%0 Journal Article
%A GLÄSSNER, UWE
%A GÜSKEN, STEPHAN
%A LIPPERT, THOMAS
%A RITZENHÖFER, GERO
%A SCHILLING, KLAUS
%A FROMMER, ANDREAS
%T HOW TO COMPUTE GREEN'S FUNCTIONS FOR ENTIRE MASS TRAJECTORIES WITHIN KRYLOV SOLVERS
%J International journal of modern physics / C Computational physics and physical computation C
%V 07
%N 05
%@ 1793-6586
%C Singapore [u.a.]
%I World Scientific
%M FZJ-2019-01113
%P 635 - 644
%D 1996
%X 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 structure A = D − m, with m proportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives x(n) of the solution vector x with respect to the parameter m and construct the Taylor expansion of x around m. 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 ≥ m at the price of one inversion at mass m.
%F PUB:(DE-HGF)16
%9 Journal Article
%R 10.1142/S0129183196000533
%U https://juser.fz-juelich.de/record/860338