An accelerated derivative-free method using Picard-Krasnoselskii iterative process with applications in motion control

This paper introduces an efficient method that hybridizes an accelerated derivative-free approach with the Picard-Krasnoselskii iterative process to solve systems of nonlinear equations. The proposed method integrates a correction parameter into the search direction using the hybrid of the Picard-Krasnoselskii approach and approximates the Jacobian matrix with an acceleration parameter. We establish the global convergence of the method under favourable conditions. Numerical experiments demonstrate the proposed method's superior performance compared to existing techniques. Additionally, the method has been effectively applied to the three-degree-of-freedom (3DOF) model of robotic motion control, showcasing its practical applicability in science and engineering.