TY  - JOUR
AU  - GLÄSSNER, UWE
AU  - GÜSKEN, STEPHAN
AU  - LIPPERT, THOMAS
AU  - RITZENHÖFER, GERO
AU  - SCHILLING, KLAUS
AU  - FROMMER, ANDREAS
TI  - HOW TO COMPUTE GREEN'S FUNCTIONS FOR ENTIRE MASS TRAJECTORIES WITHIN KRYLOV SOLVERS
JO  - International journal of modern physics / C Computational physics and physical computation C
VL  - 07
IS  - 05
SN  - 1793-6586
CY  - Singapore [u.a.]
PB  - World Scientific
M1  - FZJ-2019-01113
SP  - 635 - 644
PY  - 1996
AB  - 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.
LB  - PUB:(DE-HGF)16
DO  - DOI:10.1142/S0129183196000533
UR  - https://juser.fz-juelich.de/record/860338
ER  -