Accelerated Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

In this paper, by applying the accelerated technique and relaxation two-sweep strategy to the modulus-based matrix splitting iteration method, we establish the accelerated relaxation two-sweep modulus-based matrix splitting method. The proposed method contains the accelerated modulus-based matrix splitting and the generalized accelerated modulus-based matrix splitting methods presented recently as special cases. Compared with some existing methods, the proposed method can use more information during each iteration, which may lead to higher computational efficiency. We investigate the convergence properties of the new method, and prove that it is convergent under certain assumptions. Also, for the accelerated relaxation two-sweep modulus-based accelerated overrelaxation method, we analyze the convergence regions of the parameters in detail. Numerical examples are offered to show that the proposed method is efficient and performs better than the generalized accelerated modulus-based matrix splitting one in actual implementation.