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.
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.
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