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@ARTICLE{DiNapoli:150533,
      author       = {Di Napoli, Edoardo and Berljafa, Mario},
      title        = {{B}lock iterative eigensolvers for sequences of correlated
                      eigenvalue problems},
      journal      = {Computer physics communications},
      volume       = {184},
      number       = {11},
      issn         = {0010-4655},
      address      = {Amsterdam},
      publisher    = {North Holland Publ. Co.},
      reportid     = {FZJ-2014-00587},
      pages        = {2478 - 2488},
      year         = {2013},
      abstract     = {In Density Functional Theory simulations based on the LAPW
                      method, each self-consistent field cycle comprises dozens of
                      large dense generalized eigenproblems. In contrast to
                      real-space methods, eigenpairs solving for problems at
                      distinct cycles have either been believed to be independent
                      or at most very loosely connected. In a recent study [7], it
                      was demonstrated that, contrary to belief, successive
                      eigenproblems in a sequence are strongly correlated with one
                      another. In particular, by monitoring the subspace angles
                      between eigenvectors of successive eigenproblems, it was
                      shown that these angles decrease noticeably after the first
                      few iterations and become close to collinear. This last
                      result suggests that we can manipulate the eigenvectors,
                      solving for a specific eigenproblem in a sequence, as an
                      approximate solution for the following eigenproblem. In this
                      work we present results that are in line with this
                      intuition. We provide numerical examples where opportunely
                      selected block iterative eigensolvers benefit from the reuse
                      of eigenvectors by achieving a substantial speed-up. The
                      results presented will eventually open the way to a
                      widespread use of block iterative eigensolvers in ab initio
                      electronic structure codes based on the LAPW approach.},
      cin          = {JSC},
      ddc          = {004},
      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)16},
      eprint       = {1206.3768},
      howpublished = {arXiv:1206.3768},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1206.3768;\%\%$},
      UT           = {WOS:000324664100014},
      doi          = {10.1016/j.cpc.2013.06.017},
      url          = {https://juser.fz-juelich.de/record/150533},
}