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 <[email protected]> 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 <[email protected]> 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 <[email protected]> > > 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 <[email protected]> wrote: > > Smallest eigenvalue in magnitude or real part? > > > > > > > El 1 jul 2021, a las 11:58, Varun Hiremath <[email protected]> > > > 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 <[email protected]> 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 <[email protected]> > > > > 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 > > > > > >
