Software for estimating sparse Jacobian matrices
ACM Transactions on Mathematical Software (TOMS)
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Two FORTRAN packages for assessing initial value methods
ACM Transactions on Mathematical Software (TOMS)
Applications of differentiation arithmetic
Reliability in computing: the role of interval methods in scientific computing
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
On Combining Computational Differentiation and Toolkits for Parallel Scientific Computing
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
On the implementation of automatic differentiation tools
Higher-Order and Symbolic Computation
Editorial: Special section: Automatic differentiation and its applications
Future Generation Computer Systems
An automatic differentiation platform: Odyssée
Future Generation Computer Systems
Automatic differentiation in ACL2
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A system for interfacing MATLAB with external software geared toward automatic differentiation
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
ACM Transactions on Mathematical Software (TOMS)
Halo orbit mission correction maneuvers using optimal control
Automatica (Journal of IFAC)
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Application-tailored linear algebra algorithms: A search-based approach
International Journal of High Performance Computing Applications
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The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f $R^N$→$R^m$. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution. Automatic Differentiation of FORtran (ADIFOR) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem. ADIFOR employs the data analysis capabilities of the ParaScope Parallel Programming Environment, which enable us to handle arbitrary Fortran 77 codes and to exploit the computational context in the computation of derivatives. Experimental results show that ADIFOR can handle real-life codes and that ADIFOR-generated codes are competitive with divided-difference approximations of derivatives. In addition, studies suggest that the source transformation approach to automatic differentiation may improve the time to compute derivatives by orders of magnitude.