BibTeX
@INCOLLECTION{
         Shamseddine1996EHi,
       author = "Khodr Shamseddine and Martin Berz",
       editor = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank",
       title = "Exception Handling in Derivative Computation with Nonarchimedean Calculus",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "37--51",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Shamseddine1996EHi",
       crossref = "Berz1996CDT",
       abstract = "While conventional computational differentiation based on the forward or reverse
         modes allows highly accurate computation of derivatives, there are situations where these modes fail
         to produce the values of derivatives, although the underlying function is differentiable. Typical
         examples of this phenomenon are connected to the occurrence of branch points in coding as in IF-ELSE
         structures as well as the occurrence of some non-differentiable parts that do not affect the
         differentiability of the end result. We show that based on ideas of nonarchimedean calculus on
         Levi-Civita fields, these problems can be avoided. It is possible to rigorously decide whether a
         function is differentiable or not at any given point, and if it is, to determine its derivatives to
         any order, even if the coding exhibits branch points or non-differentiable pieces. We give details
         of an implementation of the method and examples for its use for typical pathological problems.",
       keywords = "Exception handling, nonarchimedean calculus, nonarchimedean field, Heaviside
         function, smoothness properties of computer functions, standard form of computer functions,
         derivatives are differential quotients, differentiability of computer functions, COSY INFINITY.",
       referred = "[Berz1996CaN], [Berz2002TaU], [Pusch1996JSa].",
       year = "1996"
}