Numerical Algorithms

, Volume 58, Issue 2, pp 261–292 | Cite as

A new algorithm for index determination in DAEs using algorithmic differentiation

  • René Lamour
  • Dagmar Monett
Original Paper


We present an approach for determining the tractability index using truncated polynomial arithmetic. In particular, computing the index this way generates a sequence of matrices that contains itself derivatives. We implement the time differentiations using algorithmic differentiation techniques, specially using the standard ADOL-C package, with which calculating the derivatives becomes a simple shift and scaling of coefficients. We present the theory supporting the procedure we propose, as well as the implementation issues behind it to provide a convenient interface to the standard ADOL-C functionality. We give also examples of academic and practical problems and report several experimental results we have obtained with them.


DAE Index determination Tractability index AD Algorithmic differentiation Automatic differentiation 

AMS 2000 Subject Classifications

65L80 65D25 68W30 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Computer Science Department and Department of Cooperative StudiesBerlin School of Economics and LawBerlinGermany

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