BibTeX
@INCOLLECTION{
         Rall2005PoA,
       author = "Louis B. Rall",
       title = "Perspectives on Automatic Differentiation: {P}ast, Present, and Future?",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       abstract = "Automatic (or algorithmic) differentiation (AD) is discussed from the standpoint of
         transformation of algorithms for evaluation of functions into algorithms for evaluation of their
         derivatives. Such finite numerical algorithms are commonly formulated as computer programs or
         subroutines, hence the use of the term ``automatic.'' Transformations to evaluate
         derivatives are thus based on the well-known formulas for derivatives of arithmetic operations and
         various differentiable intrinsic functions which constitute the basic steps of the algorithm. The
         chain rule of elementary calculus then guarantees the validity of the process. The chain rule can be
         applied in various ways to obtain what are called the ``forward'' and
         ``reverse'' modes of automatic differentiation. These modes are described in the context
         of the early stages of the development of AD, and a brief comparGUM1995Gttn is given. Following this
         brief survey, a view of present tasks and future prospects focuses on the need for further
         education, communication of results, and expansion of areas of application of AD. In addition, some
         final remarks are made concerning extension of the method of algorithm transformation to problems
         other than derivative evaluation.",
       crossref = "Bucker2005ADA",
       ad_theotech = "General, History",
       pages = "1--14",
       doi = "10.1007/3-540-28438-9_1"
}