[petsc-users] Eigenvalues calculations in PETSc

[Richard Mills]

Qin,

Krylov methods will find the extreme eigenvalues first (unless you do
something in particular to get at the interior values), so this is what you
are getting from PETSc.

Another thing to keep in mind is that the eigenvalue estimates using the
Hessenberg matrix from GMRES can be pretty terrible.  If you want something
better, you may want to use something like Arnoldi/Lanczos or
Jacobi-Davidson.  Yousef Saad's book at
http://www-users.cs.umn.edu/~saad/eig_book_2ndEd.pdf offers some great
explanations of these methods, which you can use via the PETSc-based SLEPc
package.

Cheers,
Richard


On Wed, Feb 26, 2014 at 5:41 PM, Qin Lu <lu_qin_2000 at yahoo.com> wrote:

> Hello,
>
> I need to find the spectrum of the a large linear system (over 100,000
> unknowns). Option -ksp_compute_eigenvalues_explicitly ran out of memory
> since the matrix is too big, then -ksp_compute_eigenvalues only gave a
> small number of eigenvalues (around 30). My questions are:
>
> 1. Is the number of computed eigenvalues determined by the number of GMRES
> iterations to converge?
> 2. Can PETSc give the extreme eigenvalues now that the number of computed
> eigenvalues is limited?
>
> Thanks a lot for your info,
> Qin
>
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