We derive a family of eighth-order multipoint methods for the solution of nonlinear equations. In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration. This implies that the efficiency index of the present methods is 1.682. Kung and Traub (1974) conjectured that multipoint iteration methods without memory based on n evaluations have optimal order2n-1. Thus, the family agrees with Kung-Traub conjecture for the casen=4. Computational results demonstrate that the developed methods are efficient and robust as compared with many well-known methods.
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