Recent results from systematic parameterizations of Ginsparg-Wilson   fermions
  The Fixed Point Dirac Operator and Chirally Improved Fermions both use large numbers of gauge paths and the full Dirac structure to approximate a solution of the Ginsparg-Wilson equation. After a brief review of the two approaches we present recent results for quenched QCD with pion masses down to 210 MeV. We discuss the limits and advantages of approximate parameterizations and outline future perspectives. 
Christof Gattringer (Regensburg)