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
New eighth-order iterative methods for solving nonlinear equations
Journal of Computational and Applied Mathematics
New modifications of Potra-Pták's method with optimal fourth and eighth orders of convergence
Journal of Computational and Applied Mathematics
Regarding the accuracy of optimal eighth-order methods
Mathematical and Computer Modelling: An International Journal
Calcolo: a quarterly on numerical analysis and theory of computation
Calcolo: a quarterly on numerical analysis and theory of computation
Hi-index | 7.29 |
A family of three-point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters. It is proved that these methods have the convergence order eight requiring only four function evaluations per iteration. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis (1974) [3] on the upper bound 2^n of the order of multipoint methods based on n+1 function evaluations. Consequently, this class of root solvers possesses very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations.