A Lepskij's stopping rule for Newton-type methods with random noise

Regularized Newton methods are one of the most popular approaches for the solution of inverse problems in differential equations. Since these problems are usually ill‐posed, an appropriate stopping rule is an essential ingredient of such methods. In this paper we suggest an a‐posteriori stopping rule of Lepskij‐type which is appropriate for data perturbed by random noise. The numerical results for this look promising.