What is the best know algorithm for solving a large sparse system of linear equations? The system I'm working on is not symmetric, not positive definite and integer. The only benefit is being sparse. I also need to point out that the matrix is not square. The dimension is $m\times n$ and it is not generally either underestimate or overestimate.
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$\begingroup$ This question is under defined: the "best method" depends on the sparsity structure... $\endgroup$– Igor RivinCommented Jul 12, 2012 at 8:11
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2$\begingroup$ I suggest asking on scicomp.stackexchange.com. But you'll want to clarify the question. $\endgroup$– David KetchesonCommented Jul 12, 2012 at 10:14
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$\begingroup$ In general, so-called "black-box" linear algebra techniques offer very good theoretical and practical performance for sparse or structured matrix operations. The basic idea is to treat matrix multiplication as an oracle: in the sparse or structured case, this will have subquadratic complexity and can be leveraged to accelerate more complex operations. $\endgroup$– Steve HuntsmanCommented Jul 12, 2012 at 14:37
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