Efficient optimal families of higher-order iterative methods with local convergence

Three-step iterative methods with optimal eighth-order convergence

In this paper, based on Ostrowski’s method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub’s conjecture. Numerical comparis...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

The iterative methods with higher order convergence for solving a system of nonlinear equations

In this paper, two variants of iterative methods with higher order convergence are developed in order to solve a system of nonlinear equations. It is proved that these two new methods have cubic convergence. Some numerical examples are given to show the efficiency and the performance of the new iterative methods, which confirm the good theoretical properties of the approach. c ©2017 All rights ...

Rate of convergence of higher order methods

Article history: Available online 30 July 2011