Opuscula Math. 33, no. 1 (2013), 163-173

Opuscula Mathematica

Some efficient seventh-order derivative-free families in root-finding

Fazlollah Soleymani

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.

Mathematics Subject Classification: 65H05.

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  • Fazlollah Soleymani
  • Islamic Azad University, Department of Mathematics, Zahedan Branch, Zahedan, Iran
  • Received: 2012-03-06.
  • Revised: 2012-06-01.
  • Accepted: 2012-06-14.
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Cite this article as:
Fazlollah Soleymani, Some efficient seventh-order derivative-free families in root-finding, Opuscula Math. 33, no. 1 (2013), 163-173, http://dx.doi.org/10.7494/OpMath.2013.33.1.163

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