Advances in Automatic Differentiation

1. Front Matter

   Pages I-XVIII

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2. Reverse Automatic Differentiation of Linear Multistep Methods

   • Adrian Sandu

   Pages 1-12

3. Call Tree Reversal is NP-Complete

   • Uwe Naumann

   Pages 13-22

4. On Formal Certification of AD Transformations

   • Emmanuel M. Tadjouddine

   Pages 23-33

5. Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation

   • Mike B. Giles

   Pages 35-44

6. A Modification of Weeks’ Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation

   • Salvatore Cuomo, Luisa D’Amore, Mariarosaria Rizzardi, Almerico Murli

   Pages 45-54

7. A Low Rank Approach to Automatic Differentiation

   • Hany S. Abdel-Khalik, Paul D. Hovland, Andrew Lyons, Tracy E. Stover, Jean Utke

   Pages 55-65

8. Algorithmic Differentiation of Implicit Functions and Optimal Values

   • Bradley M. Bell, James V. Burke

   Pages 67-77

9. Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient

   • Barak A. Pearlmutter, Jeffrey Mark Siskind

   Pages 79-90

10. A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs

    • Sanjukta Bhowmick, Paul D. Hovland

    Pages 91-102

11. On the Practical Exploitation of Scarsity

    • Andrew Lyons, Jean Utke

    Pages 103-114

12. Design and Implementation of a Context-Sensitive, Flow-Sensitive Activity Analysis Algorithm for Automatic Differentiation

    • Jaewook Shin, Priyadarshini Malusare, Paul D. Hovland

    Pages 115-125

13. Efficient Higher-Order Derivatives of the Hypergeometric Function

    • Isabelle Charpentier, Claude Dal Cappello, Jean Utke

    Pages 127-137

14. The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method

    • Isabelle Charpentier, Arnaud Lejeune, Michel Potier-Ferry

    Pages 139-149

15. Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals

    • Massimiliano Martinelli, Laurent Hascoët

    Pages 151-161

16. Parallel Reverse Mode Automatic Differentiation for OpenMP Programs with ADOL-C

    • Christian Bischof, Niels Guertler, Andreas Kowarz, Andrea Walther

    Pages 163-173

17. Adjoints for Time-Dependent Optimal Control

    • Jan Riehme, Andrea Walther, Jörg Stiller, Uwe Naumann

    Pages 175-185

18. Development and First Applications of TAC++

    • Michael Voßbeck, Ralf Giering, Thomas Kaminski

    Pages 187-197

19. TAPENADE for C

    • Valérie Pascual, Laurent Hascoët

    Pages 199-209

20. Coping with a Variable Number of Arguments when Transforming MATLAB Programs

    • H. Martin Bücker, Andre Vehreschild

    Pages 211-222

The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic “silver bullet” polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

• 3D
• AES
• Computer
• MATLAB
• OpenMP
• algorithms
• automatic differentiation
• calculus
• construction
• development
• modeling
• optimization
• programming
• programming language
• sensitivity analysis

• Institute for Scientific Computing, RWTH Aachen University, Aachen, Germany

  Christian H. Bischof, H. Martin Bücker

• Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, USA

  Paul Hovland, Jean Utke

• Software and Tools for Computational Engineering, RWTH Aachen University, Aachen, Germany

  Uwe Naumann

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