How To Compute Green'S Functions For Entire Mass Trajectories Within Krylov Solvers

The availability of efficient Krylov subspace solvers plays a vital role in the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process. Our procedure applies to matrices of structureA = D − m, withmproportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivativesx(n)of the solution vectorxwith respect to the parametermand construct the Taylor expansion ofxaroundm. We demonstrate the advantages of our method using a minimal residual solver. Here the procedure requires one intermediate vector for each Green's function to compute. As real-life example, we determine a mass trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we can obtain Green's functions at all masses≥ mat the price of one inversion at massm.