Local convergence of a novel eighth order method under hypotheses only on the first derivative

Argyros, Ioannis K and George, Santhosh and Erappa, Shobha M (2019) Local convergence of a novel eighth order method under hypotheses only on the first derivative. Khayyam Journal of Mathematics, 5 (2). pp. 96-107. ISSN 2423-4788

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Abstract

We expand the applicability of eighth order-iterative method studied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. 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: Eighth order of convergence, ball convergence, Banach space, Frechet-derivative.
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 29 Jun 2019 05:45
Last Modified: 29 Jun 2019 05:45
URI: http://eprints.manipal.edu/id/eprint/154056

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