Publication: On the efficient computation of high-order derivatives for implicitly defined functions
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On the efficient computation of high-order derivatives for implicitly defined functions

- Article in a journal -
 

Area
Physics

Author(s)
M. Wagner , B. -J. Schaefer , , A. Walther

Published in
Computer Physics Communications

Year
2010

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 Tools
ADOL-C

AD Theory and Techniques
Higher Order

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"
}


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