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Iterative GPGPU Linear Solvers for Sparse Matrices

Filip Vesely
Faculty of Electrical Engineering, Czech technical University in Prague
Faculty of Electrical Engineering, Czech technical University in Prague, 2008

@article{vesely2008iterative,

   title={Iterative GPGPU Linear Solvers for Sparse Matrices},

   author={Vesel{‘y}, B.F.},

   year={2008}

}

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The performance and the level of programmability of graphics processors (GPU) on current video cards offer new capabilities beyond the graphics applications for which they were designed. These are general-purpose computations which expose parallelism. In this thesis, I describe the iterative methods for solving sparse linear systems: the Jacobi, Gauss-Seidel, Conjugate Gradient and BiConjugate Gradient method. I explain the architecture of the GPU, their capability of the general-purpose computations and current software platforms which provide an abstraction to the GPU programming: the BrookGPU and RapidMind Multi-core platform. I discuss the iterative methods in the GPU programming environment and describe the implementation for both platforms. Then I made a performance tests between the sequential algorithms and the algorithms for Brook and Rapidmind. The results of my experiments show that the GPU is better suited for the computation with larger problem dimensions. For the iterative methods, the optimal problem size ~ 10^6 was observed, where most significant speedup compared to the sequential implementation was reached. Namely 3x speedup for Brook and 1.5x speedup for Rapidmind. Larger instances (10^7+) encountered a limitation of the graphics API. Brook has been found as faster platform than Rapidmind due to the necessary workarounds in Rapidmind implementation. The general Gauss-Seidel method has been found as not suitable for processing on the GPUs.
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