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On Newton’s Method for Solving Nonlinear Equations and Function Splitting

Published online by Cambridge University Press:  28 May 2015

Ioannis K. Argyros  and
Saïd Hilout
Ioannis K. Argyros
Affiliation:
Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA
Saïd Hilout
Affiliation:
Université de Poitiers, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France
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Abstract

We provided in [14] and [15] a semilocal convergence analysis for Newton’s method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

Keywords

65H9965H1065G9949M1547J2047H0490C3090C33Newton’s methodBanach spacemajorizing sequencesemilocal convergencesplitting of an operator
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 1 , February 2011 , pp. 53 - 67
Copyright
Copyright © Global Science Press Limited 2011

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References

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