Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Nume...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

An Efficient Derivative Free Iterative Method for Solving Systems of Nonlinear Equations

We present a derivative free method of fourth order convergence for solving systems of nonlinear equations. The method consists of two steps of which first step is the well-known Traub’s method. First-order divided difference operator for functions of several variables and direct computation by Taylor’s expansion are used to prove the local convergence order. Computational efficiency of new met...

Two derivative-free methods for solving underdetermined nonlinear systems of equations

In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line...

A Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...