Can SVD fail?

SVD promises that any matrix A can be written as A = U*S*V' where U and V are unitary matrices and D is diagonal.

Is it possible for SVD to fail?

Answer 1

[Walter Roberson]

Some SVD implementations can fail to converge; https://arxiv.org/abs/1707.07803 and http://www.stat.umn.edu/macanova/htmlhelp/node332.htm and https://stackoverflow.com/questions/24966691/catching-exception-error-svd-failed-to-converge and https://groups.google.com/forum/#!topic/gensim/pOi60wIs1Nw

It would not surprise me if Mathwork's implementation can fail to converge -- indeed, there is a svd::svdNoConvergence error message in the message catalogs.

[Kevin]

Hi Walter,

Great. Thanks for the link. I will definitely look at them. I am hoping that I can find an actual matrix that can make MATLAB SVD to fail. If If I find one, I will post the matrix here.

You mentioned "message catalog". How do you get that?

Thanks

[Walter Roberson]

The applicable message catalog is

fullfile(matlabroot, '/resources/MATLAB/en/svd.xml')

For example matrices, see the discussion http://community.wolfram.com/groups/-/m/t/1065721 which implies it is a LAPACK / MKL issue and so MATLAB would probably be affected if it is using a release from before the fix.