@Article{Scott:2014:HER,
  author =       "Jennifer Scott and Miroslav Tuma",
  title =        "{HSL MI28}: An Efficient and Robust Limited-Memory
                  Incomplete {Cholesky} Factorization Code",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       40,
  number =       4,
  year    =      2014,
  month   =      jun,
  pages =        "24:1--24:19",
  url =          "http://doi.acm.org/10.1145/2617555",
  accepted =     "18 October 2013",
  abstract =     "
                  This article focuses on the design and development of
                  a new robust and efficient general-purpose incomplete
                  Cholesky factorization package HSL_MI28, which is
                  available within the HSL mathematical software library.
                  It implements a limited memory approach that exploits
                  ideas from the positive semidefinite Tismenetsky-Kaporin
                  modification scheme and, through the incorporation of
                  intermediate memory, is a generalization of the widely
                  used ICFS algorithm of Lin and Mor\'{e}. Both the density
                  of the incomplete factor and the amount of memory used
                  in its computation are under the user's control. The
                  performance of HSL_MI28 is demonstrated using extensive
                  numerical experiments involving a large set of test
                  problems arising from a wide range of real-world
                  applications. The numerical experiments are used to
                  isolate the effects of scaling, ordering, and dropping
                  strategies so as to assess their usefulness in the
                  development of robust algebraic incomplete factorization
                  preconditioners and to select default settings
                  for HSL_MI28. They also illustrate the significant
                  advantage of employing a modest amount of intermediate
                  memory. Furthermore, the results demonstrate that, with
                  limited memory, high-quality yet sparse general-purpose
                  preconditioners are obtained. Comparisons are made with
                  ICFS, with a level-based incomplete factorization code
                  and, finally, with a state-of-the-art direct solver.",
}