Publication: The complex-step derivative approximation
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The complex-step derivative approximation

- Article in a journal -
 

Author(s)
Joaquim R. R. A. Martins , Peter Sturdza , Juan J. Alonso

Published in
ACM Transactions on Mathematical Software

Year
2003

Abstract
The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.

AD Theory and Techniques
Complex Step Differentiation

BibTeX
@ARTICLE{
         Martins2003Tcs,
       author = "Joaquim R. R. A. Martins and Peter Sturdza and Juan J. Alonso",
       title = "The complex-step derivative approximation",
       journal = "{ACM} Transactions on Mathematical Software",
       volume = "29",
       number = "3",
       pages = "245--262",
       year = "2003",
       coden = "ACMSCU",
       doi = "http://doi.acm.org/10.1145/838250.838251",
       issn = "0098-3500",
       bibdate = "Thu Aug 7 14:01:48 MDT 2003",
       bibsource = "http://www.acm.org/pubs/contents/journals/toms/",
       abstract = "The complex-step derivative approximation and its application to numerical
         algorithms are presented. Improvements to the basic method are suggested that further increase its
         accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general
         procedure for the implementation of the complex-step method is described in detail and a script is
         developed that automates its implementation. Automatic implementations of the complex-step method
         for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The
         complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities
         are compared to results given by finite differences. The resulting sensitivities are shown to be as
         accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make
         these complex-step derivative approximation tools very attractive options for sensitivity
         analysis.",
       month = "sep",
       ad_theotech = "Complex Step Differentiation"
}


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