Adaptive Choice of the Regularization Parameter in Numerical Differentiation (Journal of Computational Mathematics, 2018)
We investigate a novel adaptive choice rule of the Tikhonov regularization parameterin numerical differentiation which is a classic ill-posed problem. By assuming a generalunknown Hölder type error estimate derived for numerical differentiation, we choose aregularization parameter in a geometric set providing a nearly optimal convergence ratewith very limited a-priori information. Numerical simulation in image edge detectionverifies reliability and efficiency of the new adaptive approach.