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
