Smallest eigenvalue in magnitude or real part?


> El 1 jul 2021, a las 11:58, Varun Hiremath <varunhiremath@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@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@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
>