文章基本信息

标题：A family of optimal iterative methods with fifth and tenth 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：2012
卷号：2012
DOI：10.5899/2012/jiasc-00012
出版社：ISPACS GmbH
摘要：In this paper, we propose a two-step method with fifth-order convergence and a family of optimal three-step method with tenth-order convergence for finding the simple roots of nonlinear equations. The optimal efficiency indices are all found to be $5^{\frac{1}{3}}\approx1.71$ and $10^{\frac{1}{4}}\approx1.78.$ Some numerical examples illustrate that the algorithms are more efficient and performs better than other methods.
关键词：Nonlinear equation; Iterative method; Three-step; Convergence order; Efficiency index