An efficient modified conjugate gradient parameter for solving the system of symmetric nonlinear equations with application in motion control of coplanar robot

In this article, we proposed a new modified conjugate gradient (CG) parameter via the parallelization of the CG and the quasi-Newton methods. The proposed CG parameter is implemented using the approximate gradient of the underlying function. We further developed an efficient iterative algorithm for solving both the smooth and non-smooth large-scale nonlinear system of symmetric nonlinear equations based on a matrix approximation. Under some assumptions, which include the Jacobian symmetric property, we establish the global convergence of the proposed method. Finally, some numerical results are derived to show the proposed method's efficiency for solving large-scale symmetric nonlinear systems and the method's application to the motion control of a two-joint planar robotic manipulator.