Approximate Ginsparg-Wilson fermions: a first test

We construct a 4-d lattice Dirac operator D using a systematical expansion in terms of simple operators on the lattice. The Ginsparg-Wilson equation t urns into a system of coupled equations for the expansion coefficients of D . We solve these equations for a finite parametrization of D and find an ap proximate solution of the Ginsparg-Wilson equation. We analyze the spectral properties of our D for various ensembles of quenched SU(3) configurations . Improving the gauge field action considerably improves the spectral prope rties of our D. (C) 2001 Elsevier Science B.V. All rights reserved.