An accelerated derivative-free method for solving large-scale nonlinear non-monotone equations

Based on the Picard-Mann hybrid process, in this paper we propose an accelerated derivative-free method for solving large-scale nonlinear non-monotone equations, which can be regarded as a modification of the spectral gradient method containing the acceleration and correction parameters. Under the reasonable assumptions, its search direction satisfies the sufficient descent property without any line search. Moreover, it is proved to be globally convergence for nonlinear non-monotone equations. The preliminary numerical results show that it is effective and robust by comparing with the current method.