What is the algorithm used by svd function?

Question

怜也河本 2021-2-18

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编辑： Jan 2021-2-19

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I want to estimate computational complexity of svd function.

So, I command

edit svd

but I get a description of the comment of only how to use this function.

What algorithm is used by svd function? Could you tell me sorce code or documentation about svd function.

Thanks.

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Answer 1

Christine Tobler 2021-2-18

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We don't give information on what SVD algorithm we use, look up the LAPACK library for detailed descriptions. For practical purposes, you can assume the complexity of doing

[U, S, V] = svd(X, 'econ')

is O(m*n*min(m,n)), while the complexity of doing

[U, S, V] = svd(X)

is O(m*n*max(m,n)).

This wouldn't be easy to proof, since the SVD computation involves an iteration that needs to converge to each of the singular values, but the complexities above are the ones that dominate in all practical cases.