A Fast GPU Implementation for Solving Sparse Ill-Posed Linear Equation Systems

Florian Stock, Andreas Koch
Embedded Systems and Applications Group, Technische Universitat Darmstadt
Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, 2010, Volume 6067/2010, 457-466


   title={A fast GPU implementation for solving sparse ill-posed linear equation systems},

   author={Stock, F. and Koch, A.},

   journal={Parallel Processing and Applied Mathematics},





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Image reconstruction, a very compute-intense process in general, can often be reduced to large linear equation systems represented as sparse under-determined matrices. Solvers for these equation systems (not restricted to image reconstruction) spend most of their time in sparse matrix-vector multiplications (SpMV). In this paper we will present a GPU-accelerated scheme for a Conjugate Gradient (CG) solver, with focus on the SpMV. We will discuss and quantify the optimizations employed to achieve a soft-real time constraint as well as alternative solutions relying on FPGAs, the Cell Broadband Engine, a highly optimized SSE-based software implementation, and other GPU SpMV implementations.
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