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[Lapack] eigenvalue problem



The matrices are not Hermitian and the eigenvalues are complex.

 det(A)

ans =

     3.335644330640469e+144 +1.055810386796784e+145i

det(B)

ans =

    -1.457124348497662e+128 +2.185687979871937e+125i

cond(A)

ans =

    7.893694109796931e+013

cond(B)

ans =

    8.354843024851492e+013



spy(A)
spy(B)

A and B have the block  structure as shown in attached file.

Thanks,
Ahmed

________________________________________
From: Ming Gu [mgu@Domain.Removed]
Sent: Friday, August 02, 2013 12:34 PM
To: James W DEMMEL
Cc: Langou, Julien; Ahmed Kaffel; lapack@Domain.Removed
Subject: Re: [Lapack] eigenvalue problem

Are there any additional structures to your matrices, beyond one of them being 
singular?
I.e., are they Hermitian (and positive definite)? Do you expect all eigenvalues 
to be real?
All the best,
Ming Gu



On Wed, Jul 31, 2013 at 4:09 PM, James W DEMMEL 
<demmel@Domain.Removed<mailto:demmel@Domain.Removed>> wrote:
Let me add that if B is close to singular, tiny rounding errors can cause B to 
become
exactly singular and so create infinite eigenvalues. This is a standard issue 
with
(nearly) singular matrices, that very tiny errors from roundoff (or just 
computing the
matrix entries in the first place) can switch them from singular to nonsingular 
or vice-versa,
and so is an issue in solving linear systems, least squares and eigenproblems.
Generally some problem-specific information is needed to decide whether the the
singularity is a feature or a bug, and to choose how to deflate or regularize 
the problem.
I agree with Julien's advice as a starting point.
Jim Demmel



On Tue, Jul 30, 2013 at 11:50 AM, Langou, Julien 
<Julien.Langou@Domain.Removed<mailto:Julien.Langou@Domain.Removed>> wrote:
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<mailto: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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