Summary
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.
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Sandu, A. (2008). Reverse Automatic Differentiation of Linear Multistep Methods. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds) Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_1
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DOI: https://doi.org/10.1007/978-3-540-68942-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68935-5
Online ISBN: 978-3-540-68942-3
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