Preconditioned SSOR methods for the linear complementarity problem with $M$-matrix

In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an $M$-matrix. Based on the generalized Gunawardena's preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.