Re: [eigen] Generalized selfadjoint eigenvalues

[Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx>]

On 10 Jun, Jitse Niesen wrote:
> On Thu, 10 Jun 2010, Gael Guennebaud wrote:
> 
>> I have some API concerns about the generalized selfadjoint eigenvalues.
> 
> Oops, I postponed that part of the Eigenvalues module because I don't know 
> much about generalized eigenvalue problems and promptly forgot about it.
> 
>> [...] 1 - we might also want to offer the possibility to solve the two 
>> other variants:
>> BAx = lambda x
>> ABx = lambda x
> 
> Stupid question: why not compute the (non-generalized) eigenvalues of the 
> product BA or AB? If the normalization x^* B x = 1 is important, that can 
> easily be fixed afterwards?

Just a comment.
If one transforms the generalized eigenvalue problem A*x= lambda*B*x
to a standard one :: B_inverse * A * x = lambda*x

one has to invert B and to mupliply two matrices.
This costly and introduce unnecessary rounding errors!

-- 
Helmut Jarausch

Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany