Sparse eigenvalue problem for large matrixes

[Malova_Anna]

Hello,

Im trying to solve sparse symmetry eigenvalue problem using MKL LAPACK.

My matrix leads from PDE and has 5 non-zero diagonals (with wide band), it is symmetry and not positive-define. Matrix is large (order ~ 10^4 and more) or very large (order ~ 10^7 and more).

I need to find all eigenvalies and all eigenvectors. I would like to get all eigenvectors not simultaneous, but gradually at several portions because of large size of matrix.

Now I use dsbev() or such sequence of routines:

1. dsbtrd(), vect = `V`,
2. dstebz(),
3. dstein(),
4. dgemm() for getting eigenvectors of A from eigenvectors of tridiagonal T.

My questions are:

• Is it possible to store orthogonal matrix Q from dsbtrd() in some compact storage sheme?
• Is there another way to get all eigenvectors at several steps for large (sparse band) matrixes?

Thank you in advance for help,

Anna

[Aleksandr_Z_Intel]

Dear Anna,

You may use ?sbevx for partial spectrum calculation. But the matrices you described are not so big indeed and it could be better to compute the full spectrumat once.Also you may use ?sbevd for better performance.

And as of orthogonal matrix Q, it doesn't make a sense to keep it in compact storage shemebecause Q is a dense matrixin general.

[Malova_Anna]

Dear Alexandr,

Thank you for your advice.