4 citations · 6 across the 9 of their papers we have counts for
12 papers
Sparse variational regularization with oversmoothing penalty term in the scale of sequence spaces
Robert Plato, Bernd Hofmann
In this work, we consider a class of linear ill-posed problems with operators that map from the sequence space () into a Banach space and in addition satisfy a…
A class of regularization schemes for linear ill-posed problems in Banach spaces under low order source conditions
Robert Plato
In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source rep…
New results for variational regularization with oversmoothing penalty term in Banach spaces
Bernd Hofmann, Chantal Klinkhammer, Robert Plato
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our mo…
Analysis of the discrepancy principle for Tikhonov regularization under low order source conditions
Chantal Klinkhammer, Robert Plato
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepanc…
Variational regularization with oversmoothing penalty term in Banach spaces
Robert Plato, Bernd Hofmann
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-f…
Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles
Bernd Hofmann, Christopher Hofmann, Peter Mathé +1
The analysis of Tikhonov regularization for nonlinear ill-posed equations with smoothness promoting penalties is an important topic in inverse problem theory. With focus on Hilbert…
Convergence results and low order rates for nonlinear Tikhonov regularization with oversmoothing penalty term
Bernd Hofmann, Robert Plato
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, wh…
Convergence rates of a penalized variational inequality method for nonlinear monotone ill-posed equations in Hilbert spaces
Robert Plato, Bernd Hofmann
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regu…
The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data
Robert Plato
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind…
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…
Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems
Robert Plato
This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturat…
The regularizing properties of multistep methods for first kind Volterra integral equations with smooth kernels
Robert Plato
We study quadrature methods for solving Volterra integral equations of the first kind with smooth kernels under the presence of noise in the right-hand sides, with the quadrature m…