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@ARTICLE{Winkelmann:860709,
      author       = {Winkelmann, Jan and Di Napoli, Edoardo},
      title        = {{N}on-linear {L}east-{S}quares {O}ptimization of {R}ational
                      {F}ilters for the {S}olution of {I}nterior {H}ermitian
                      {E}igenvalue {P}roblems},
      journal      = {Frontiers in applied mathematics and statistics},
      volume       = {5},
      issn         = {2297-4687},
      address      = {Lausanne},
      publisher    = {Frontiers Media},
      reportid     = {FZJ-2019-01374},
      pages        = {5},
      year         = {2019},
      abstract     = {Rational filter functions can be used to improve
                      convergence of contour-based eigensolvers, a popular family
                      of algorithms for the solution of the interior eigenvalue
                      problem. We present a framework for the optimization of
                      rational filters based on a non-convexweighted Least-Squares
                      scheme. When used in combination with a contour based
                      eigensolvers library, our filters out-perform existing ones
                      on a large and representative set of benchmark problems.
                      This work provides a detailed description of: (1) a set up
                      of the optimization process that exploits symmetries of the
                      filter function for Hermitian eigenproblems, (2) a
                      formulation of the gradient descent and Levenberg-Marquardt
                      algorithms that exploits the symmetries, (3) a method to
                      select the starting position for theoptimization algorithms
                      that reliably produces effective filters, (4) a constrained
                      optimization scheme that produces filter functions with
                      specific properties that may be beneficial to the
                      performance of the eigensolver that employs them.},
      cin          = {JSC / JARA-HPC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406 / $I:(DE-82)080012_20140620$},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / Simulation and Data Laboratory Quantum
                      Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001050584000001},
      doi          = {10.3389/fams.2019.00005},
      url          = {https://juser.fz-juelich.de/record/860709},
}