Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
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
Three-step iterative methods with optimal eighth-order convergence
Journal of Computational and Applied Mathematics
Approximation of artificial satellites' preliminary orbits: The efficiency challenge
Mathematical and Computer Modelling: An International Journal
Calcolo: a quarterly on numerical analysis and theory of computation
Hi-index | 7.29 |
In this paper, we present two new iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Both methods are obtained by modifying Potra-Ptak's method trying to get optimal order. We prove that the new methods reach orders of convergence four and eight with three and four functional evaluations, respectively. So, Kung and Traub's conjecture Kung and Traub (1974) [2], that establishes for an iterative method based on n evaluations an optimal order p=2^n^-^1 is fulfilled, getting the highest efficiency indices for orders p=4 and p=8, which are 1.587 and 1.682. We also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with Potra-Ptak's method from which they have been derived, and with other recently published eighth-order methods.