Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
An Ada library for automatic evaluation of derivatives
Applied Mathematics and Computation
Automatic differentiation in MATLAB
Applied Numerical Mathematics
Precise interprocedural chopping
SIGSOFT '95 Proceedings of the 3rd ACM SIGSOFT symposium on Foundations of software engineering
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Algorithms and design for a second-order automatic differentiation module
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Advanced compiler design and implementation
Advanced compiler design and implementation
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Circumventing Storage Limitations in Variational Data Assimilation Studies
SIAM Journal on Scientific Computing
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
ADMIT-1: automatic differentiation and MATLAB interface toolbox
ACM Transactions on Mathematical Software (TOMS)
Dynamic computation of derivatives
Communications of the ACM
A simple automatic derivative evaluation program
Communications of the ACM
Investigation of a new analytical method for numerical derivative evaluation
Communications of the ACM
Hybrid system for multi-language and multi-environment generation of numerical codes
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Optimizing compilers for modern architectures: a dependence-based approach
Optimizing compilers for modern architectures: a dependence-based approach
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Functional Differentiation of Computer Programs
Higher-Order and Symbolic Computation
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Functional automatic differentiation with dirac impulses
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Automatic differentiation using almost any language
ACM SIGNUM Newsletter
ADIFOR-Generating Derivative Codes from Fortran Programs
Scientific Programming
Hierarchical automatic differentiation by vertex elimination and source transformation
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Term Graphs for Computing Derivatives in Imperative Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic differentiation in ACL2
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Hybrid static/dynamic activity analysis
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Advances in Engineering Software
Journal of Computational and Applied Mathematics
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Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a wide variety of scientific computing applications, including numerical optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. We describe the forward and reverse modes of automatic differentiation and provide a survey of implementation strategies. We describe some of the challenges in the implementation of automatic differentiation tools, with a focus on tools based on source transformation. We conclude with an overview of current research and future opportunities.