Derivative-free optimal multiple-root finding family of iterative methods

A new family of iterative methods for finding multiple roots of nonlinear problems is proposed. The family is derivative-free and optimal in the sense of Kung–Traub’s conjecture. The two-step family includes a weight function. The stability analysis uses two different weight functions: a polynomial and a rational function. Furthermore, a numerical benchmark is carried out on these two weight functions, showing the competitiveness concerning similar methods in the literature.