41 citations · 324 across the 37 of their papers we have counts for
4 papers · 1 filter
On -regularization under continuity of the forward operator in weaker topologies
Daniel Gerth, Bernd Hofmann
Our focus is on the stable approximate solution of linear operator equations based on noisy data by using -regularization as a sparsity-enforcing version of Tikhonov regula…
On ill-posedness concepts, stable solvability and saturation
Bernd Hofmann, Robert Plato
We consider different concepts of well-posedness and ill-posedness and their relations for solving nonlinear and linear operator equations in Hilbert spaces. First, the concepts of…
Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
Bernd Hofmann, Peter Mathé
We study the Tikhonov regularization for ill-posed non-linear operator equations in Hilbert scales. Our focus is on the interplay between the smoothness-promoting properties of the…
A regularization approach for an inverse source problem in elliptic systems from single Cauchy data
Michael Hinze, Bernd Hofmann, Tran Nhan Tam Quyen
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variationa…