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Pearlmutter, Barak A. and Siskind, Jeffrey Mark (2007) Lazy Multivariate Higher-Order Forward-Mode AD. POPL '07: Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages. pp. 155-160.
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Abstract
A method is presented for computing all higher-order partial
derivatives of a multivariate function Rn → R. This method works
by evaluating the function under a nonstandard interpretation, lifting
reals to multivariate power series. Multivariate power series,
with potentially an infinite number of terms with nonzero coefficients,
are represented using a lazy data structure constructed
out of linear terms. A complete implementation of this method
in SCHEME is presented, along with a straightforward exposition,
based on Taylor expansions, of the method’s correctness.
| Item Type: | Article |
|---|---|
| Keywords: | Algorithms; Languages; Power series; Nonstandard interpretation; |
| Academic Unit: | Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
| Item ID: | 2049 |
| Depositing User: | Barak Pearlmutter |
| Date Deposited: | 14 Jul 2010 15:49 |
| Journal or Publication Title: | POPL '07: Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages |
| Publisher: | ACM (Association for Computing Machinery) |
| Refereed: | No |
| 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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