[petsc-users] SLEPc: smallest eigenvalues

[Varun Hiremath]

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
>
>
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