The connection between the complex-step derivative approximation and algorithmic differentiation

Abstract

This paper presents improvements to the complexstep derivative approximation method which increase its accuracy and robustness. These improvements unveil the connection to algorithmic dierentiation theory. The choice between these two methods then hinges on a trade-o between ease of implementation and execution eciency. Automatic implementations for Fortran and C/C++ are presented and their relative merits are discussed. These new methods were successfully implemented in two very large multidisciplinary programs and the resulting sensitivities are shown to be as accurate as the analyses. Accuracy and ease of implementation make these tools very attractive options for sensitivity analysis.