article

The complex-step derivative approximation

Authors:

Joaquim R. R. A. Martins,

Juan J. AlonsoAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 29, Issue 3

Pages 245 - 262

https://doi.org/10.1145/838250.838251

Published: 01 September 2003 Publication History

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.

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The complex-step derivative approximation

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 29, Issue 3

September 2003

107 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/838250

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Copyright © 2003 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2003

Published in TOMS Volume 29, Issue 3

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