Re: [eigen] generalized eigenvalue problem with complex matrices

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 08.08.2013 23:04, Manav Bhatia wrote:
>     I need to solve the eigenproblem   A x = \lambda B x, where A and B are
> complex matrices. I noticed that the GeneralizedEigenSolver supports only
> real A and B.
>
>     Is there any other class available to support complex A& B, or anything
> else in the works?

If A and B were selfadjoint, you could instead use 
GeneralizedSelfAdjointEigenSolver.

If B is invertible, you can solve the equivalent (but numerically less 
stable) problem (using the normal EigenSolver):
  (A*B.inverse()) * x = lambda * x.
Equivalently, if A is invertible:
  recip_lambda * x = (A.inverse()*B) * x

Of course, the best way would be to find someone able (and willing) to 
implement GeneralizedEigenSolver for complex matrices ^^


Regards,
Christoph

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Dipl.-Inf., Dipl.-Math. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
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