We identify a class of iterative processes that can be used in the definition of a function while preserving the good behavior of automatic differentiation codes on this function. By iterative process, we mean a process where the number of iterations is determined by a stopping criterion, which can depend on the independent variables. By good behavior, we mean that the derivatives will be calculated correctly, asymptotically. The class contains the Newton method.
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Jean Charles Gilbert (1992) studied this question.
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