Lazy Multivariate Higher-Order Forward-Mode AD

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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
URI:	https://mu.eprints-hosting.org/id/eprint/2049
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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Lazy Multivariate Higher-Order Forward-Mode AD

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