On multipoint iterative processes of efficiency index higher than Newton's method

Volume 2, Issue 3, pp 195--203 http://dx.doi.org/10.22436/jnsa.002.03.08

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Authors

Ioannis K. Argyros - Cameron university, Department of Mathematics Sciences, Lawton, OK 73505, USA.. Saïd Hilout - Poitiers university, Laboratoire de Math´ematiques et Applications, Bd. Pierre et Marie Curie, T´el´eport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France..

Abstract

We provided a convergence analysis of third–order multipoint iterative processes of efficiency index higher than Newton’s. Our convergence analysis is finer than the corresponding one in [8], under the same or weaker hypotheses and computational cost.

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Keywords

• Banach space
• Multipoint iterative procedure
• Newton–type method
• Majorizing sequences

MSC

•  65H10
•  65H05
•  47H99
•  49M15

References

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• [2] I. K. Argyros , On the Newton–Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. , 169 (2004), 315–332.


• [3] I. K. Argyros, A unifying local–semilocal convergence analysis and applications for two– point Newton–like methods in Banach space, J. Math. Anal. Appl. , 298 (2004), 374–397.


• [4] I. K. Argyros, Approximating solutions of equations using Newton’s method with a modified Newton’s method iterate as a starting point , Revue d’Analyse Numér. Th. Approx. , 36 (2007), 123–137.


• [5] I. K. Argyros, Approximating solutions of equations by combining Newton–like methods , J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. , 15 (2008), 35–45.


• [6] I. K. Argyros, Convergence and Applications of Newton–type iterations, Springer–Verlag Publ., New York (2008)


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• [8] J. A. Ezquerro, M. A. Hernández, An optimization of Chebyshev’s method, J. Complexity, (in press.),


• [9] L. V. Kantorovich, G. P. Akilov , Functional analysis in normed spaces, Pergamon Press, Oxford (1982)


• [10] S. Weerakoon, T. G. I. Fernando, A variant of Newton’s method with accelerated third–order convergence, Appl. Math. Lett., 13 (2000), 87–93.