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@ARTICLE{Willems:57019,
      author       = {Willems, P. R. and Lang, B. and Vömel, C.},
      title        = {{C}omputing the bidiagonal {SVD} using multiple relatively
                      robust representations},
      journal      = {SIAM journal on matrix analysis and applications},
      volume       = {28},
      issn         = {0895-4798},
      address      = {Philadelphia, Pa.},
      publisher    = {Soc.},
      reportid     = {PreJuSER-57019},
      pages        = {907 - 926},
      year         = {2006},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {We describe the design and implementation of a new
                      algorithm for computing the singular value decomposition
                      (SVD) of a real bidiagonal matrix. This algorithm uses ideas
                      developed by Grosser and Lang that extend Parlett's and
                      Dhillon's multiple relatively robust representations (MRRR)
                      algorithm for the tridiagonal symmetric eigenproblem. One
                      key feature of our new implementation is that k singular
                      triplets can be computed using only O(nk) storage units and
                      floating point operations, where n is the dimension of the
                      matrix. The algorithm will be made available as routine
                      xBDSCR in the upcoming new release of the LAPACK library.},
      keywords     = {J (WoSType)},
      cin          = {ZAM},
      ddc          = {510},
      cid          = {I:(DE-Juel1)VDB62},
      pnm          = {Scientific Computing},
      pid          = {G:(DE-Juel1)FUEK411},
      shelfmark    = {Mathematics, Applied},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000243280600002},
      doi          = {10.1137/050628301},
      url          = {https://juser.fz-juelich.de/record/57019},
}