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    The Principles of First Order Automatic Differentiation


    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]


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    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:

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