Abstract
In this paper, we present a family of eighth order methods for solving nonlinear equations. Formula is composed of three steps, namely; Newton iteration in the first step and weighted-Newton iterations in second and third steps. Hence the name weighted-Newton methods. In terms of computational cost, the family requires three evaluations of function and one of first derivative. Therefore, it is optimal in the sense of Kung–Traub conjecture and has efficiency index 1.682 which is better than that of Newton method of efficiency index 1.414 and many other higher order methods. Numerical examples are considered to support that the method thus obtained is competitive with other similar robust methods. Moreover, basins of attraction are presented to demonstrate the performance in complex plane.
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