Abstract. In this paper, a new one parameter family of iterative methods with eighth-order of convergence for solving nonlinear equations is presented and analyzed. This new family of iterative methods is obtained by composing an iterative method proposed by Chun [3] with Newton's method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The proposed family is optimal since its efficiency index is 8^1/4 ≈ 1.6818. The convergence analysis of the new family is studied in this paper. Several numerical examples are presented to illustrate the efficiency and accuracy of the family.

Received: July 26, 2011

AMS Subject Classification: 41A25, 65H05

Key Words and Phrases: Newton's method, iterative methods, efficiency index, order of convergence, optimal eighth-order

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