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@ARTICLE{vandenEshof:860300,
      author       = {van den Eshof, J. and Frommer, A. and Lippert, Th. and
                      Schilling, K. and van der Vorst, H. A.},
      title        = {{N}umerical methods for the {QCD}d overlap operator. {I}.
                      {S}ign-function and error bounds},
      journal      = {Computer physics communications},
      volume       = {146},
      number       = {2},
      issn         = {0010-4655},
      address      = {Amsterdam},
      publisher    = {North Holland Publ. Co.},
      reportid     = {FZJ-2019-01075},
      pages        = {203 - 224},
      year         = {2002},
      abstract     = {The numerical and computational aspects of the overlap
                      formalism in lattice quantum chromodynamics are extremely
                      demanding due to a matrix–vector product that involves the
                      sign function of the Hermitian Wilson matrix. In this paper
                      we investigate several methods to compute the product of the
                      matrix sign-function with a vector, in particular Lanczos
                      based methods and partial fraction expansion methods. Our
                      goal is two-fold: we give realistic comparisons between
                      known methods together with novel approaches and we present
                      error bounds which allow to guarantee a given accuracy when
                      terminating the Lanczos method and the multishift-CG solver,
                      applied within the partial fraction expansion methods.},
      ddc          = {530},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1016/S0010-4655(02)00455-1},
      url          = {https://juser.fz-juelich.de/record/860300},
}