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Recently a family of promising face recognition algorithms based on sparse representation and l1-minimization (l1-min) have been developed. These algorithms have not yet seen commercial application, largely due to higher computational cost compared to other traditional algorithms. This paper studies techniques for leveraging the massive parallelism available in GPU and CPU hardware to accelerate l1-min based on augmented Lagrangian method (ALM) solvers. For very large problems, the GPU is faster due to higher memory bandwidth, while for problems that fit in the larger CPU L3 cache, the CPU is faster. On both architectures, the proposed implementations significantly outperform naive library-based implementations, as well as previous systems. The source code of the algorithms will be made available for peer evaluation.