There are many methods for solving nonlinear algebraic equations. Some of these methods are just rediscovered old ones. In this note we show that the modified super Halley scheme is the same as one of Jarratt’s methods. Published by Elsevier Inc.

A binomial sampling method for the potato aphid, Macrosiphum euphorbiae (Thomas), on processing tomato plants, Lycopersicon esculentum (Mill), is proposed. Relationships between mean number of M. euphorbiae per leaf and proportion of leaves infested [P(I)] with M. euphorbiae for both upper and interior leaves of the processing tomato varieties 'Alta' and 'Halley' are presented. A split-plot des...

In this article, we have combined two well known third order methods one is Chebyshev and another Super- Halley to form an iterative method of for solving polynomial equations with multiple zeros. This constructed basically the mean Super-Halley, so name as C-S Combined Mean Method. We proposed some local convergence theorems Method establish computation a For establishment theorem, key role pe...

In this paper, we propose a new cubically convergent family of superHalley method based on power means. Some well-known methods can be regarded as particular cases of the proposed family. New classes of higher (third and fourth) order multipoint iterative methods free from second order derivative are derived by semi-discrete modifications of above-mentioned methods. It is shown that super-Halle...

The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...

We present a unified local convergence analysis for Chebyshev-Halleytype methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Chebyshev; Halley; super-Halley and other high order methods. The convergence ball and error estimates are given for these methods under the same conditions. Numerical examples are also provided in this stu...