1) If one of the matrix is positive definite, you might want to use SSYGST/DSYGST/CHEGST/ZHEGST.

2) If you only want a few of the eigenvalues, then you do not want to use LAPACK. LAPACK uses direct method. So all cost will be O(n^3).

You want to use iterative methods where the cost will be closer from O(n^2) for a few eigenvalues. There are good packages out there.

The standard reference is ARPACK from Lehoucq, Maschhoff, Sorensen and Yang:

http://www.caam.rice.edu/software/ARPACK/It is used by matlab eigs function for example. This starts to be a little outdated and more modern alternatives would be:

PRIMME from Stathopoulos:

http://www.cs.wm.edu/~andreas/software/LOBPCG from Knyazev:

http://code.google.com/p/blopex/JDCG and JADAMILU from Notay:

http://homepages.ulb.ac.be/~ynotay/I think all three can solve symmetric generalized eigenvalue problem but one of the matrices need to be positive definite.

Cheers,

Julien.