On Lanczos-type methods for Wilson fermions. (English) Zbl 1187.65161
Frommer, Andreas (ed.) et al., Numerical challenges in lattice quantum chromodynamics. Joint interdisciplinary workshop of John von Neumann Institute for Computing, Jülich, and Institute of Applied Computer Science, Wuppertal Univ., Germany, August 1999. Berlin: Springer (ISBN 3-540-67732-1/pbk). Lect. Notes Comput. Sci. Eng. 15, 48-64 (2000).
Summary: Numerical simulations of lattice gauge theories with fermions rely heavily on the iterative solution of huge sparse linear systems of equations. Due to short recurrences, which mean small memory requirement, Lanczos-type methods (including suitable versions of the conjugate gradient method when applicable) are best suited for this type of problem.
The Wilson formulation of the lattice Dirac operator leads to a matrix with special symmetry properties that makes the application of the classical biconjugate gradient (BICG) particularly attractive, but other methods, for example BICGSTAB and BICGSTAB2 have also been widely used. We discuss some of the pros and cons of these methods.
In particular, we review the specific simplification of BICG, clarify some details, and discuss general results on the roundoff behavior.
For the entire collection see [Zbl 0957.00052].
The Wilson formulation of the lattice Dirac operator leads to a matrix with special symmetry properties that makes the application of the classical biconjugate gradient (BICG) particularly attractive, but other methods, for example BICGSTAB and BICGSTAB2 have also been widely used. We discuss some of the pros and cons of these methods.
In particular, we review the specific simplification of BICG, clarify some details, and discuss general results on the roundoff behavior.
For the entire collection see [Zbl 0957.00052].
