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
On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
SIAM Journal on Numerical Analysis
Three-step iterative methods with optimal eighth-order convergence
Journal of Computational and Applied Mathematics
On generalized multipoint root-solvers with memory
Journal of Computational and Applied Mathematics
MULTIPOINT METHODS FOR SOLVING NONLINEAR EQUATIONS
MULTIPOINT METHODS FOR SOLVING NONLINEAR EQUATIONS
On efficient two-parameter methods for solving nonlinear equations
Numerical Algorithms
Hi-index | 7.29 |
A general family of biparametric n-point methods with memory for solving nonlinear equations is proposed using an original accelerating procedure with two parameters. This family is based on derivative free classes of n-point methods without memory of interpolatory type and Steffensen-like method with two free parameters. The convergence rate of the presented family is considerably increased by self-accelerating parameters which are calculated in each iteration using information from the current and previous iteration and Newton's interpolating polynomials with divided differences. The improvement of convergence order is achieved without any additional function evaluations so that the proposed family has a high computational efficiency. Numerical examples are included to confirm theoretical results and demonstrate convergence behavior of the proposed methods.