BLAS/Atlas/LAPACK/...

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BLAS is a optimized library for linear algebra. For certain operations (especially matrix multiplication) BLAS provides a very significant increase in speed over hand-written operations. The Intel version in particular is extreamly fast, as it is designed to take advantage of vectorization instructions and multiple CPUs. It is available for free for non-commercial use on Linux [1]. Also, the ATLAS project provides an implementation of BLAS that will automatically tune itself to your particular system, though is not as optimized [2].