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Re: SingularValueDecomposition bug: fifty examples

• To: mathgroup at smc.vnet.net
• Subject: [mg60774] Re: [mg60753] SingularValueDecomposition bug: fifty examples
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Wed, 28 Sep 2005 01:41:14 -0400 (EDT)
• References: <906C0B48-1EB7-403C-A2F4-ED8FEA05BE1F@u.washington.edu> <200509270745.DAA18971@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Sep 27, 2005, at 3:45 AM, John Sidles wrote:

> Needless to say, a call to SingularValueDecomposition[] should  
> never fail ...

Would that that were true.

 From the implementation notes (§A.9.4 in the Help Browser) Singular  
Value Decomposition is done using a QR based algorithm.  I believe  
that as of version 5.0 this is actually a version of the QR based SVD  
algorithm from LAPACK (xGESVD).  Looking at the LAPACK implementation  
of SVD (available here http://www.netlib.org/cgi-bin/netlibfiles.txt? 
format=txt&blas=0&filename=lapack%2Fsingle%2Fsgesvd.f) it  is quite  
clear that the algorithm can fail to compute an SVD with a message  
that it did not converge.  For example see the description of the  
parameter info in the LAPACK routine.

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.

Regards,

Ssezi

• References:
  • SingularValueDecomposition bug: fifty examples
    • From: John Sidles <sidles@u.washington.edu>