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I need to compute the Singular Value Decomposition (SVD) of many $4 \times 4$ matrices. I'm looking for SVD algorithms specialized for small matrices. I've read that the std::vector sorting algorithm in the C++ STL is often hardcoded for short vectors for optimal performance. I want to hard code the SVD for the case $4 \times 4$ matrices.

What information is there about optimally solving small cases of SVD?

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