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Lazy multivariate higher-order forward-mode AD

Published:17 January 2007Publication History
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Abstract

A method is presented for computing all higher-order partial derivatives of a multivariate function R n → 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.

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      • Published in

        cover image ACM SIGPLAN Notices
        ACM SIGPLAN Notices  Volume 42, Issue 1
        Proceedings of the 2007 POPL Conference
        January 2007
        379 pages
        ISSN:0362-1340
        EISSN:1558-1160
        DOI:10.1145/1190215
        Issue’s Table of Contents
        • cover image ACM Conferences
          POPL '07: Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
          January 2007
          400 pages
          ISBN:1595935754
          DOI:10.1145/1190216

        Copyright © 2007 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 17 January 2007

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