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Re: SingularValueDecomposition bug: fifty examples

  • To: mathgroup at
  • Subject: [mg60818] Re: SingularValueDecomposition bug: fifty examples
  • From: John Sidles <sidles at>
  • Date: Thu, 29 Sep 2005 05:41:54 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Hello Ssezi

Please give my regards to my friend, and your colleague
colleague at JEOL, namely, Yohsuke Yoshinari !!

Yohsuke will understand that the "terrain" that my SVD-based
algorithm is following is a *quantum* terrain (which is why the 
SVD matrices contain complex numbers).  Someday, perhaps
JEOL will build microscopes that track this complex terrain.

> it is quite clear that the algorithm can fail to compute an SVD 
> with a message that it did not converge

Hmmm ... twenty-five of the examples compute an invalid SVD,
but with *no* message that convergence failed.  So it seems most
likely that that the problem is a bug in the implementation, not in 
the algorithm or the matrices.

> I am unsure of the details as to what properties of a matrix 
> could cause a failure, but it seems to be related to issues of 
> numeric precision and not dependent on the condition number.

Yes, it can't depend on the condition number, because otherwise 
SVD could not be used as the basis of Mathematica's MatrixRank[].
So I am not sure exactly what the circumstances are that lead to
failure.  Most (but not all) failing matrices have dimension 100 to 
200, with rank roughly half the dimension.  I have now found
non-Hermitian matrices that fail, so the symmetry of the matrix
does not seem to be critical.  I will report back when I know more.

Sincerely ... John Sidles

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