文章基本信息

标题：Three-step iterative methods with eighth-order convergence for solving nonlinear equations
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作者：M. Matinfar ; M. Aminzadeh
期刊名称：Journal of Interpolation and Approximation in Scientific Computing
印刷版ISSN：2194-3907
电子版ISSN：2194-3907
出版年度：2013
卷号：2013
DOI：10.5899/2013/jiasc-00013
出版社：ISPACS GmbH
摘要：A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.
关键词：Nonlinear equation; Iterative method; Three-step; Convergence order; Efficiency index