On improved Steffensen type methods with optimal eighth-order of convergence Kansal Munish*, Kanwar V.**, Bhatia Saurabh*** University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India *E-mail: mkmaths23@pu.ac.in
**vmithil@yahoo.co.in
***s_bhatia@pu.ac.in
Mathematics Subject Classification (2000): 65H05, 65B99 Abstract This paper presents an improvement of the existing eighth-order derivative involved method [14] into derivative-free scheme, holding the order of convergence of the original method. Each member of the family requires only four function evaluations per iteration to achieve the eighth-order of convergence, while they are totally free from derivative evaluation. Hence, they agree with the optimality conjecture of Kung-Traub for providing multipoint iterations without memory. The proposed methods are compared with their closest competitors in a series of numerical experiments. Numerical experiments show that such derivative-free, high order schemes offer significant advantages over the derivative involved methods. Top Keywords Nonlinear equations, Steffensen's method, King's method, Ostrowski's method, Efiiciency index, Optimal order of convergence. Top |