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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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This question is under defined: the "best method" depends on the sparsity structure... –  Igor Rivin Jul 12 '12 at 8:11
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I suggest asking on scicomp.stackexchange.com. But you'll want to clarify the question. –  David Ketcheson Jul 12 '12 at 10:14
    
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. –  Steve Huntsman Jul 12 '12 at 14:37

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