The if-problem in automatic differentiation
Within the last decade it has become apparent that the derivative of an explicitly given function can be computed efficiently by automatic differentiation techniques. These can be classified into two groups: the bottom-up and the top-down methods. The if-problem appears in both modes, so that the authors choose the bottom-up mode. Many computer programs defining a function use statements of the form: if \(B(x)\) then S1 else S2, where \(B(x)\) is a Boolean expression and S1 and S2 denote subprograms. This often leads to a piecewise definition of a function under consideration. In order to obtain correct results the authors make distinction between a function and its representations. In particular, they introduce the notion of derivative-consistent. Automatic differentiation applied to a derivative-consistent representation of a function yields correct results.
derivative-consistent representation of a function
scientific article; zbMATH DE number 643748