• To: eigen@xxxxxxxxxxxxxxxxxxx
• Subject: Re: [eigen] Generalized selfadjoint eigenvalues
• From: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
• Date: Thu, 10 Jun 2010 17:00:56 +0200
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```On Thu, Jun 10, 2010 at 1:56 PM, Helmut Jarausch
<jarausch@xxxxxxxxxxxxxxxxxxx> wrote:
> On 10 Jun, Jitse Niesen wrote:
>> On Thu, 10 Jun 2010, Gael Guennebaud wrote:
>>
>>
>> Oops, I postponed that part of the Eigenvalues module because I don't know
>>
>>> [...] 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!

Well the main problem is that the product of two selfadjoint matrices
is not selfadjoint anymore, and so you would have to use a much more
expensive eigenvalue routine.

gael

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

```

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