@Article{Fraysse:2005:ASG,
  author =       "Val\'{e}rie Frayss\'{e} and Luc Giraud and Serge Gratton and 
                 Julien Langou",
  title =        "Algorithm 842: A Set of {GMRES} Routines for Real and Complex 
                 Arithmetics on High Performance Computers",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "31",
  number =       "2",
  month =        jun,
  year =         "2005",
  pages =        "228--238",
  URL =          " http://doi.acm.org/10.1145/1067967.1067970",
  abstract =     "In this paper we describe our implementations of the GMRES algorithm 
                 for both real and complex, single and double precision arithmetics 
                 suitable for serial, shared memory and distributed memory computers. 
                 For the sake of portability, simplicity, flexibility and effciency 
                 the GMRES solvers have been implemented in Fortran 77 using the 
                 reverse communication mechanism for the matrix-vector product, the 
                 preconditioning and the dot product computations. For distributed 
                 memory computation, several orthogonalization procedures have been 
                 implemented to reduce the cost of the dot product calculation, that 
                 is a well-known bottleneck of effciency for the Krylov methods. Either 
                 implicit or explicit calculation of the residual at restart are 
                 possible depending on the actual cost of the matrix-vector product. 
                 Finally the implemented stopping criterion is based on a normwise 
                 backward error.",
}