MANY MASSES ON ONE STROKE - ECONOMIC COMPUTATION OF QUARK PROPAGATORS

The computational effort in the calculation of Wilson fermion quark pr opagators in Lattice Quantum Chromodynamics can be considerably reduce d by exploiting the Wilson fermion matrix structure in inversion algor ithms based on the non-symmetric Lanczos process. We consider two such methods: QMR (quasi minimal residual) and BCG (biconjugate gradients) . Based on the decomposition M/kappa = 1/kappa-D of the Wilson mass ma trix, using QMR, one can carry out inversions on a whole trajectory of masses simultaneously, merely at the computational expense of a singl e propagator computation. In other words, one has to compute the propa gator corresponding to the lightest mass only, while all the heavier m asses are given for free, at the price of extra storage. Moreover, the symmetry gamma 5 M = M(+) gamma 5 can be used to cut the computationa l effort in QMR and BCG by a factor of two. We show that both methods then become - in the critical regime of small quark masses - competiti ve to BiCGStab and significantly better than the standard MR method, w ith optimal relaxation factor, and CG as applied to the normal equatio ns.