A general preconditioner for linear complementarity problem with an M-matrix

In this paper, we first present a general preconditioner P for solving linear complementarity problem (LCP) associated with an M-matrix A and a vector f, and prove that the LCP(A,f) is equivalent to the LCP(PA,Pf). Then based on this general preconditioner P, two preconditioned SSOR methods for solving the linear complementarity problems are proposed. We show that this general preconditioner P accelerates the convergence of two SSOR methods under the assumption that PA is a Z-matrix. In addition, we also give a practically concrete choice for the preconditioner P satisfying aforementioned assumption. Numerical examples are used to illustrate the theoretical results obtained.