# Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition

@inproceedings{Griewank2000EvaluatingD, title={Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition}, author={Andreas Griewank and Andrea Walther}, booktitle={Frontiers in applied mathematics}, year={2000} }

Algorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions. AD has been applied in particular to optimization, parameter identification… Expand

#### Topics from this paper

#### 2,764 Citations

Special section: Automatic differentiation and its applications

- Computer Science
- Future Gener. Comput. Syst.
- 2005

The evaluation of derivatives of mathematical functions is a crucial ingredient in a variety of computational techniques in numerical simulations, especially in large-scale computer simulations which are increasingly becoming an important part of many scientific investigations. Expand

An introduction to algorithmic differentiation

- Computer Science
- Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
- 2020

This work provides an introduction to AD and presents its basic ideas and techniques, some of its most important results, the implementation paradigms it relies on, the connection it has to other domains including machine learning and parallel computing, and a few of the major open problems in the area. Expand

Algorithmic Differentiation of Numerical Methods: Second-Order Adjoint Solvers for Parameterized Systems of Nonlinear Equations

- Computer Science
- ICCS
- 2016

Adjoint mode algorithmic differentiation (AD) transforms implementations of multivariate vector functions as computer programs into first-order adjoint code, of particular interest in large-scale gradient-based nonlinear optimization due to the independence of its computational cost on the number of free variables. Expand

Algorithmic Differentiation of Numerical Methods : Second-Order Tangent and Adjoint Solvers for Systems of Parametrized Nonlinear Equations

- 2014

Forward and reverse modes of algorithmic differentiation (AD) transform implementations of multivariate vector functions F : IR → IR as computer programs into tangent and adjoint code, respectively.… Expand

A review of automatic differentiation and its efficient implementation

- Computer Science, Mathematics
- Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
- 2019

Automatic differentiation is a powerful tool to automate the calculation of derivatives and is preferable to more traditional methods, especially when differentiating complex algorithms and mathematical functions. Expand

Algorithmic Differentiation of Numerical Methods : Tangent-Linear and Adjoint Solvers for Systems of Nonlinear Equations

- 2012

We discuss software tool support for the Algorithmic Differentiation (also known as Automatic Differentiation; AD) of numerical simulation programs that contain calls to solvers for parameterized… Expand

Efficient (Partial) Determination of Derivative Matrices via Automatic Differentiation

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2013

Here it is shown how the popular graph-coloring approach to AD can be adapted to account for cases where some elements may be constant for all iterates, with resulting gains in efficiency. Expand

Algorithmic Differentiation of Numerical Methods: Tangent and Adjoint Solvers for Parameterized Systems of Nonlinear Equations

- Mathematics, Computer Science
- TOMS
- 2015

The algorithmic formalism is developed building on prior work by other colleagues and an implementation based on the AD software dco/c++ is presented, which supports the theoretically obtained computational complexity results with practical runtime measurements. Expand

Introduction to Automatic Differentiation and MATLAB

- Computer Science
- 2010

A survey of more advanced topics in automatic differentiation includes an introduction to the reverse mode (the authors' implementation is forward mode) and considerations in arbitrary-order multivariable series computation. Expand

Automatic versus manual model differentiation to compute sensitivities and solve non-linear inverse problems

- Computer Science
- 2002

The Odyssee software, one such tool for automatic differentiation of computer programs, has been tested on a sample model that solves a 2D non-linear diffusion-type equation, and the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odys see's capability to produce error-free codes. Expand