Thank you for the link to the paper, it's quite interesting and pretty close to what I'm doing. I'm currently also using the "inexact" approach for my application, and in general it works, as long as the ksp tolerance is low enough. However, I was hoping to speed up convergence towards the "interesting" eigenvalues by using Cayley.
Now as a test I tried to follow the approach from your paper, choosing mu = -sigma, and mu in the order of magnitude of the imaginary part of the most amplified eigenvalue. I know the most amplified eigenvalue for my problem is -0.0398+0.724i, so I tried running SLEPc with the following settings: -st_type cayley -st_shift -1 -st_cayley_antishift 1 But I never get the correct eigenvalue, instead SLEPc returns only the value of st_shift: [0] Number of iterations of the method: 1 [0] Solution method: krylovschur [0] Number of requested eigenvalues: 1 [0] Stopping condition: tol=1e-08, maxit=19382 [0] Number of converged eigenpairs: 16 [0] [0] k ||Ax-kx||/||kx|| [0] ----------------- ------------------ [0] -1.000000 0.0281754 [0] -1.000000 0.0286815 [0] -1.000000 0.0109186 [0] -1.000000 0.140883 [0] -1.000000 0.203036 [0] -1.000000 0.00801616 [0] -1.000000 0.0526871 [0] -1.000000 0.022244 [0] -1.000000 0.0182197 [0] -1.000000 0.0107924 [0] -1.000000 0.00963378 [0] -1.000000 0.0239422 [0] -1.000000 0.00472435 [0] -1.000000 0.00607732 [0] -1.000000 0.0124056 [0] -1.000000 0.00557715 Also, it doesn't matter if I'm using exact or inexact solves. Changing the values of shift and antishift also doesn't change the behaviour. Do I need to make additional adjustments to get cayley to work? Best regards, Michael Am 25.09.19 um 17:21 schrieb Jose E. Roman: > >> El 25 sept 2019, a las 16:18, Michael Werner via petsc-users >> <petsc-users@mcs.anl.gov> escribió: >> >> Hello, >> >> I'm looking for advice on how to set shift and antishift for the cayley >> spectral transformation. So far I've been using sinvert to find the >> eigenvalues with the smallest real part (but possibly large imaginary >> part). For this, I use the following options: >> -st_type sinvert >> -eps_target -0.05 >> -eps_target_real >> >> With sinvert, it is easy to understand how to chose the target, but for >> Cayley I'm not sure how to set shift and antishift. What is the >> mathematical meaning of the antishift? >> >> Best regards, >> Michael Werner > In exact arithmetic, both shift-and-invert and Cayley build the same Krylov > subspace, so no difference. If the linear solves are computed "inexactly" > (iterative solver) then Cayley may have some advantage, but it depends on the > application. Also, iterative solvers usually are not robust enough in this > context. You can see the discussion here > https://doi.org/10.1108/09615530410544328 > > Jose >