[petsc-users] SLEPc - st_type cayley choice of shift and antishift

[Jose E. Roman]

> El 25 sept 2019, a las 16:18, Michael Werner via petsc-users <petsc-users at 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