@Article{Soleymani2013,
author = "Soleymani, Fazlollah",
title = "Some efficient seventh-order derivative-free families in root-finding",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "1",
pages = "163--173",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.1.163",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.1.163",
abstract = "The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.",
keywords = "numerical analysis, derivative-free families, order, iterative methods",
issn = "1232-9274"
}