PARA'04 State-of-the-Art
in Scientific Computing
June 20-23, 2004 (Home page)
Updated: January 29, 2004

Automatic Differentiation

Andrea Walther
Technical University of Dresden
Germany
email: awalther@math.tu-dresden.de

This tutorial gives a detailed introduction into the chainrule based technique of automatic differentiation (AD) that provides first and higher derivatives without incurring any truncation errors. In particular, the following topics will be covered:

• forward and reverse mode to compute first derivatives
• second order adjoint to calculate second derivatives
• computation of higher order derivatives using Taylor arithmetic
• analysis of the derivative evaluation costs
• implementation strategies and challenges

Several examples will illustrate the theoretical results. Furthermore, some AD tools, selected as a reasonably representative sample, can be tested in supervised, hands-on exercises.

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