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On Newton's method and nondiscrete mathematical induction

Published online by Cambridge University Press:  17 April 2009

Ioannis K. Argyros
Ioannis K. Argyros
Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, NM. 88003, United States of America
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Abstract

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The method of nondiscrete mathematical induction is used to find sharp error bounds for Newton's method. We assume only that the operator has Hölder continuous derivatives. In the case when the Fréchet-derivative of the operator satisfies a Lipschitz condition, our results reduce to the ones obtained by Ptak and Potra in 1972.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 131 - 140
Copyright
Copyright © Australian Mathematical Society 1988

References

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