Lazy multivariate higher-order forward-mode AD

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.

• Type: Conference
• Year: 2007
• Where: POPL
• Authors: Barak A. Pearlmutter, Jeffrey Mark Siskind
• Keywords: Function Rn R, Lazy Data Structure, Multivariate Power Series, POPL 2007, Programming Languages