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@ARTICLE{Kollnig:872963,
      author       = {Kollnig, Konrad and Bientinesi, Paolo and Di Napoli,
                      Edoardo},
      title        = {{R}ational {S}pectral {F}ilters with {O}ptimal
                      {C}onvergence {R}ate},
      journal      = {SIAM journal on scientific computing},
      volume       = {43},
      number       = {4},
      issn         = {0196-5204},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2020-00420},
      pages        = {A2660–A2684},
      year         = {2021},
      abstract     = {In recent years, contour-based eigensolvers have emerged as
                      a standard approach for the solution of large and sparse
                      eigenvalue problems. Building upon recent performance
                      improvements through nonlinear least-squares optimization of
                      so-called rational filters, we introduce a systematic method
                      to design these filters by minimizing the worst-case
                      convergence rate and eliminate the parametric dependence on
                      weight functions. Further, we provide an efficient way to
                      deal with the box-constraints which play a central role for
                      the use of iterative linear solvers in contour-based
                      eigensolvers. Indeed, these parameter-free filters
                      consistently minimize the number of iterations and the
                      number of FLOPs to reach convergence in the eigensolver. As
                      a byproduct, our rational filters allow for a simple
                      solution to load balancing when the solution of an interior
                      eigenproblem is approached by the slicing of the sought
                      after spectral interval.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / Simulation and Data
                      Laboratory Quantum Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2001.04184},
      howpublished = {arXiv:2001.04184},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2001.04184;\%\%$},
      UT           = {WOS:000692204700003},
      doi          = {10.1137/20M1313933},
      url          = {https://juser.fz-juelich.de/record/872963},
}