LAPACK Archives

### [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 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> 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" 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 _______________________________________________ Lapack mailing list Lapack@Domain.Removed http://lists.eecs.utk.edu/mailman/listinfo/lapack `````` _______________________________________________ Lapack mailing list Lapack@Domain.Removed http://lists.eecs.utk.edu/mailman/listinfo/lapack `````` _______________________________________________ Lapack mailing list Lapack@Domain.Removed http://lists.eecs.utk.edu/mailman/listinfo/lapack ``````-------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.eecs.utk.edu/mailman/private/lapack/attachments/20130802/58ac2b55/attachment-0001.html ```
 Current Thread [Lapack] eigenvalue problem, Ahmed Kaffel [Lapack] eigenvalue problem, Langou, Julien Message not available [Lapack] eigenvalue problem, Ming Gu <= [Lapack] eigenvalue problem, Ahmed Kaffel

For additional information you may use the LAPACK/ScaLAPACK Forum.
Or one of the mailing lists, or