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How to solve this generalizaed eigen problem efficiently?

PostPosted: Tue Nov 15, 2005 4:06 am
by phygjd
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.

Re: How to solve this generalizaed eigen problem efficiently

PostPosted: Tue Nov 15, 2005 4:19 am
by sven
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.

PostPosted: Tue Nov 15, 2005 5:13 am
by phygjd
Thank you very much.