Least squares and approximate differentiation (Q418219)

This paper deals with the notions of least squares derivative and approximate derivative, which are both generalizations of the usual derivative. The existence of either of these generalized derivatives does not guarantee the existence of the other. This paper provides several examples of such functions. In addition, conditions for which the existence of the approximate derivative implies the existence of the least squares derivative are stated and proved. These conditions involve the notion of Hölder continuity and a stronger version of approximate differentiability.