Based on Newton’s method and interpolation method, we establish two
iterative methods for solving the nonlinear equations by using n+1
evaluations of the function(or the first derivative) per iteration.
Analysis of convergence shows that our methods arrive at the optimal
order of convergence 2^n, where the n is any a nature number. This
work also proves the conjecture of Kung-Traub (J.ACM643-651,1974) for
constructing multipoint optimal iterations.