@Article{Voemel:2009:SMA,
  author =       "Christof Voemel",
  title =        "ScaLAPACK's MRRR Algorithm",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "37",
  number =       "1",
  accepted =     "6 March 2009",
  upcoming =     "true", 
  abstract =     "
                 The sequential algorithm of Multiple Relatively Robust
                 Representations, MRRR, can compute numerically orthogonal
                 eigenvectors of a symmetric tridiagonal matrix T with
                 O(n^2) cost. This paper describes the design of the
                 new MRRR-based ScaLAPACK driver PDSYEVR for dense
                 real symmetric matrices. Compared to other ScaLAPACK
                 codes, this new code has two advantages. Unlike Divide and
                 Conquer and QR, MRRR can compute subsets of eigenpairs at
                 reduced cost. And in contrast to inverse iteration, it
                 is guaranteed to produce the right answer. We describe
                 in detail the algorithmic part of our new code and
                 analyze its performance on a number of matrices from
                 industrial applications.",
}