@Article{Hogg:2009:FRM,
  author =       "Jonathan Hogg and Jennifer Scott",
  title =        "A fast and robust mixed precision solver for the solution of sparse symmetric linear
                  systems",
  journal =      "{ACM} Transactions on Mathematical Software",
  accepted =     "30 October 2009",
  upcoming =     "true", 
  abstract =     "
                 In many current and emerging computing architectures,
                 single precision calculations are at least twice as
                 fast as double precision calculations. In addition, the
                 use of single precision may reduce pressure on memory
                 bandwidth. The penalty for using single precision for the
                 solution of linear systems is a potential loss of accuracy
                 in the computed solutions. For sparse linear systems,
                 the use of mixed precision in which double precision
                 iterative methods are preconditioned by a single precision
                 factorization can enable the recovery of high precision
                 solutions more quickly and use less memory than a sparse
                 direct solver run using double precision arithmetic.
                 
                 In this paper, we consider the use of single precision
                 within direct solvers for sparse symmetric linear systems,
                 exploiting both the reduction in memory requirements and
                 the performance gains. We develop a practical algorithm to
                 apply a mixed precision approach and suggest parameters
                 and techniques to minimize the number of solves required
                 by the iterative recovery process. These experiments
                 provide the basis for our new code hsl_ma79 --- a fast,
                 robust, mixed precision sparse symmetric solver that will
                 be included in the mathematical software library HSL.
                 
                 Numerical results for a wide range of problems from
                 practical applications are presented.",
}