A Derivative-Free Liu–Storey Method for Solving Large-Scale Nonlinear Systems of Equations

A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...

A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations

We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the pr...

New Efficient Optimal Derivative-Free Method for Solving Nonlinear Equations

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...

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...

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