A Family of Iterative Methods with Accelerated Eighth-Order Convergence

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...

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

Three-step iterative methods with eighth-order convergence for solving nonlinear equations

A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency i...

Family of Optimal Eighth-Order of Convergence for Solving Nonlinear Equations

In this paper, a new family of optimal eighth-order iterative methods are presented. The new family is developed by combining Traub-Ostrowski’s fourth-order method adding Newton’s method as a third step and using the forward divided difference and three real-valued functions in the third step to reduce the number of function evaluations. We employed several numerical comparisons to demonstrate ...

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...