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arXiv · hep-lat/9605008

How to compute Green's Functions for entire Mass Trajectories within Krylov Solvers

U. Glaessner·S. Guesken·Th. Lippert·G. Ritzenhoefer·K. Schilling·A. Frommer
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Abstract

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 $m$.

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U. Glaessner, S. Guesken, Th. Lippert, G. Ritzenhoefer, K. Schilling, A. Frommer. 1996-05-09. How to compute Green's Functions for entire Mass Trajectories within Krylov Solvers. https://doi.org/10.1142/s0129183196000533

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