Mathematical Programming

, Volume 112, Issue 2, pp 427–441

Optimal Jacobian accumulation is NP-complete


DOI: 10.1007/s10107-006-0042-z

Cite this article as:
Naumann, U. Math. Program. (2008) 112: 427. doi:10.1007/s10107-006-0042-z


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.


Automatic differentiation Complexity NP-completeness 

Mathematics Subject Classification (2000)

26B10 68Q17 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Software and Tools for Computational Engineering, Department of Computer ScienceRWTH Aachen UniversityAachenGermany

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