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In this paper, the authors analyze the potential of asynchronous relaxation methods on Graphics Processing Units (GPUs). They develop asynchronous iteration algorithms in CUDA and compare them with parallel implementations of synchronous relaxation methods on CPU- or GPU-based systems. For a set of test matrices from UFMC they investigate convergence behavior, performance and tolerance to hardware failure. They observe that even for their most basic asynchronous relaxation scheme, the method can efficiently leverage the GPUs computing power and is, despite its lower convergence rate compared to the Gauss-Seidel relaxation, still able to provide solution approximations of certain accuracy in considerably shorter time than Gauss-Seidel running on CPUs or GPU-based Jacobi.
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