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Measuring Gauss-Seidel loop-carried dependency and fixing it via loop unrolling

Photo: Hacker News

What happened

Last time, we explored the Gauss-Seidel method. We arrived at the following conclusion: the math says Gauss-Seidel takes half as many iterations to converge, and this is backed up by our numerical test case. Yet, despite requiring only half the number of iterations, the Gauss-Seidel solver takes 4 to 5 times as long as the Jacobi one. A seemingly puzzling fact if you think about it: how can a method which is better…

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