[petsc-users] Lower spectrum limit for Lanczos type eigensolvers

[Umut Tabak]

Dear all,

I am trying to experiment with a block Lanczos eigensolver code of mine 
for symmetric systems.

I have a practical question which I could not find a direct answer yet.

For large sparse matrices, what should be the number of eigenvalues to 
be extracted with this Krylov subspace based solver? I am looking for a 
ratio or a rule of thumb like 'if you want k eigenvalues and your system 
size is n, then the ratio given by k/n should not exceed 0.01'. In this 
case '0.01' is just a coefficient, say r, any practical experience on 
choosing this coefficient r? I know Lanczos method is efficient on 
extracting extreme values over the spectrum but is there a, more or 
less, a practical limit like the one I tried to explain?

Best regards,
Umut