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Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index

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  • F. Soleymani

Abstract

Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation ð ‘“ ( ð ‘¥ ) = 0 . New techniques can be taken into account as the generalizations of the one-step method of Steffensen. Theoretical proofs of the main theorems are furnished to reveal the eighth-order convergence. Per computing step, the derived methods require only four function evaluations. Experimental results are also given to add more supports on the underlying theory of this paper as well as lead us to draw a conclusion on the efficiency of the developed classes.

Suggested Citation

  • F. Soleymani, 2012. "Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, September.
    • Handle: RePEc:hin:jijmms:932420
    DOI: 10.1155/2012/932420
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    References listed on IDEAS

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    1. F. Soleymani & S. Karimi Vanani & M. Jamali Paghaleh, 2012. "A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, February.
    2. Fazlollah Soleymani & Mahdi Sharifi & Bibi Somayeh Mousavi, 2012. "An Improvement of Ostrowski’s and King’s Techniques with Optimal Convergence Order Eight," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 225-236, April.
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