Dense Matrix Algorithms -- Chapter 8 Introduction
Dense Matrix Algorithms -- Chapter 8 Introduction
Dense Matrix Algorithms -- Chapter 8 Introduction
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3<br />
Fewer Than n Processors<br />
• Suppose the number of processors p < n<br />
• Place n/p rows per processor of both A and x<br />
• An all-to-all broadcast distributed n/p elements of x<br />
• Each processor computes n/p elements of y<br />
• No further distribution of y is needed<br />
• The broadcast takes: t s log p + t w (n/p)(p–1) ≈ t s log p + t w n<br />
• The computation per processor is: (n/p)n = n 2 /p<br />
• The total parallel runtime T P is: n 2 /p + t s log p + t w n<br />
• The cost is: n 2 + t s p log p + t w np = Θ(n 2 )<br />
• The work W = n 2<br />
• The algorithm is cost-optimal, provided p = O(n)<br />
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Diagram Of The Computational And<br />
Communication Process For 1-D Row<br />
Partition <strong>Matrix</strong>-Vector Multiplication<br />
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