@Article{Bientinesi:2005:RLA,
  author =       "Paolo Bientinesi and Enrique S. Quintana-Ort\'{i} and Robert A. 
                 van de Geijn",
  title =        "Representing Linear Algebra Algorithms in Code: The {FLAME} 
                  Application Programming Interfaces",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "31",
  number =       "1",
  month =        mar,
  year =         "2005",
  pages =         "27--59",
  URL =          "http://doi.acm.org/10.1145/1055531.1055533", 
  abstract =     "In this paper, we present a number of Application Program
                 Interfaces (APIs) for coding linear algebra algorithms.  On the
                 surface, these APIs for the MATLAB M-script and C programming
                 languages appear to be simple, almost trivial, extensions of those
                 languages.  Yet with them, the task of programming and maintaining
                 families of algorithms for a broad spectrum of linear algebra
                 operations is greatly simplified.  In combination with our Formal
                 Linear Algebra Methods Environment (FLAME) approach to deriving such
                 families of algorithms, dozens of algorithms for a single linear
                 algebra operation can be derived, verified to be correct, implemented,
                 and tested, often in a matter of minutes per algorithm.  Since the
                 algorithms are expressed in code much like they are explained in a
                 classroom setting, these APIs become not just a tool for implementing
                 libraries, but also a valuable tool for teaching the algorithms that
                 are incorporated in the libraries.  In combination with an extension
                 of the Parallel Linear Algebra Package (PLAPACK) API, the approach
                 presents a migratory path from algorithm to MATLAB implementation to
                 high-performance sequential implementation to parallel implementation.
                 Finally, the APIs are being used to create a repository of algorithms
                 and implementations for linear algebra operations, the FLAME Interface
                 REpository (FIRE), which already features hundreds of algorithms for
                 dozens of commonly encountered linear algebra operations.",
}