Three-step iterative methods with optimal eighth-order convergence |
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| Authors: | Alicia Cordero María P Vassileva |
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| Institution: | a Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022, Valencia, Spainb Instituto Tecnológico de Santo Domingo (INTEC), Avda. Los Próceres, Gala, Santo Domingo, République dominicaine |
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| Abstract: | In this paper, based on Ostrowski’s method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub’s conjecture. Numerical comparisons are made to show the performance of the new family. |
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| Keywords: | Nonlinear equations Iterative methods Convergence order Efficiency index Ostrowski&rsquo s method Optimal order |
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