölder Continuous First Derivative. Journal of Optimization Theory and Applications 109, 631–648 (2001). https://doi.org/10.1023/A:1017571906739

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  • DOI: https://doi.org/10.1023/A:1017571906739

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