The Newton Method for Operators with Hölder Continuous First Derivative

M. A. Hernández
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M. A. Hernández: University of La Rioja

Journal of Optimization Theory and Applications, 2001, vol. 109, issue 3, No 9, 648 pages

Abstract: 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.

Keywords: nonlinear equations in Banach spaces; Newton method; semilocal convergence theorem; recurrence relations; a priori error bounds; Hammerstein integral equation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017571906739

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