Numerical analysis: an introduction
Numerical analysis: an introduction
Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
Some variants of Ostrowski's method with seventh-order convergence
Journal of Computational and Applied Mathematics
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Journal of Computational and Applied Mathematics
A family of three-point methods of optimal order for solving nonlinear equations
Journal of Computational and Applied Mathematics
On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
SIAM Journal on Numerical Analysis
Optimal Steffensen-type methods with eighth order of convergence
Computers & Mathematics with Applications
Regarding the accuracy of optimal eighth-order methods
Mathematical and Computer Modelling: An International Journal
| Hi-index | 7.29 |
In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung and Traub's conjecture [7] for four function evaluations per iteration. Notice that Bi et al.'s method in [2] and [3] are special cases of the developed families of methods. In this study, several new examples of eighth-order methods with efficiency index 1.682 are provided after the development of each family of methods. Numerical comparisons are made with several other existing methods to show the performance of the presented methods.