D. Gerth

activity

20132022

most citedA new interpretation of (Tikhonov) regularization

34 citations · 62 across the 12 of their papers we have counts for

collaborators

Showing 2017Show all

3 papers · 1 filter

math.NA2017

Using Landweber method to quantify source conditions - a numerical study

Daniel Gerth

Source conditions of the type $x^{†} \in R ((A^{*} A)^{μ})$ are an important tool in the theory of inverse problems to show convergence rates of regularized solutions as the no…

math.FA2017

On $ℓ^{1}$ -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 $ℓ^{1}$ -regularization as a sparsity-enforcing version of Tikhonov regula…

math.FA2017★ 1 cited

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization

Jens Flemming, Daniel Gerth

We show that the convergence rate of $ℓ^{1}$ -regularization for linear ill-posed equations is always $O (δ)$ if the exact solution is sparse and if the considered operator is injec…

Using Landweber method to quantify source conditions - a numerical study

On ℓ1-regularization under continuity of the forward operator in weaker topologies

Injectivity and weak*-to-weak continuity suffice for convergence rates in ℓ1-regularization

On $ℓ^{1}$ -regularization under continuity of the forward operator in weaker topologies

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization