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SingularValueDecomposition bug: fifty examples


Dear Mathgroup folks


I have documented fifty different examples of matrices for which
SingularValueDecomposition[] fails under Mathematica 5.2
(Mac OS X, Tiger).  Full details are here:

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

The matrices themselves (plus a notebook to successively load them and
document the SVD failure) are in this gzipped tarball:

     http://faculty.washington.edu/sidles/mma_svd_failure_example/ 
SVDfailures.tar.gz

A Makefile is included -- run "make unpack" to unpack the tarball:

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

Just as a point of interest, the above files include:

   -> 25 matrices that generate the following (undocumented) error  
message:

      "SingularValueDecomposition::cfail:  Algorithm failed to  
converge."

   -> 25 matrices for which SingularValueDecomposition[] returns a
         wrong result, with no error message.

Needless to say, a call to SingularValueDecomposition[] should never fail ...
our application (a terrain-following mapping program) surely depends  
on this!

Sincerely
John Sidles


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