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@ARTICLE{Singer:864105,
      author       = {Singer, Sanja and Di Napoli, Edoardo and Novaković, Vedran
                      and Čaklović, Gayatri},
      title        = {{T}he {LAPW} {M}ethod with {E}igendecomposition {B}ased on
                      the {H}ari--{Z}immermann {G}eneralized {H}yperbolic {SVD}},
      journal      = {SIAM journal on scientific computing},
      volume       = {42},
      number       = {5},
      issn         = {0196-5204},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2019-04005},
      pages        = {C265–C293},
      year         = {2020},
      abstract     = {In this paper we propose an accurate, highly parallel
                      algorithm for the generalized eigendecomposition of a matrix
                      pair $(H, S)$, given in a factored form $(F^{\ast} J F,
                      G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and
                      Hermitian, and $S$ is positive definite. These type of
                      matrices emerge from the representation of the Hamiltonian
                      of a quantum mechanical system in terms of an overcomplete
                      set of basis functions. This expansion is part of a class of
                      models within the broad field of Density Functional Theory,
                      which is considered the golden standard in Condensed Matter
                      Physics. The overall algorithm consists of four phases, the
                      second and the fourth being optional, where the two last
                      phases are computation of the generalized hyperbolic SVD of
                      a complex matrix pair $(F,G)$, according to a given matrix
                      $J$ defining the hyperbolic scalar product. If $J = I$, then
                      these two phases compute the GSVD in parallel very
                      accurately and efficiently.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / PhD no Grant - Doktorand ohne besondere
                      Förderung (PHD-NO-GRANT-20170405) / Simulation and Data
                      Laboratory Quantum Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)PHD-NO-GRANT-20170405 /
                      G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000600650100021},
      doi          = {10.1137/19M1277813},
      url          = {https://juser.fz-juelich.de/record/864105},
}