In this paper, based on King's methods, a new family of eighth-order methods for solving nonlinear equations is derived. This family of methods includes method given in [9] as a particular case. The optimal choice of the iteration parameter allows us to accelerate and improve the convergence of iterations. At each iteration of these methods requires three evaluation of the function and one evaluation of its first derivative, which has optimal efficiency index 1.682, according to Kung and Traube's conjecture. Numerical comparisons are made to show the performance of the presented methods.
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