A Hitchhiker’s Guide to Automatic Differentiation
This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the idea of lifting functions to the algebra of dual numbers, the m...
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| Veröffentlicht in: | Numerical algorithms 2016-07, Vol.72 (3), p.775-811 |
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| container_title | Numerical algorithms |
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| creator | Hoffmann, Philipp H. W. |
| description | This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product 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, and explain why they all reduce to the same actual chain of computations.We further give a short mathematical description of some methods of higher-order Forward AD and, at the end of this paper, briefly describe the Reverse Mode of Automatic Differentiation. |
| doi_str_mv | 10.1007/s11075-015-0067-6 |
| format | Article |
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| ispartof | Numerical algorithms, 2016-07, Vol.72 (3), p.775-811 |
| issn | 1017-1398 1572-9265 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Algorithms Computer Science Differentiation Mathematical analysis Matrix algebra Numeric Computing Numerical Analysis Operators (mathematics) Original Paper Series expansion Taylor series Theory of Computation |
| title | A Hitchhiker’s Guide to Automatic Differentiation |
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