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@INPROCEEDINGS{DiNapoli:185571,
      author       = {Di Napoli, Edoardo},
      title        = {{E}stimating the number of eigenvalues in a interval using
                      the eigenproblem resolvent},
      reportid     = {FZJ-2014-06997},
      year         = {2011},
      abstract     = {Symmetric generalized eigenvalue problems arise in many
                      applications in chemistry physics and engineering. In
                      several cases only a small fraction of the eigenpairs,
                      usually located in a interval at one of the extremities of
                      the spectrum, is required. Obtaining previous knowledge of
                      the number of eigenvalues within the interval boudaries is
                      often beneficial. For instance, for those iterative methods
                      where a projector is used in conjunction with a
                      Rayleigh-Ritz quotient this is an essential ingredient for
                      reducing the number of iterations and increasing the
                      accuracy. We present a potentially inexpensive technique to
                      estimate the number of eigenvalues in a generic interval
                      based on numerical manipulations of the eigenproblem
                      resolvent.},
      month         = {Dec},
      date          = {2011-12-13},
      organization  = {25th Umbrella Symposium, Aachen
                       (Germany), 13 Dec 2011 - 15 Dec 2011},
      subtyp        = {Invited},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411) / Simulation and Data Laboratory Quantum
                      Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF2-411 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/185571},
}