Approximation methods with inertial term for large-scale nonlinear monotone equations

In recent years, systems of nonlinear equations have attracted widespread attention and have been extensively studied. The recent designed Fletcher-Reeves (FR) type methods of Papp and Rapajić [Appl. Math. Comput. 269 (2015) 816–823] [27] are efficient in solving large-scale monotone nonlinear equations due to the simple iterative form. In this paper, we propose an accelerated variant of these FR-type methods for approximating the solutions of nonlinear equations involving monotone and Lipschitz continuous mappings. Under suitable assumptions, we prove that the sequence generated by the new algorithm converges globally. Some numerical results are reported to illustrate the computational performance of the new methods.