A multiplicative multisplitting method for solving the linear complementarity problem

The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to the H-compatible splitting and the multiplicative Schwarz method, separately. Finally, we establish the monotone convergence of the multiplicative multisplitting method under appropriate conditions.