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schulzey

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03-20-2017
03:08 AM

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Incorrect Results from Feast Generalized Eigenvalue Solver

The correct eigenvalues for my text case are -1.18725, -0.28274 and 1.711014. I have verified these using Matlab and also in Excel using the Matrix.xla routines. I have also checked that the equation Ax=yBx is satisfied using the returned eigenvalues and eigenvectors.

Interestingly, if I zero all the non-diagonal terms of the B matrix then dfeast_sygv returns the correct eigenvalues of -1.650985, 0.4497689 and 6.284550. This shows that the problem only occurs when there are non-zero terms away from the diagonal of the B matrix.

Am I doing something that the Feast solver isn't meant for? I am using MKL v2017.2 with the latest 2017.2 Intel Fortran compiler in VS2015.

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schulzey

New Contributor I

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03-21-2017
06:43 PM

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I have switched to using a Lapack mkl routine and am getting good results with that, but is it possible to use the Feast solver somehow to solve indefinite matrices?

Irina_S_Intel

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03-24-2017
02:00 PM

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Hello,

Thank you for your interest in Extended Eigensolver. I'm afraid there has been some misunderstanding here. Extended Eigensolver is designed for eigenvalue problems with real eigenvalues, so only B matrix must be positive definite(not B-1A as you suggested) and both matrices must be Hermitian. Output eigenvalues of the problem can be negative. In your example matrix B is not positive definite that can be checked by solving eigenvalue problem Bx=lx.

If you indeed want to solve eigenvalue problem with complex eigenvalues, can I ask in what kind of application do you plan to use it?

Thank you in advance,

Irina

schulzey

New Contributor I

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04-04-2017
06:14 PM

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My application is in structural engineering and it calculates the buckling strength of a structural member such as a beam or column. In this application the A and B matrices are the member's elastic and geometric stiffness matrices respectively.

In my first post the example matrices were just simplified samples, but I have now attached actual A and B matrices that show what I am dealing with.

Regards,

Peter

Irina_S_Intel

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04-07-2017
02:37 PM

269 Views

Thank you, Peter!

Couple more questions. Do you usually know in which interval to search eigenvalues or there are several max or min eigenvalues that are required to find? Is the size 40 is a typical size for your problem? If so, did you tried using MKL LAPACK functionality?

Irina

schulzey

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04-07-2017
03:21 PM

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Wallin__Mathias

Beginner

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07-05-2018
08:07 AM

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Hi Peter,

Which LAPACK routine do you recommend for solving the generalized eigenvalue problem when B is indefine?

Thanks

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