HOW TO COMPUTE GREENS-FUNCTIONS FOR ENTIRE MASS TRAJECTORIES WITHIN KRYLOV SOLVERS

The availability of efficient Krylov subspace solvers plays a vital ro le in the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new gene ral numerical method to compute many Green's functions for complex non -singular matrices within one iteration process. Our procedure applies to matrices of structure A = D - m, with m proportional to the unit m atrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives x((n)) of the solution vector a:with respect to the parameter m and construct the Taylor expansion of x around m. W e demonstrate the advantages of our method using a minimal residual so lver. Here the procedure requires one intermediate vector for each Gre en's function to compute. As real-life example, we determine a mass tr ajectory of the Wilson fermion matrix for lattice QCD. Here we find th at we can obtain Green's functions at all masses greater than or equal to m at the price of one inversion at mass m.