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 >
