Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
A simple automatic derivative evaluation program
Communications of the ACM
Performance optimization of numerically intensive codes
Performance optimization of numerically intensive codes
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
Compiling fast partial derivatives of functions given by algorithms
Compiling fast partial derivatives of functions given by algorithms
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
An automatic differentiation platform: odyssée
Future Generation Computer Systems
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Computationally efficient and accurate derivatives are important to the success of many different types of numerical methods. Automatic differentation (AD) approaches compute truncation-free derivatives and can be efficient in many cases. Although present AD tools can provide a convenient implementation mechanism, the computational efficiency rarely compares to analytically derived versions that have been carefully implemented. The focus of this work is to combine the strength of these methods into a hybrid strategy that attempts to achieve an optimal balance of implementation and computational efficiency by selecting the appropriate components of the target algorithms for AD and analytical derivation. Although several AD approaches can be considered, our focus is on the use of template overloading forward AD tools in C++ applications. We demonstrate this hybrid strategy for a system of partial differential equations in gas dynamics. These methods apply however to other systems of differentiable equations, including DAEs and ODEs.