A Leibniz notation for automatic differentiation

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

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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.
Original languageEnglish
Title of host publicationRecent Advances in Algorithmic Differentiation
PublisherSpringer Nature
Pages1-9
ISBN (Print)978-3-642-30022-6
DOIs
Publication statusPublished - 2012

Publication series

NameLecture Notes in Computational Science and Engineering
PublisherSpringer
Volume87

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