Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing

[Markus Moll <markus.moll@xxxxxxxxxxxxxxxx>]

Hi

Sorry for reviving an "ancient" thread, but: 
I recently had to extract roots of a fourth order polynomial. Using Eigen to 
find the eigenvalues of the companion matrix, I found that some roots were 
horribly bad (compared to matlab, which gave much more reliable results). I 
soon figured that the difference is that Matlab balances the matrices 
beforehand. In this thread, Manuel said he had written a balancer, but I 
cannot find it among the unsupported modules, nor can I find his bitbucket 
account any more.

Because I wasn't aware of this previous effort, I had already translated 
LAPACK's dgebal (the diagonal scaling part only) to C++. As I feel that 
balancing should be supported in Eigen (via another EigenSolver flag?), I 
wonder if this could be included. The original LAPACK dgebal.f is published 
under the 3-clause BSD license, so the licenses should be compatible according 
to my understanding.

Regards
Markus