The if-problem in automatic differentiation
type: Item
instance of: scholarly article
title: The if-problem in automatic differentiation
zbMATH Open document ID: 0811.65014
DOI: 10.1016/0377-0427(94)90294-1
author: Herbert Fischer
author: Thomas L. Beck
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-22T00:00:00Z
review text: Within the last decade it has become apparent that the derivative of an explicitly given function can be computed efficiently by automatic differentiation techniques. These can be classified into two groups: the bottom-up and the top-down methods. The if-problem appears in both modes, so that the authors choose the bottom-up mode. Many computer programs defining a function use statements of the form: if \(B(x)\) then S1 else S2, where \(B(x)\) is a Boolean expression and S1 and S2 denote subprograms. This often leads to a piecewise definition of a function under consideration. In order to obtain correct results the authors make distinction between a function and its representations. In particular, they introduce the notion of derivative-consistent. Automatic differentiation applied to a derivative-consistent representation of a function yields correct results.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D20
zbMATH DE Number: 643748
zbMATH Keywords: piecewise defined function
zbMATH Keywords: bottom-up method
zbMATH Keywords: automatic differentiation
zbMATH Keywords: if-problem
zbMATH Keywords: derivative-consistent representation of a function
reviewed by: Dimitrie D. Stancu
describes a project that uses: Pascal-SC
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90294-1
OpenAlex ID: W2035667607
cites work: Automatic differentiation of characterizing sequences
cites work: Automatic differentiation of the vector that solves a parametric linear system
cites work: Q4028381
cites work: Q4028413
cites work: The Variable Reduction Method for Nonlinear Programming
cites work: Q3881909
cites work: Differentiation in PASCAL-SC: type GRADIENT
description: scientific article; zbMATH DE number 643748