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.

中文翻译：

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解决并行计算机上水平线性互补问题的基于模的同步多重分裂方法

在本文中，我们将基于模数的同步多重分裂方法推广到水平线性互补问题。特别是，首先，我们定义我们关注的方法，并在适当的平滑度假设下证明它们的收敛性。还特别注意基于模量的多分裂加速过松弛方法。然后，由于多重拆分方法非常适合并行计算，因此我们分析了所提出程序的并行行为。尤其是，我们通过并行实现多重分裂方法来解决各种测试问题，从而做到了这一点。在这种情况下，我们使用CUDA在GPU上执行并行计算。