# eigsh (Lanczos algorithm) slows down for degenerate eigenvalues

I have a complex Hermitian matrix of size about $$70000\times 70000$$. I want about 100 eigenvalues near 0. However, I know that every eigenvalues are two-fold degenerate. I found out that the running time of eigsh is extremely slow (more than 5 times) compared to the situation with no degeneracy.

Also, I found out from the following link Computation time of eigenvalues with ARPACK depends on what? that degeneracy is bad to eigsh algorithm.

What can I do to make my code run faster? In the answer of the link suggests to increase the size of the Krylov subspace, but what size is the adequate one?

• Are you using the shifting method? Jun 2 at 13:35
• @nicoguaro Yes, I am using the shift invert method with sigma=0. Jun 3 at 14:30

ARPACK recommends to use ncv > 2 nev. The default value of ncv would fit that constraint. A couple of suggestions:
• increase ncv to 300?
• increase the tolerance tol to $$1.0e-14$$.