Hierarchical blocking and data flow analysis for numerical linear algebra

The optimization of BLAS2 and BLAS3 for linear algebra on computers with hierarchical memory systems is discussed. A novel blocking strategy called hierarchical blocking and data-flow analysis is proposed, and its applications are given. Numerical results on IBM RISC System/6000 Model 530 are given. It is shown that data flow direction and leading dimensions are crucial factors in optimizing linear algebra programs. Since the proposed method follows the data flow of a program, it can reveal the effect of pipelining between data loading units and computational units.<
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