Many modern numerical methods in computational science and engineering rely on derivatives of mathematical models for the phenomena under investigation . The computation of these derivatives often represents the bottleneck in termsof overall runtime performance . The chain rule of differentiation is the fundamental prerequisite for computing accurate derivatives of composite functions which perform apotentially very large number of elemental function evaluations . Pointers to research on its approximate solutionare given . We formulate the Chain Rule Differentiation and we prove it to be NP-complete. Pointers are given .

Author(s) : Uwe Naumann

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Keywords : rule - chain - derivatives - pointers - computational -

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