A multiplicative Schwarz iteration scheme for solving the linear complementarity problem with an H-matrix

In this paper, we consider an algebraic multiplicative Schwarz iteration scheme for solving the linear complementarity problem that involves an H+-matrix. We show that the sequence generated by the multiplicative Schwarz iteration scheme converges to the unique solution of the problem without any restriction on the initial point. For different overlapping sizes, the convergence rate of the proposed method is analyzed in an algebraic setting. Moreover, we establish monotone convergence of the proposed method under appropriate conditions. Numerical results show that efficiency can be achieved by the multiplicative Schwarz iteration scheme.