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On Lanczos-Type Methods for Wilson Fermions

  • Conference paper
Book cover Numerical Challenges in Lattice Quantum Chromodynamics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 15))

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Abstract

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.

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Author information

Authors and Affiliations

  1. ETH Zürich, ETH-Zentrum, Seminar for Applied Mathematics , CH-8092, Zürich, Switzerland

    Martin H. Gutknecht

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  1. Martin H. Gutknecht
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Editors and Affiliations

  1. Department of Mathematics, University of Wuppertal, Wuppertal, 42097, Germany

    Andreas Frommer  & Björn Medeke  & 

  2. Department of Physics, University of Wuppertal, Wuppertal, 42097, Germany

    Thomas Lippert

  3. John von Neumann Institute for Computing, FZ-Jülich, Jülich, 52425, Germany

    Klaus Schilling

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© 2000 Springer-Verlag Berlin Heidelberg

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Gutknecht, M.H. (2000). On Lanczos-Type Methods for Wilson Fermions. In: Frommer, A., Lippert, T., Medeke, B., Schilling, K. (eds) Numerical Challenges in Lattice Quantum Chromodynamics. Lecture Notes in Computational Science and Engineering, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58333-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-58333-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67732-1

  • Online ISBN: 978-3-642-58333-9

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