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The availability of efficient Krylov subspace solvers play a vital role forthe solution of a variety of numerical problems in computational science. Herewe consider lattice field theory. We present a new general numerical method tocompute many Green's functions for complex non-singular matrices within oneiteration process. Our procedure applies to matrices of structure $A=D-m$, with$m$ proportional to the unit matrix, and can be integrated within any Krylovsubspace solver. We can compute the derivatives $x^{(n)}$ of the solutionvector $x$ with respect to the parameter $m$ and construct the Taylor expansionof $x$ around $m$. We demonstrate the advantages of our method using a minimalresidual solver. Here the procedure requires $1$ intermediate vector for eachGreen's function to compute. As real life example, we determine a masstrajectory of the Wilson fermion matrix for lattice QCD. Here we find that wecan obtain Green's functions at all masses $\geq m$ at the price of oneinversion at mass $m$.Comment: 11 pages, 2 eps-figures, needs epsf.st

HOW TO COMPUTE GREEN'S FUNCTIONS FOR ENTIRE MASS TRAJECTORIES WITHIN KRYLOV SOLVERS