Nonmonotone backtracking inexact quasi-Newton algorithms for solving smooth nonlinear equations

A family of inexact quasi-Newton algorithms in association with nonmonotone backtracking line search technique is proposed for solving smooth nonlinear equations. Global convergence of the proposed algorithms are established under the reasonable conditions. We characterize the order of local convergence based on convergence behaviour of the approximate matrix of the Jacobian and indicate how to choose an inexact forcing sequence which preserves the rapid convergence of the proposed algorithms.