A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations
From MaRDI portal
Publication:2228726
DOI10.1016/j.matcom.2015.08.011OpenAlexW2197860359MaRDI QIDQ2228726
Somayeh Sharifi, Taher Lotfi, Mehdi Salimi, Stefan Siegmund
Publication date: 19 February 2021
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.2633
computational efficiencyoptimal order of convergencesimple rootKung and Traub conjecturefour-step iterative method
Related Items (20)
A reliable algorithm to check the accuracy of iterative schemes for solving nonlinear equations: an application of the CESTAC method ⋮ Optimal Newton–Secant like methods without memory for solving nonlinear equations with its dynamics ⋮ New modification of Maheshwari's method with optimal eighth order convergence for solving nonlinear equations ⋮ Bifurcation and chaos in real dynamics of a two-parameter family arising from generating function of generalized Apostol-type polynomials ⋮ An efficient class of optimal sixteenth-order root-finding methods and their basins of attraction ⋮ An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics ⋮ A new family of adaptive methods with memory for solving nonlinear equations ⋮ Computing multiple zeros by using a parameter in Newton-secant method ⋮ Developing a new family of Newton-Secant method with memory based on a weight function ⋮ On general families of multipoint iterations by inverse interpolation and their applications ⋮ Chaotic behaviour and bifurcation in real dynamics of two-parameter family of functions including logarithmic map ⋮ Unnamed Item ⋮ A multi-point iterative method for solving nonlinear equations with optimal order of convergence ⋮ Fast switch and spline scheme for accurate inversion of nonlinear functions: the new first choice solution to Kepler's equation ⋮ Two improved classes of Broyden's methods for solving nonlinear systems of equations ⋮ Efficacy of optimal methods for nonlinear equations with chemical engineering applications ⋮ Some real-life applications of a newly constructed derivative free iterative scheme ⋮ Review of some iterative methods for solving nonlinear equations with multiple zeros ⋮ Unnamed Item ⋮ Sixteenth-order optimal iterative scheme based on inverse interpolatory rational function for nonlinear equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Basin attractors for various methods
- Basin attractors for various methods for multiple roots
- Basins of attraction for several methods to find simple roots of nonlinear equations
- On a 4-point sixteenth-order King family of iterative methods for solving nonlinear equations
- Algorithm for forming derivative-free optimal methods
- Multipoint methods for solving nonlinear equations: a survey
- A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index
- A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function
- A new optimal eighth-order family of iterative methods for the solution of nonlinear equations
- A fourth order iterative method for solving nonlinear equations
- Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
- Dynamics of the King and Jarratt iterations
- Dynamics of a family of third-order iterative methods that do not require using second derivatives
- Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior
- Basins of attraction for Zhou-Chen-song fourth order family of methods for multiple roots
- Basins of attraction for several optimal fourth order methods for multiple roots
- Two optimal general classes of iterative methods with eighth-order
- A new class of three-point methods with optimal convergence order eight and its dynamics
- Multipoint iterative methods for finding all the simple zeros in an interval
- Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations
- A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function
- A note on the priority of optimal multipoint methods for solving nonlinear equations
- Mathematica®: A Problem-Centered Approach
- On a family of multipoint methods for non-linear equations
- Optimal Order of One-Point and Multipoint Iteration
- Some Fourth Order Multipoint Iterative Methods for Solving Equations
- A Family of Fourth Order Methods for Nonlinear Equations
- A variant of Newton's method with accelerated third-order convergence
- A new family of modified Ostrowski's methods with accelerated eighth order convergence
This page was built for publication: A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations