BibTeX
@INCOLLECTION{
         Kaminski2005ESf,
       author = "Thomas Kaminski and Ralf Giering and Michael Vo{\ss}beck",
       title = "Efficient Sensitivities for the Spin-up Phase",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       abstract = "In geosciences, it is common to spin up models by integrating with annually
         repeated boundary conditions. AD-generated code for evaluating sensitivities of the final
         cyclo-stationary state with respect to model parameters or boundary conditions usually includes a
         similar iteration for the derivative statements, possibly with a reduced number of iterations. We
         evaluate an alternative strategy that first carries out the spin-up, then evaluates the full
         Jacobian for the final iteration and then applies the implicit function theorem to solve for the
         sensitivities of the cyclo-stationary state. We demonstrate the benefit of the strategy for the
         spin-up of a simple box-model of the atmospheric transport. We derive a heuristic inequality for
         this benefit, which increases with the number of iterations and decreases with the size of the state
         space.",
       crossref = "Bucker2005ADA",
       ad_tools = "TAF",
       pages = "285--293",
       doi = "10.1007/3-540-28438-9_25",
       ad_area = "General",
       ad_theotech = "Iteration",
       PDF = "http://www.FastOpt.com/papers/kaminskial04b.pdf"
}