Modulus-based synchronous multisplitting methods for solving horizontal linear complementarity problems on parallel computers

In this article, we generalize modulus-based synchronous multisplitting methods to horizontal linear complementarity problems. In particular, first we define the methods of our concern and prove their convergence under suitable smoothness assumptions. Particular attention is devoted also to modulus-based multisplitting accelerated overrelaxation methods. Then, as multisplitting methods are well-suited for parallel computations, we analyze the parallel behavior of the proposed procedures. In particular, we do so by solving various test problems by a parallel implementation of our multisplitting methods. In this context, we carry out parallel computations on GPU with CUDA.