Ball convergence for an eighth order efficient method under weak conditions in Banach spaces

Argyros, Ioannis K and George, Santhosh and Erappa, Shobha M (2016) Ball convergence for an eighth order efficient method under weak conditions in Banach spaces. SeMA Journal, 74 (1). pp. 1-9. ISSN 2254-3902

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Official URL: http://link.springer.com/article/10.1007/s40324-01...

Abstract

We present a local convergence analysis of an eighth order- iterative method in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies have used hypotheses up to the fourth derivative although only the first derivative appears in the definition of these methods. In this study we only use the hypothesis on the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Item Type: Article
Uncontrolled Keywords: Newton’s method, Radius of convergence, Local convergence
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 06 Jan 2017 09:48
Last Modified: 06 Jan 2017 09:48
URI: http://eprints.manipal.edu/id/eprint/147912

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