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Memory bandwidth is a major limiting factor in the scalability of parallel iterative algorithms that rely on sparse matrix-vector multiplication (SpMV). This paper introduces Hierarchical Diagonal Blocking (HDB), an approach which we believe captures many of the existing optimization techniques for SpMV in a common representation. Using this representation in conjuction with precision-reduction techniques, we develop and evaluate high-performance SpMV kernels. We also study the implications of using our SpMV kernels in a complete iterative solver. Our method of choice is a Combinatorial Multigrid solver that can fully utilize our fastest reduced-precision SpMV kernel without sacrificing the quality of the solution. We provide extensive empirical evaluation of the effectiveness of the approach on a variety of benchmark matrices, demonstrating substantial speedups on all matrices considered.

G. E. Blelloch, G. L. Miller, I. Koutis and K. Tangwongsan, "Hierarchical Diagonal Blocking and Precision Reduction Applied to Combinatorial Multigrid," 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis(SC), New Orleans, LA, 1899, pp. 1-12.
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