BibTeX
@ARTICLE{
         Wagner2010Ote,
       title = "On the efficient computation of high-order derivatives for implicitly defined
         functions",
       author = "M. Wagner, B.-J. Schaefer, and A. Walther",
       year = "2010",
       journal = "Computer Physics Communications",
       volume = "181",
       pages = "756--764",
       abstract = "Scientific studies often require the precise calculation of derivatives. In many
         cases an analytical calculation is not feasible and one resorts to evaluating derivatives
         numerically. These are error-prone, especially for higher-order derivatives. A technique based on
         algorithmic differentiation is presented which allows for a precise calculation of higher-order
         derivatives. The method can be widely applied even for the case of only numerically known, implicit
         dependencies which totally hamper a semi-analytical calculation of the derivatives. As a
         demonstration the method is applied to a quantum field theoretical physical model. The results are
         compared with standard numerical derivative methods.",
       ad_area = "Physics",
       ad_tools = "ADOL-C",
       ad_theotech = "Higher Order"
}