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Optimal Jacobian accumulation is NP-complete

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Abstract

We show that the problem of accumulating Jacobian matrices by using a minimal number of floating-point operations is NP-complete by reduction from Ensemble Computation. The proof makes use of the fact that, deviating from the state-of-the-art assumption, algebraic dependences can exist between the local partial derivatives. It follows immediately that the same problem for directional derivatives, adjoints, and higher derivatives is NP-complete, too.

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  1. Software and Tools for Computational Engineering, Department of Computer Science, RWTH Aachen University, 52056, Aachen, Germany

    Uwe Naumann

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  1. Uwe Naumann
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Correspondence to Uwe Naumann.

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Naumann, U. Optimal Jacobian accumulation is NP-complete. Math. Program. 112, 427–441 (2008). https://doi.org/10.1007/s10107-006-0042-z

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  • DOI: https://doi.org/10.1007/s10107-006-0042-z

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