Abstract. Many of the current automatic differentiation (AD) tools have similar characteristics. Unfortunately, it is often the case that the similarities between these various AD tools can not be easily ascertained by reading the corresponding documentation. To clarify this situation, a taxonomy of AD tools is presented. The taxonomy places AD tools into the Elemental, Extensional, Integral, Operational and Symbolic classes. This taxonomy is used to classify twenty-nine AD tools. Each tool is examined individually with respect to the mode of differentiation used and the degree of derivatives computed. A list detailing the availability of the surveyed AD tools is provided in Appendix A.
|
243
|
AMPL: A Modeling Language for
– Fourer, Gay, et al.
- 1993
|
|
126
|
ADOL-C: A package for the automatic differentiation of algorithms written
– Griewank, Juedes, et al.
- 1996
|
|
115
|
On automatic differentiation
– Griewank
- 1989
|
|
18
|
Solving ordinary differential equations using Taylor series
– Corliss, Chang
- 1982
|
|
18
|
Automatic Hessians by reverse accumulation
– Christianson
- 1992
|
|
17
|
Differential algebraic description of beam dynamics to very high orders
– Berz
- 1989
|
|
14
|
Methods of Fast Automatic Differentiation and Applications, Research memorandum RMI
– Iri, Kubota
- 1987
|
|
12
|
An efficient method for the numerical evaluation of partial derivatives of arbitrary order
– Neidinger
- 1992
|
|
6
|
Computational Aspects of Design and Simulation
– Berz
- 1990
|
|
5
|
Automatic generation of Taylor series in Pascal--SC: Basic operations and applications to differential equations
– Corliss, Rall
- 1983
|
|
4
|
The differential algebra FORTRAN precompiler DAFOR
– Berz
- 1987
|
|
4
|
Differential algebra precompiler version 3 reference manual
– Berz
- 1990
|
|
4
|
COSY INFINITY, an arbitrary order general purpose optics code
– Berz
- 1990
|
|
4
|
MXYZPTLK: A practical, user-friendly C++ implementation of differential algebra: User's guide
– Michelotti
- 1990
|
|
3
|
Adaptive, self-validating quadrature
– Corliss, Rall
- 1987
|
|
3
|
Automatic differentiation using almost any language
– Jerrell
- 1989
|
|
2
|
A SLANG Simulation of an Initially Strong Shock Wave Downstream of an Infinite Area
– Adamsom, Winant
- 1969
|
|
2
|
Function Minimization and Automatic Differentiation
– Jerrell
- 1989
|
|
2
|
Implementing automatic differentiation efficiently
– Juedes, Griewank
- 1990
|
|
1
|
COSY INFINITY Version 3 Reference
– Berz
- 1990
|
|
1
|
Computing the Range of Derivatives, to appear
– Corliss, Rall
|
|
1
|
Overloading Point and Interval Taylor Operators, submitted to
– Corliss
- 1991
|
|
1
|
Response to electronic mail survey
– Flanders
- 1991
|
|
1
|
Response to electronic mail survey
– Gay
- 1991
|
|
1
|
A System for the Automatic Differentiation of FORTRAN programs, presented at the
– Garcia
- 1991
|
|
1
|
Users Guide for JAKEF, Technical Memorandum ANL/MCS-TM-16
– Hillstrom
- 1985
|
|
1
|
Sensitivity Analysis of AIRDOSEPA Using ADGEN with Matrix Reduction Algorithms
– Horwedel, Raridon, et al.
- 1989
|
|
1
|
Sensitivity Analysis of EQ3
– Horwedel, Wright, et al.
- 1990
|
|
1
|
Automatization of the Computation of Partial Derivatives, Master's Thesis
– Iwata
- 1984
|
|
1
|
Automatic Differentiation Using C
– Jerrell
- 1990
|
|
1
|
The Structure of Synthetic Calculus
– Krinsky, Thames
- 1984
|
|
1
|
PADRE2, version 1 - User's Manual, Research memorandum RMI
– Kubota, Iri
- 1990
|
|
1
|
Computing Derivatives using W-Arithmetic and U-Arithmetic
– Lawson
- 1971
|
|
1
|
PCOMP: A FORTRAN code for automatic differentiation Report No.254
– Liepelt, Schittkowski
- 1990
|
|
1
|
Response to electronic mail survey
– Lindell
- 1991
|
|
1
|
3.0, A Library of Mathematical Subprograms for Fortran 77
– MATH77
- 1989
|
|
1
|
Integration of Automatic Differentiation into Application Programs for PC's, submitted to
– Mazourik
- 1991
|
|
1
|
The Q Approach to
– McCully
- 1969
|
|
1
|
Response to electronic mail survey
– Monagan
- 1991
|
|
1
|
Automatic Differentiation in
– Pfeiffer
- 1987
|
|
1
|
A General Purpose Higher Level Language, Procedure Manual (Pub. No. 84003000 Rev
– PROSE
- 1977
|
