Optimal Jacobian accumulation is NP-complete

Authors:
Uwe Naumann
Affiliations:
RWTH Aachen University, Software and Tools for Computational Engineering, Department of Computer Science, 52056, Aachen, Germany
Venue:
Mathematical Programming: Series A and B
Year:
2007

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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.