In this paper, we establish a preconditioned modulus-based iteration method for solving linear complementarity problems with the system matrix being an -matrix. The convergence analysis of the proposed method is given. In particular, we propose a class of special nondiagonal preconditioners with some parameters for the new method, and then give the convergence domain. Numerical examples show that the proposed method is efficient.

In this paper, the convergence conditions of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear complementarity problems of H-matrices are weakened. The convergence domain given by the proposed theorems is larger than the existing ones.