Beautiful differentiation

@inproceedings{Elliott2009BeautifulD,
  title={Beautiful differentiation},
  author={Conal Elliott},
  booktitle={ICFP},
  year={2009}
}
Automatic differentiation (AD) is a precise, efficient, and convenient method for computing derivatives of functions. Its forward-mode implementation can be quite simple even when extended to compute all of the higher-order derivatives as well. The higher-dimensional case has also been tackled, though with extra complexity. This paper develops an implementation of higher-dimensional, higher-order, forward-mode AD in the extremely general and elegant setting of calculus on manifolds and derives… CONTINUE READING