Efficient matrix-free direction method with line search for solving large scale systems of nonlinear equations

Abstract

A matrix-free direction method in association with inexact line search technique, is presented for solving systems of nonlinear equations, by means of double
direction approach. In this article, we approximated the Jacobian matrix by appropriately constructed matrix-free method via acceleration parameter. The global
convergence of our method is established under mild conditions. Numerical comparisons reported in this paper using a set of large scale test problems show that
the proposed method is efficient for large-scale problems.