Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error

摘要

We provide a new method to estimate the derivatives of a digital function by linear programming or other geometrical algorithms. Knowing the digitization of a real continuous function / with a resolution h, this approach provides an approximation of the kth derivative f^kx) with a maximal error in O(/iT+T) where the constant depends on an upper bound of the absolute value of the (k + l)th derivative of / in a neighborhood of a;. This convergence rate ^y should be compared to the two other methods already providing such uniform convergence results, namely | from Lachaud et. at (only for the first order derivative) and (|)fc from Malgouyres et al.