<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method"^^ . "Starting by King's method, we propose a modified families of fourth- and eighth-order of convergence iterative methods for nonlinear equations. The fourth-order method requires at each iteration three function evaluations, while the eighth-order methods both need four function evaluations. The proposed methods are derivative-free. Based on the conjecture of Kung and Traub, the new methods attain the optimality with efficiency index 1.587 for the fourth-order method and 1.68 for the eighth-order methods. The convergence analyses of the methods are given, and comparisons with some well-known schemes having identical order of convergence demonstrate the efficiency of the present techniques. © 2018 The Authors"^^ . "2019" . . "31" . "4" . . "Elsevier B.V."^^ . . . "Journal of King Saud University - Science"^^ . . . "10183647" . . . . . . . . . . . . . "I."^^ . "Hashim"^^ . "I. Hashim"^^ . . "S.A."^^ . "Abdul Karim"^^ . "S.A. Abdul Karim"^^ . . "O."^^ . "Said Solaiman"^^ . "O. Said Solaiman"^^ . . . . . "HTML Summary of #11301 \n\nOptimal fourth- and eighth-order of convergence derivative-free modifications of King's method\n\n" . "text/html" . .