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From the previous discussion, we see that matrix multiplication is actually very rarely used in scientific computing for large N. (Yet it's a favorite computer science algorithm!)
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Full matrix equation solvers are sometimes used but not very common. Of course equation solvers are incredibly important for sparse matrices because if the matrix is large
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the physics of the problem will make it sparse
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it will be insoluble unless it is sparse
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In solving , formally , but this is NOT normally the best numerical method.
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If is sparse, both and the better LU decomposition are NOT sparse.
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