Publication: Reverse Automatic Differentiation of Linear Multistep Methods
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Reverse Automatic Differentiation of Linear Multistep Methods

- incollection -
 

Author(s)
Adrian Sandu

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. In this paper we analyze the consistency and stability properties of discrete adjoints of linear multistep methods. The analysis reveals that the discrete linear multistep adjoints are, in general, inconsistent approximations of the adjoint ODE solution along the trajectory. The discrete adjoints at the initial time converge to the adjoint ODE solution with the same order as the original linear multistep method. Discrete adjoints inherit the zero-stability properties of the forward method. Numerical results confirm the theoretical findings.

Cross-References
Bischof2008AiA

AD Theory and Techniques
Adjoint

BibTeX
@INCOLLECTION{
         Sandu2008RAD,
       title = "Reverse Automatic Differentiation of Linear Multistep Methods",
       doi = "10.1007/978-3-540-68942-3_1",
       author = "Adrian Sandu",
       abstract = "Discrete adjoints are very popular in optimization and control since they can be
         constructed automatically by reverse mode automatic differentiation. In this paper we analyze the
         consistency and stability properties of discrete adjoints of linear multistep methods. The analysis
         reveals that the discrete linear multistep adjoints are, in general, inconsistent approximations of
         the adjoint ODE solution along the trajectory. The discrete adjoints at the initial time converge to
         the adjoint ODE solution with the same order as the original linear multistep method. Discrete
         adjoints inherit the zero-stability properties of the forward method. Numerical results confirm the
         theoretical findings.",
       crossref = "Bischof2008AiA",
       pages = "1--12",
       booktitle = "Advances in Automatic Differentiation",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_theotech = "Adjoint"
}


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