Abstract
Many problems in the areas of scientific computing and engineering applications can lead to the solution of the linear complementarity problem LCP ( M , q ) . It is well known that the matrix multisplitting methods have been found very useful for solving LCP ( 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 ) . Convergence results for these two methods are presented when M is an H -matrix (and also an M -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.
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