[petsc-users] SLEPc: smallest eigenvalues

[Jose E. Roman]

Then I would try Davidson methods https://doi.org/10.1145/2543696
You can also try Krylov-Schur with "inexact" shift-and-invert, for instance, with preconditioned BiCGStab or GMRES, see section 3.4.1 of the users manual.

In both cases, you have to pass matrix A in the call to EPSSetOperators() and the preconditioner matrix via STSetPreconditionerMat() - note this function was introduced in version 3.15.

Jose



> El 1 jul 2021, a las 13:36, Varun Hiremath <varunhiremath at gmail.com> escribió:
> 
> Thanks. I actually do have a 1st order approximation of matrix A, that I can explicitly compute and also invert. Can I use that matrix as preconditioner to speed things up? Is there some example that explains how to setup and call SLEPc for this scenario? 
> 
> On Thu, Jul 1, 2021, 4:29 AM Jose E. Roman <jroman at dsic.upv.es> wrote:
> For smallest real parts one could adapt ex34.c, but it is going to be costly https://slepc.upv.es/documentation/current/src/eps/tutorials/ex36.c.html
> Also, if eigenvalues are clustered around the origin, convergence may still be very slow.
> 
> It is a tough problem, unless you are able to compute a good preconditioner of A (no need to compute the exact inverse).
> 
> Jose
> 
> 
> > El 1 jul 2021, a las 13:23, Varun Hiremath <varunhiremath at gmail.com> escribió:
> > 
> > I'm solving for the smallest eigenvalues in magnitude. Though is it cheaper to solve smallest in real part, as that might also work in my case? Thanks for your help.
> > 
> > On Thu, Jul 1, 2021, 4:08 AM Jose E. Roman <jroman at dsic.upv.es> wrote:
> > Smallest eigenvalue in magnitude or real part?
> > 
> > 
> > > El 1 jul 2021, a las 11:58, Varun Hiremath <varunhiremath at gmail.com> escribió:
> > > 
> > > Sorry, no both A and B are general sparse matrices (non-hermitian). So is there anything else I could try?
> > > 
> > > On Thu, Jul 1, 2021 at 2:43 AM Jose E. Roman <jroman at dsic.upv.es> wrote:
> > > Is the problem symmetric (GHEP)? In that case, you can try LOBPCG on the pair (A,B). But this will likely be slow as well, unless you can provide a good preconditioner.
> > > 
> > > Jose
> > > 
> > > 
> > > > El 1 jul 2021, a las 11:37, Varun Hiremath <varunhiremath at gmail.com> escribió:
> > > > 
> > > > Hi All,
> > > > 
> > > > I am trying to compute the smallest eigenvalues of a generalized system A*x= lambda*B*x. I don't explicitly know the matrix A (so I am using a shell matrix with a custom matmult function) however, the matrix B is explicitly known so I compute inv(B)*A within the shell matrix and solve inv(B)*A*x = lambda*x.
> > > > 
> > > > To compute the smallest eigenvalues it is recommended to solve the inverted system, but since matrix A is not explicitly known I can't invert the system. Moreover, the size of the system can be really big, and with the default Krylov solver, it is extremely slow. So is there a better way for me to compute the smallest eigenvalues of this system?
> > > > 
> > > > Thanks,
> > > > Varun
> > > 
> > 
>