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>