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Analysis of semilocal convergence for ameliorated super-Halley methods with less computation for inversion

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  01 October 2016

Xiuhua Wang  and
Jisheng Kou
Xiuhua Wang
Affiliation:
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China email wangxiuhua163email@163.com
Jisheng Kou
Affiliation:
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China email jishengkou@163.com

Abstract

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In this paper, the semilocal convergence for ameliorated super-Halley methods in Banach spaces is considered. Different from the results in [J. M. Gutiérrez and M. A. Hernández, Comput. Math. Appl. 36 (1998) 1–8], these ameliorated methods do not need to compute a second derivative, the computation for inversion is reduced and the $R$-order is also heightened. Under a weaker condition, an existence–uniqueness theorem for the solution is proved.

MSC classification

Primary: 65D10: Smoothing, curve fitting 65D99: None of the above, but in this section
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 293 - 302
Copyright
© The Author(s) 2016 

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