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MathGroup Archive 2005

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Re: SingularValueDecomposition bug: fifty examples

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61183] Re: SingularValueDecomposition bug: fifty examples
  • From: John Sidles <sidles at u.washington.edu>
  • Date: Wed, 12 Oct 2005 01:42:08 -0400 (EDT)
  • References: <200510060745.DAA08051@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup folks

Per my exploration of errors in SingularValueDecomposition[],
the directory:

    http://faculty.washington.edu/sidles/mma_svd_failure_example/

contains an updated tarball whose contents are summarized in
the PDF file "readme_v4.0.pdf".

The new findings include:

  (1) SingularValueDecomposition[] is shown to fail on both G4 and G5
      computers.  However, the patterns of failure are slightly
      different for the two architectures.  Reason unknown.

  (2) Formerly, the only examples of SVD failure in Mathematica
      were of Hermitian matrices.  Now, the tarball includes
      examples of failing non-Hermitian matrices.  These are generated
      by randomly permuting the rows and columns of the failing
      Hermitian matrices.

One plausible explanation might be that Mathematica's implementation
does not set LAPACK's machine precision parameters (which determine
convergence) quite right for the new 64-bit archtecture of the G4
and G5.  This would be easy to fix.

This concludes my posting on this topic until December, which
will be the earliest time that I can further investigate this
topic.  Hopefully, by then Wolfram Research will have fixed
the problem!

Sincerely ... John Sidles


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