Abstract
Notwithstanding the superiority of the Leibniz notation for differential
calculus, the dot-and-bar notation predominantly used by the Automatic Differentiation community is resolutely Newtonian. In this paper we extend the Leibnitz notation to include the reverse (or adjoint) mode of Automatic Differentiation, and use it to demonstrate the stepwise numerical equivalence of the three approaches using the reverse mode to obtain second order derivatives, namely forward-over-reverse, reverse-over-forward, and reverse-over-reverse.
calculus, the dot-and-bar notation predominantly used by the Automatic Differentiation community is resolutely Newtonian. In this paper we extend the Leibnitz notation to include the reverse (or adjoint) mode of Automatic Differentiation, and use it to demonstrate the stepwise numerical equivalence of the three approaches using the reverse mode to obtain second order derivatives, namely forward-over-reverse, reverse-over-forward, and reverse-over-reverse.
| Original language | English |
|---|---|
| Title of host publication | Recent Advances in Algorithmic Differentiation |
| Publisher | Springer Nature |
| Pages | 1-9 |
| ISBN (Print) | 978-3-642-30022-6 |
| DOIs | |
| Publication status | Published - 2012 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Publisher | Springer |
| Volume | 87 |