### How to solve this generalizaed eigen problem efficiently?

Posted:

**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.

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.