BibTeX
@ARTICLE{
         Naumann2005ADE,
       author = "Uwe Naumann and Jan Riehme",
       title = "A Differentiation-Enabled {Fortran} 95 Compiler",
       journal = "{ACM} Transactions on Mathematical Software",
       volume = "31",
       number = "4",
       year = "2005",
       pages = "458--474",
       ad_tools = "NAGWare Fortran 95",
       url = "http://doi.acm.org/10.1145/1114268.1114270",
       abstract = "The availability of first derivatives of vector functions is crucial for the
         robustness and effciency of a large number of numerical algorithms. An upcoming new version of the
         differentiation-enabled NAGWare Fortran 95 compiler is described that uses programming language
         extensions and a semantic code transformation known as automatic differentiation to provide
         Jacobians of numerical programs with machine accuracy. We describe a new user interface as well as
         the relevant algorithmic details. In particular, we focus on the source transformation approach that
         generates locally optimal gradient code for single assignments by vertex elimination in the
         linearized computational graph. Extensive tests show the superiority of this method over the current
         overloading-based approach. The robustness and convenience of the new compiler-feature is
         illustrated by various case studies."
}