We consider projection methods using rational Krylov subspaces for solving large-scale matrix equations.
In each step of these rational Krylov subspace methods, a large linear system has to be solved.
The main focus is the situation when these linear systems are solved inexactly.
We discuss the effects of the resulting errors and, in particular, investigate how large they are allowed to be without sacrificing the convergence of the rational Krylov method.