Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-05-08
Physics
High Energy Physics
High Energy Physics - Lattice
11 pages, 2 eps-figures, needs epsf.sty
Scientific paper
10.1142/S0129183196000533
The availability of efficient Krylov subspace solvers play a vital role for 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 $1$ 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 $\geq m$ at the price of one inversion at mass $m$.
Frommer Andreas
Glaessner U.
Guesken S.
Lippert Th.
Ritzenhoefer G.
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