How to solve this generalizaed eigen problem efficiently?

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How to solve this generalizaed eigen problem efficiently?

Postby phygjd » Tue Nov 15, 2005 4:06 am

I am going to solve
E U=A1 A2 U,
where E is eigenvalue, U is corresponding eigenvector, A1 and A2 are real symmetric tridiagonal matrixs.
I tried to use DPOTRF and DSYGST to reduce the problem to a standard eigen problem. However, in my numberical calculation, I found that both A2 and A1 are not positive definite.
Now I am wondering how to solve my problem using Lapack routines.
phygjd
 
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Re: How to solve this generalizaed eigen problem efficiently

Postby sven » Tue Nov 15, 2005 4:19 am

There is no routine in LAPACK that will allow you to take advantage of the tridiagonal nature of A1 and A2. For band matrices, LAPACK only handles the case A1 u = e A2 u, with A1 and A2 symmetric and A2 positive definite.

You could try ARPACK for which you do not need to supply A1 and A2 explicitly. For your problem to be a generalized symmetric eigenvalue problem you need one of A1 or A2 to be positive definite (and preferably well-conditioned).

Best wishes,

Sven Hammarling.
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Postby phygjd » Tue Nov 15, 2005 5:13 am

Thank you very much.
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