Automatic differentiation of iterative processes
Automatic differentiation is a method for computing the derivative values of a function \(f: D\subseteq \mathbb{R}^ n\to \mathbb{R}\), which is given in the form of an algorithm A. By using automatic differentiation it is intended to convert A into another algorithm \(\text{A}'\), which describes the forward mode of automatic differentiation. It permits to calculate the values of the derivative of a real-valued function given by a code list. In this paper the differentiation of a function \(f\) defined by an infinite code list or iterative process is studied. From previous investigations of application of automatic differentiation to iterative processes the contributions of \textit{J. C. Gilbert} [Optim. Methods Software 1, 13-21 (1992)] should be mentioned. The author ends his paper stating that for some special iterative processes, like some Newton methods, it can be proved that the differentiation can be done automatically.
scientific article; zbMATH DE number 643747
scientific article