Automatic differentiation in prose
ACM SIGNUM Newsletter
Series reversion as the reversed chain rule
ACM SIGNUM Newsletter
An APL approach to differential calculus yields a powerful tool
APL '89 Conference proceedings on APL as a tool of thought
An efficient method for the numerical evaluation of partial derivatives of arbitrary order
ACM Transactions on Mathematical Software (TOMS)
GRADIENT: algorithmic differentiation in Maple
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
ACM Transactions on Mathematical Software (TOMS)
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Automatic Differentiation and Interval Arithmetic for Estimation of Disequilibrium Models
Computational Economics - Special issue on computational economics in Geneva: volume 1: computational econometrics, statistics, and optimization
Dynamic computation of derivatives
Communications of the ACM
Investigation of a new analytical method for numerical derivative evaluation
Communications of the ACM
Wengert's numerical method for partial derivatives, orbit determination and quasilinearization
Communications of the ACM
Symbolic derivatives without list processing, subroutines, or recursion
Communications of the ACM
Survey of formula manipulation
Communications of the ACM
General time-varying systems error sensitivities program
Communications of the ACM
Computational Divided Differencing and Divided-Difference Arithmetics
Higher-Order and Symbolic Computation
Making Automatic Differentiation Truly Automatic: Coupling PETSc with ADIC
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
New languages from old: The extension of programming languages by embedding, with a case study
ICSE '76 Proceedings of the 2nd international conference on Software engineering
A computer system for algebra and analytic differentiation
SYMSAC '66 Proceedings of the first ACM symposium on Symbolic and algebraic manipulation
Computer Science in Perspective
The inverse source problem based on the radiative transfer equation in optical molecular imaging
Journal of Computational Physics
Some advances related to nonlinear programming
ACM SIGMAP Bulletin
A differentiation-enabled Fortran 95 compiler
ACM Transactions on Mathematical Software (TOMS)
Making automatic differentiation truly automatic: coupling PETSc with ADIC
Future Generation Computer Systems
First-class nonstandard interpretations by opening closures
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Lazy multivariate higher-order forward-mode AD
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator
ACM Transactions on Programming Languages and Systems (TOPLAS)
OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes
ACM Transactions on Mathematical Software (TOMS)
Hybrid differentiation strategies for simulation and analysis of applications in C++
ACM Transactions on Mathematical Software (TOMS)
Sensitivity Analysis of a Dynamical System Using C++
Scientific Programming - The First Annual Object-Oriented Numerics Conference (OON-SKI '93)
On the implementation of automatic differentiation tools
Higher-Order and Symbolic Computation
Nesting forward-mode AD in a functional framework
Higher-Order and Symbolic Computation
Fast higher-order derivative tensors with Rapsodia
Optimization Methods & Software
The Q approach to problem solving
AFIPS '69 (Fall) Proceedings of the November 18-20, 1969, fall joint computer conference
Making automatic differentiation truly automatic: coupling PETSc with ADIC
Future Generation Computer Systems
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Paper: Automation of chemical plant modelling
Automatica (Journal of IFAC)
Hi-index | 48.32 |
A procedure for automatic evaluation of total/partial derivatives of arbitrary algebraic functions is presented. The technique permits computation of numerical values of derivatives without developing analytical expressions for the derivatives. The key to the method is the decomposition of the given function, by introduction of intermediate variables, into a series of elementary functional steps. A library of elementary function subroutines is provided for the automatic evaluation and differentiation of these new variables. The final step in this process produces the desired function's derivative.The main feature of this approach is its simplicity. It can be used as a quick-reaction tool where the derivation of analytical derivatives is laborious and also as a debugging tool for programs which contain derivatives.