Re: SingularValueDecomposition bug: fifty examples

*To*: mathgroup at smc.vnet.net*Subject*: [mg60818] Re: SingularValueDecomposition bug: fifty examples*From*: John Sidles <sidles at u.washington.edu>*Date*: Thu, 29 Sep 2005 05:41:54 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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