The double-relaxation modulus-based matrix splitting iteration method for linear complementarity problems

Abstract

For the large sparse linear complementarity problems (LCP), by adopting the relaxation and relaxation two-sweep techniques for the modulus-based matrix splitting (MMS) iteration method, we establish a double-relaxation two-sweep modulus-based matrix splitting (DRTMMS) iteration method. This new method contains some known ones developed recently. Some sufficient conditions for guaranteeing the convergence of the DRTMMS method are presented when the system matrices are positive definite matrices and H+-matrices, which generalize some existing results. And the parameter selection strategy of the DRTMMS iteration method is given. Besides, the convergence analyses of the DRTM accelerated overrelaxation (DRTMAOR) method are given. Finally, numerical experiments illustrate that the DRTMMS method is efficient and has better performance than several existing MMS-like methods, and outperforms the projected splitting methods in some cases.