Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

Error analysis of regularization methods in Hilbert spaces is based on smoothness
assumptions in terms of source conditions. In the traditional setup, ie when smoothness is in …

The stable approximate solution of ill-posed linear operator equations in Hilbert spaces
requires regularization. Tight bounds for the noise-free part of the regularization error are …

In the recent past the authors, with collaborators, have published convergence rate results
for regularized solutions of linear ill-posed operator equations by avoiding the usual …

For tracking type distributed optimal control problems subject to second‐order elliptic partial
differential equations, we analyze the regularization error of the state u ϱ and the target u‾ …

We study linear inverse problems under the premise that the forward operator is not at hand
but given indirectly through some input-output training pairs. We demonstrate that …

In this paper we consider a collocation method for solving Fredholm integral equations of the
first kind, which is known to be an ill-posed problem. An “unregularized” use of this method …

For solving linear ill-posed problems, regularization methods are required when the right-
hand side and/or the operator are corrupted by some noise. In the present paper …

For the Tikhonov regularization of ill-posed nonlinear operator equations, convergence is
studied in a Hilbert scale setting. We include the case of oversmoothing penalty terms, which …

In the analysis of ill-posed inverse problems the impact of solution smoothness on accuracy
and convergence rates plays an important role. For linear ill-posed operator equations in …