Using parfor to Solve System of Linear Equations

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Adam Li 2016-9-22

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https://ww2.mathworks.cn/matlabcentral/answers/304104-using-parfor-to-solve-system-of-linear-equations

评论： Edric Ellis 2016-9-23

I am trying to solve a system of linear equations for N different cases. Let's say N=140. So at each iteration, there is a portion of my code, where I want to do X = A\b;.

However, I am aware to a beginner's level that A\b implements parallelization when the matrices are sufficiently large. Would adding this loop:

parfor i=1:140
    ... % set A and b and other book-keeping stuff
    X = A\b;
end

make things slower? My A matrix is around 500,000 x 7000 and b is 500,000 x 1, so I am pretty sure that A\b already uses parallelization, but I want to see if there is anyway to improve the operating speed of this overall computation.

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Edric Ellis 2016-9-23

It is almost certain that using parfor will actually make this slower - assuming you have access only to the 'local' cluster type. That's because as you observe, A\b is already implicitly multithreaded by MATLAB. The workers run in single-computational-thread mode, so even disregarding data transfer overheads, they can't perform faster than the multi-threaded client. The data transfer overheads will simply serve to slow things down. (If you have access to a remote cluster, the situation is different because there you'll have the opportunity to use more computational resources).

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