Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions. In particular, AD has been applied to optimization, parameter identification, equation solving, the numerical integration of differential equations, and combinations thereof. Apart from quantifying sensitivities numerically, AD techniques can also provide structural information, e.g., sparsity pattern and generic rank of Jacobian matrices.
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Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions. In particular, AD has been applied to optimization, parameter identification, equation solving, the numerical integration of differential equations, and combinations thereof. Apart from quantifying sensitivities numerically, AD techniques can also provide structural information, e.g., sparsity pattern and generic rank of Jacobian matrices.
Andreas Griewank is a former senior scientist of Argonne National Laboratory and authored the first edition of this book in 2000. He holds a Ph.D. from the Australian National University and is currently Deputy Director of the Institute of Mathematics at Humboldt University Berlin and a member of the DFG Research Center Matheon, Mathematics for Key Technologies. His main research interests are nonlinear optimization and scientific computing.
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