Two class of synchronous matrix multisplitting schemes for solving linear complementarity problems

Many problems in the areas of scientific computing and engineering applications can lead to the solution of the linear complementarity problem LCP (M,q)(M,q). It is well known that the matrix multisplitting methods have been found very useful for solving LCP (M,q)(M,q). In this article, by applying the generalized accelerated overrelaxation (GAOR) and the symmetric successive overrelaxation (SSOR) techniques, we introduce two class of synchronous matrix multisplitting methods to solve LCP (M,q)(M,q). Convergence results for these two methods are presented when MM is an HH-matrix (and also an MM-matrix). Also the monotone convergence of the new methods is established. Finally, the numerical results show that the introduced methods are effective for solving the large and sparse linear complementary problems.