Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Xianming Kong and Liang Fang
Pages: [71] - [78]
Received Date: November 26, 2010
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Ujević et al. introduced a family of methods for solving nonlinear equations in [7]. For certain choices of parameters, firstly, they showed that the classical Newton’s method is a member of this family and their methods are better than classical Newton’s method. Then they introduced a particular method. However, in most cases, their efficiency is worse than classical Newton’s method. This is the main aim of this paper. We also point out some flaws in the results of Ujević et al.. Based on this, we present a further results about the Algorithm 3 and obtain a family of cubically convergent methods, whose efficiency index is equal to 1.44225, which is better than that of Newton’s method 1.414. Several examples demonstrate the efficiency and performance of some family members in the presented family and their comparison with some other methods.
nonlinear equations, Newton’s method, iterative method, order of convergence.
