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Hoffmann, Philipp (2014) The Principles of First Order Automatic Differentiation. Working Paper. arXiv.org.
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Official URL: arXiv:1411.0583 [math.NA]
Abstract
This article provides a short overview of the theory of First Order Automatic Differentiation (AD) for readers unfamiliar with this topic. In particular, we summarize different characterisations of Forward AD, like the
vector-matrix based approach, the idea of lifting functions to the algebra
of dual numbers, the method of Taylor series expansion on dual numbers
and the application of the push-forward operator. We give short, but precise mathematical descriptions of these methods and show why they all
reduce to the same actual chain of computations (and are, hence, equivalent). Finally, we give a short summary of Reverse AD and again point
out the underlying computational steps.
| Item Type: | Monograph (Working Paper) |
|---|---|
| Additional Information: | This work was supported by Science Foundation Ireland grant 09/IN.1/I2637. |
| Keywords: | Automatic Differentiation; Forward AD; Reverse AD; Dual Numbers; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 5857 |
| Depositing User: | Philipp Hoffmann |
| Date Deposited: | 18 Feb 2015 15:34 |
| Publisher: | arXiv.org |
| Refereed: | No |
| Funders: | Science Foundation Ireland (SFI) |
| URI: | https://mu.eprints-hosting.org/id/eprint/5857 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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