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[Lapack] eigenvalue problem

Hi Ahmed, 

I am going to try to throw one or two keywords in there and hope you can
figure this out by yourself. As you wrote, LAPACK and matlab solve the
generalized eigenvalue AX=cBX whether A or B is singular or nonsingular
for the matter. In the case of B being singular, you have infinite
eigenvalues. Correct. If you do not want infinite eigenvalues, do not give
a singular B! ;) Now, reading your email, I guess what you would like to
do is to deflate the infinite eigenvalues from your pencil. So you want to
work on the projected pencil I guess. I am not expert in this, so I let
you figure this out by yourself. This is not something LAPACK (nor Matlab)
is doing. You need to do it yourself. I think you can also reorder the
eigenvalues to remove the one close to zeros. You should play with
"ordeig" and "ordschur" in Matlab to find the invariant subspace you are
interested in. Have a look. (Then there are a corresponding LAPACK
functions to reorder, but first I would advise you prototype in matlab.)

Cheers, 
Julien.




On 7/27/13 4:36 AM, "Ahmed Kaffel" <kaffel@Domain.Removed> wrote:




Hello:

I found that  eig and qz  matlab functions give infinite spurious modes,
I think  the elimination of the spurious modes is needed when the matrix
B  is singular.

Could you help me about this issue and provide me a matlab package or
lapack routine which can solve the eigenvalue problem A X= c B X when A
and B are complex and one of the matrices is singular ?

I really appreciate your help.

Best regards

Ahmed
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