Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
Introduction to Interval Analysis
Introduction to Interval Analysis
Journal of Computational Methods in Sciences and Engineering
Mathematica: A Problem-Centered Approach
Mathematica: A Problem-Centered Approach
Revisit of Jarratt method for solving nonlinear equations
Numerical Algorithms
Accurate fourteenth-order methods for solving nonlinear equations
Numerical Algorithms
Optimal Steffensen-type methods with eighth order of convergence
Computers & Mathematics with Applications
Numerical Analysis
| Hi-index | 0.00 |
In this study, the sixteenth-order iterative scheme of Li et al. [X. Li, C. Mu, J. Ma, C. Wang, Sixteenth-order method for nonlinear equations, Appl. Math. Com. 215 2010, 3754--3758] is considered. We increase its efficiency index from 1.587 to 1.644, by reducing the number of evaluations from six to five per iteration. This goal is achieved by providing an approximation for the first-order derivative of the function in the fourth step. Error analysis will also be studied. In the sequel, some numerical instances are given to show the accuracy of the new obtained twelfth-order technique. Therein, another objective of this paper is achieved by proposing a hybrid method for finding all the real solutions of nonlinear equations.