Transactions of the American Mathematical Society, Vol. 263, No. 2 (Feb., 1981), pp. 493-500 (8 pages) Let $\Delta'$ be the class of all derivatives. The main goal of this paper is the investigation ...

Let A → Ar be the map that takes a positive definite matrix to its rth power, and let DAr be the Fréchet derivative of this map. It is known that ∥DAr∥ = ∥rAr−1∥ if r ≤ 1 or if r ≥ 2, and also that ...

Automatic Differentiation (AD) forms a cornerstone in the optimisation of machine learning models, providing an efficient computational method to obtain accurate derivatives. This technique underpins ...