Abstract. This article is concerned with numerical solution of nonlinear scalar equations by multi-point iterations. To this end, a general three-step eighth-order class of second derivative-free methods is presented, which is in fact a generalization of the three-point family of methods given by Geum and Kim in [3]. Analysis of convergence is studied and numerical examples are taken into account to support the new results in this paper.

Received: July 22, 2011

AMS Subject Classification: 65H05, 65G20

Key Words and Phrases: multi-point iterations, order, without memory method, efficiency index, optimality

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