We address the Desynchronization problem of achieving an equally spaced transmission schedule in a cooperative fashion. This problem arises in a shared medium communication and is of importance to achieve a fair multiple access schedule at the Medium Access Control (MAC) layer in the context of Wireless Sensor Networks (WSNs). In this paper, we investigate the convergence rate of different optimization algorithms and the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that the Gauss-Seidel method can yield a faster convergence than previously proposed methods that employ a version of the Nesterov's method. Our approach also poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Through simulations, we provide evidence to support future research on optimizing the parameter selection and also on categorizing the conditions under which one solution might be better in detriment of another.