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GRADIENT: Algorithmic Differentiation in Maple

Monagan, M. and Neuenschwander, W.M.
International Symposium on Symbolic and Algebraic Computation
July 1993


Many scientific applications require computation of the derivatives of a function f : R^n -> R^m as well as the function values of f itself. All computer algebra systems can differentiate functions represented by formulae. But not all functions can be described by formulae. And formulae are not always the most effective means for representing functions and derivatives. In this paper we describe the algorithms used by the Maple routine GRADIENT that accepts as input a Maple procedure for the computation of f and outputs a new Maple procedure that computes the gradient of f. The design of the GRADIENT routine is such that it is also trivial to generate Maple procedures for the computation Jacobians and Hessians.

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  author = {Monagan and M. and Neuenschwander and W.M.},
  title = {GRADIENT: Algorithmic Differentiation in Maple},
  booktitle = {International Symposium on Symbolic and Algebraic Computation},
  year = {1993},
  month = {July},
  pages = {68-76},
  keywords = {Algorithmic Differentiation, Chain Rule, Computer Algebra,}