Iterative methods for overlap and twisted mass fermions

We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice quantum chromodynamics (QCD). In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass (TM) fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 and 720 MeV. For overlap fermions we address adaptive precision and low-mode preconditioning while for TM fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30–120 more expensive than with the TM operator.