BibTeX
@INCOLLECTION{
Pusch1996JSa,
author = "Gordon D. Pusch",
editor = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank",
title = "Jet Space as the Geometric Arena of Automatic Differentiation",
booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
pages = "5362",
publisher = "SIAM",
address = "Philadelphia, PA",
key = "Pusch1996JSa",
crossref = "Berz1996CDT",
abstract = "I discuss the connection between the differential geometric concept of a {\em
jet\/} and Berz's differential algebra (DA) method of automatic differentiation to
arbitrarily high order with respect to arbitrarily many variables. A DAvalued object is a
representation of the {\em targetspace projection\/} of a jet under a particular
coordinate chart. Jets generalize the coordinateindependent concept of the {\em tangent
map\/} of a function to higher orders of contact. Since the tangent map unifies the concepts of
derivative, tangent vector, and the tangent linear model into a single geometrical object, the
geometrical framework of higherorder differentiation and its natural connections to perturbation
theory and to higherorder tangent models become clear. Jets contain additional structure beyond
that of DA vectors; in particular, the jet concept meshes nicely with both the
``applicative'' and ``object oriented'' programming paradigms. The jet concept
may therefore provide insights to guide new implementations of automatic differentiation. In
particular, jets may help to define derivatives of composite objects such as structures; they also
introduce a new means of errorchecking, since operations combining jets originating from different
source points are undefined.",
keywords = "Jet spaces, differential geometry, coordinatefree differentiation, fiber
bundles.",
year = "1996"
}
