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@ARTICLE{DiNapoli:811979,
      author       = {Di Napoli, Edoardo and Polizzi, Eric and Saad, Yousef},
      title        = {{E}fficient estimation of eigenvalue counts in an interval},
      journal      = {Numerical linear algebra with applications},
      volume       = {23},
      number       = {4},
      issn         = {1070-5325},
      address      = {New York, NY [u.a.]},
      publisher    = {Wiley},
      reportid     = {FZJ-2016-04280},
      pages        = {674-692},
      year         = {2016},
      abstract     = {Estimating the number of eigenvalues located in a given
                      interval of a large sparse Hermitian matrix is an important
                      problem in certain applications, and it is a prerequisite of
                      eigensolvers based on a divide-and-conquer paradigm. Often,
                      an exact count is not necessary, and methods based on
                      stochastic estimates can be utilized to yield rough
                      approximations. This paper examines a number of techniques
                      tailored to this specific task. It reviews standard
                      approaches and explores new ones based on polynomial and
                      rational approximation filtering combined with a stochastic
                      procedure. We also discuss how the latter method is
                      particularly well- suited for the FEAST eigensolver.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      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:000383673200006},
      doi          = {10.1002/nla.2048},
      url          = {https://juser.fz-juelich.de/record/811979},
}