Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
The Mathematica Book
Three-step iterative methods with eighth-order convergence 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
Efficient polynomial root-refiners: A survey and new record efficiency estimates
Computers & Mathematics with Applications
Hi-index | 7.29 |
A biparametric family of four-step multipoint iterative methods of order sixteen to numerically solve nonlinear equations are developed and their convergence properties are investigated. The efficiency indices of these methods are all found to be 16^1^/^5~1.741101, being optimally consistent with the conjecture of Kung-Traub. Numerical examples as well as comparison with existing methods developed by Kung-Traub and Neta are demonstrated to confirm the developed theory in this paper.