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Lazy Multivariate Higher-Order Forward-Mode AD

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;
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Computer Science
Item ID: 2049
Depositing User: Dr. 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:

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