[petsc-users] SLEPc: smallest eigenvalues

Jose E. Roman jroman at dsic.upv.es
Thu Jul 1 04:43:54 CDT 2021

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.


> 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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