@Article{Hogg:2013:PST,
  author =       "Jonathan D. Hogg and Jennifer A.Scott",
  title =        "Pivoting strategies for tough sparse indefinite systems",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "40",
  number =       "1",
  year =         "2013",
  month =        oct,
  pages =        "4:1--4:19",
  url =          "http://doi.acm.org/10.1145/2513109.2513113",
  accepted =     "11 April 2013",
  abstract =     "
                  The performance of a sparse direct solver is dependent upon
                  the pivot sequence that is chosen before the factorization
                  begins.  In the case of symmetric indefinite systems,
                  it may be necessary to modify this sequence during
                  the factorization to ensure numerical stability. These
                  modifications can have serious consequences in terms
                  of time as well as the memory and flops required for
                  the factorization and subsequent solves.  This study
                  focuses on hard-to-solve sparse symmetric indefinite
                  problems for which standard threshold partial pivoting
                  leads to significant modifications.  We perform a
                  detailed review of pivoting strategies that are  aimed
                  at reducing the modifications without compromising
                  numerical stability. Extensive numerical experiments
                  are performed on a set of tough problems arising
                  from practical applications. Based on our findings,
                  we make recommendations on which strategy to use and,
                  in particular, a matching-based approach is recommended
                  for numerically challenging problems.",
}