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What is the algorithm used by svd function?

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怜也 河本
怜也 河本 on 18 Feb 2021
Edited: Jan on 19 Feb 2021
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.

Answers (2)

Christine Tobler
Christine Tobler on 18 Feb 2021
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.

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