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Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov SubspaceMethods

  • Guido Arnold
  • Nigel Cundy
  • Jasper van den Eshof
  • Andreas Frommer
  • Stefan Krieg
  • Thomas Lippert
  • Katrin Schäfer
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 47)

Summary

We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger’s overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are optimal for the respective formulation. We compare these methods in theory and practice to find the overall optimal one. For the first time, we apply the so-called SUMR method of Jagels and Reichel to the shifted unitary version of Neuberger’s operator, and show that this method is in a sense the optimal choice for propagator computations. When solving the “squared” equations in a dynamical simulation with two degenerate flavours, it turns out that the CG method should be used.

Keywords

Krylov Subspace Matrix Vector Multiplication Unitary Form Krylov Subspace Method Propagator Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Guido Arnold
    • 1
  • Nigel Cundy
    • 1
  • Jasper van den Eshof
    • 2
  • Andreas Frommer
    • 3
  • Stefan Krieg
    • 1
  • Thomas Lippert
    • 1
  • Katrin Schäfer
    • 3
  1. 1.Department of PhysicsUniversity of WuppertalGermany
  2. 2.Department of MathematicsUniversity of DüsseldorfGermany
  3. 3.Department of MathematicsUniversity of WuppertalGermany

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