@Article{Koikari:2008:ABS,
  author =       "S. Koikari",
  title =        "Algorithm 894: On a Block {Schur--Parlett} Algorithm for 
		  $\varphi$-functions Based on the sep-inverse Estimate",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "36",
  number =       "2",
  pages =        "12:1--12:20",
  URL =          "http://doi.acm.org/10.1145/1499096.1499101",
  month =        mar,
  year =         2009,
  accepted =     "3 September 2008",
  abstract =     "
		 FORTRAN 95 software is provided
		 for computing the matrix values
		 of $\varphi$-functions required in
		 exponential integrators. The subroutines
		 in the library accept as their argument a
		 full, diagonal, or upper quasi-triangular
		 matrix with real or complex entries in
		 one of four precisions. Two different
		 algorithms are implemented, one is the
		 scaling and squaring method, and the
		 other is a modified block Schur--Parlett
		 algorithm. In the latter algorithm,
		 a recursive three-by-three blocking
		 is applied to the argument based on an
		 estimate of the sep-inverse function. The
		 estimation of the sep-inverse function
		 is carried out by Hager--Higham estimator
		 implemented as the subroutine {\tt xLACON}
		 in LAPACK. Our modifications to the block
		 Schur--Parlett algorithm are described
		 together with the results of numerical
		 experiments.",
}