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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria |
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Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov
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Newton's method under different Lipschitz conditions
by
José M. Gutiérrez
Universidad de La Rioja
Coauthors: Miguel A. Hernández (Universidad de La Rioja)
The classical Kantorovich theorem on Newton's method assumes that the
derivative of the operator involved satisfies a Lipschitz condition
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||F'(x)-F'(y)|| <= L ||x-y||. |
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In this communication, we analyse the different modifications of this condition,
with a special emphasis in the center-Lipschitz condition:
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||F'(x)-F'(x0)|| <= w(||x-x0||), |
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being w a positive increasing real function and x0 the starting point for
Newton's iteration.
Date received: January 25, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caeb-11.