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"
}