  We introduce a new class of optimal iterative methods without memory for
approximating a simple root of a given nonlinear equation. The proposed class
uses four function evaluations and one first derivative evaluation per
iteration and it is therefore optimal in the sense of Kung and Traub's
conjecture. We present the construction, convergence analysis and numerical
implementations, as well as comparisons of accuracy and basins of attraction
between our method and existing optimal methods for several test problems.
