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@INPROCEEDINGS{DiNapoli:21977,
      author       = {Di Napoli, E.},
      title        = {{B}lock iterative solvers for sequences of correlated dense
                      eigenvalue problems},
      reportid     = {PreJuSER-21977},
      year         = {2012},
      note         = {Record converted from VDB: 12.11.2012},
      comment      = {7th International Conference on Parallel Matrix Algorithms
                      and Applications (PMAA 2012)},
      booktitle     = {7th International Conference on
                       Parallel Matrix Algorithms and
                       Applications (PMAA 2012)},
      abstract     = {Simulations in Density Functional Theory are made of dozens
                      of sequences, where each sequence groups together
                      eigenproblems with increasing self-consistent cycle
                      iteration index. In a recent study, it has been shown a high
                      degree of correlation between successive eigenproblems of
                      each sequence. In particular, by tracking the evolution over
                      iterations of the angles between eigenvectors of successive
                      eigenproblems, it was shown that eigenvectors are almost
                      collinear after the first few iterations. This result
                      suggests we could use eigenvectors, computed at a certain
                      iteration, as approximate solutions for the problem at the
                      successive one. The key element is to exploit the
                      collinearity between vectors of adjacent problems in order
                      to improve the performance of the eigensolver. In this study
                      we provide numerical examples where opportunely selected
                      block iterative eigensolvers benefit from the re-use of
                      eigenvectors when applied to sequences of eigenproblems
                      extracted from simulations of real-world materials. In our
                      investigation we vary several parameters in order to address
                      how the solvers behave under different conditions. In most
                      cases our study shows that, when the solvers are fed
                      approximated eigenvectors as opposed to random vectors, they
                      obtain a substantial speed-up and could become a valid
                      alternative to direct methods.},
      month         = {Jun},
      date          = {2012-06-28},
      organization  = {London, UK, 28 Jun 2012},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing / Simulation and Data Laboratory
                      Quantum Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/21977},
}