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@ARTICLE{Cundy:50021,
      author       = {Cundy, N. and Eshof v. d., J. and Frommer, A. and Krieg, S.
                      and Lippert, T. and Schäfer, K.},
      title        = {{N}umerical {M}ethods for the {QCD} {O}verlap {O}perator.
                      {III}. {N}ested {I}terations},
      journal      = {Computer physics communications},
      volume       = {165},
      issn         = {0010-4655},
      address      = {Amsterdam},
      publisher    = {North Holland Publ. Co.},
      reportid     = {PreJuSER-50021},
      pages        = {221 - 242},
      year         = {2005},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {The numerical and computational aspects of chiral fermions
                      in lattice quantum chromodynamics are extremely demanding.
                      In the overlap framework, the computation of the fermion
                      propagator leads to a nested iteration where the matrix
                      vector multiplications in each step of an outer iteration
                      have to be accomplished by an inner iteration; the latter
                      approximates the product of the sign function of the
                      hermitian Wilson fermion matrix with a vector.In this paper
                      we investigate aspects of this nested paradigm. We examine
                      several Krylov subspace methods to be used as an outer
                      iteration for both propagator computations and the Hybrid
                      Monte-Carlo scheme. We establish criteria on the accuracy of
                      the inner iteration which allow to preserve an a priori
                      given precision for the overall computation. It will turn
                      out that the accuracy of the sign function can be relaxed as
                      the outer iteration proceeds. Furthermore, we consider
                      preconditioning strategies, where the preconditioner is
                      built upon an inaccurate approximation to the sign function.
                      Relaxation combined with preconditioning allows for
                      considerable savings in computational efforts up to a factor
                      of 4 as our numerical experiments illustrate. We also
                      discuss the possibility of projecting the squared overlap
                      operator into one chiral sector. (C) 2004 Elsevier B.V. All
                      rights reserved.},
      keywords     = {J (WoSType)},
      cin          = {ZAM},
      ddc          = {004},
      cid          = {I:(DE-Juel1)VDB62},
      pnm          = {Betrieb und Weiterentwicklung des Höchstleistungsrechners},
      pid          = {G:(DE-Juel1)FUEK254},
      shelfmark    = {Computer Science, Interdisciplinary Applications / Physics,
                      Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000226893500003},
      doi          = {10.1016/j.cpc.2004.10.005},
      url          = {https://juser.fz-juelich.de/record/50021},
}